Chapter 5: Circular Motion; Gravitation

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Drtaylor
D
Drtaylor
Community Contributor
Quizzes Created: 57 | Total Attempts: 82,017
| Attempts: 1,807 | Questions: 80
Please wait...
Question 1 / 80
0 %
0/100
Score 0/100
1. Consider a particle moving with constant speed such that its acceleration of constant magnitude is always perpendicular to its velocity.

Explanation

If the acceleration of the particle is always perpendicular to its velocity, it means that the particle is constantly changing its direction but maintaining the same speed. This type of motion is characteristic of circular motion, where the acceleration is always directed towards the center of the circle. Therefore, the particle is moving in a circle.

Submit
Please wait...
About This Quiz
Chapter 5: Circular Motion; Gravitation - Quiz

Explore the fundamentals of circular motion and gravitation in this engaging quiz. Topics include acceleration in constant speed, circular path dynamics, and the relationship between velocity and acceleration... see morevectors. Essential for students mastering physics concepts. see less

2. What type of acceleration does an object moving with constant speed in a circular path experience?

Explanation

An object moving with constant speed in a circular path experiences centripetal acceleration. This type of acceleration is directed towards the center of the circle and is necessary to keep the object moving in a curved path. It is caused by the inward force, known as centripetal force, acting on the object. This acceleration does not change the speed of the object, but it does change its direction, allowing it to continuously move in a circular path.

Submit
3. What force is needed to make an object move in a circle?

Explanation

Centripetal force is the force required to make an object move in a circle. It is directed towards the center of the circle and keeps the object constantly changing direction. Without this force, the object would move in a straight line instead of a curved path. Kinetic friction and static friction are forces that oppose motion and are not specifically related to circular motion. Weight is the force exerted by gravity on an object and is not directly involved in making an object move in a circle.

Submit
4. A car goes around a curve of radius r at a constant speed v. What is the direction of the net force on the car?

Explanation

When a car goes around a curve, it experiences a centripetal force that acts towards the center of the curve. This force is necessary to keep the car moving in a curved path and prevent it from moving in a straight line. Therefore, the direction of the net force on the car is towards the curve's center.

Submit
5. A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's gravity?

Explanation

The correct answer is "It is never beyond the pull of Earth's gravity." This is because gravity is a force that extends infinitely into space and is always present, no matter how far away an object is from the source of gravity. Therefore, even when the spaceship is closer to the Moon than to Earth, it is still under the influence of Earth's gravity.

Submit
6. As a rocket moves away from the Earth's surface, the rocket's weight

Explanation

As a rocket moves away from the Earth's surface, the rocket's weight decreases. This is because weight is the force exerted on an object due to gravity, and the force of gravity decreases as the distance between the rocket and the Earth's surface increases. Therefore, as the rocket moves further away, the gravitational force acting on it decreases, resulting in a decrease in its weight.

Submit
7. Who was the first person to realize that the planets move in elliptical paths around the Sun?

Explanation

Johannes Kepler was the first person to realize that the planets move in elliptical paths around the Sun. He made this discovery based on the detailed observations and data collected by his mentor, Tycho Brahe. Kepler's laws of planetary motion revolutionized our understanding of the solar system and laid the foundation for modern astronomy.

Submit
8. When an object experiences uniform circular motion, the direction of the net force is

Explanation

When an object experiences uniform circular motion, it is constantly changing its direction. In order to change its direction, there must be a force acting on the object. This force is directed towards the center of the circular path, as it is responsible for keeping the object moving in a circular path. This force is called the centripetal force. Therefore, the net force in uniform circular motion is directed toward the center of the circular path.

Submit
9. A roller coaster car is on a track that forms a circular loop in the vertical plane. If the car is to just maintain contact with track at the top of the loop, what is the minimum value for its centripetal acceleration at this point?

Explanation

At the top of the loop, the car must experience a centripetal acceleration towards the center of the loop in order to maintain contact with the track. Since the car is at the top of the loop, the acceleration must be directed downwards, opposite to the direction of gravity. Therefore, the minimum value for the centripetal acceleration at this point is equal to the acceleration due to gravity (g) but in the opposite direction, hence "g downward".

Submit
10. A car is negotiating a flat curve of radius 50 m with a speed of 20 m/s. The centripetal force provided by friction is 1.2 * 10^4 N. What is the mass of the car?

Explanation

The centripetal force acting on an object moving in a circular path is given by the equation F = (mv^2)/r, where F is the force, m is the mass, v is the velocity, and r is the radius of the curve. In this case, the centripetal force provided by friction is given as 1.2 * 10^4 N, the radius is 50 m, and the speed is 20 m/s. Rearranging the equation, we can solve for the mass of the car. Therefore, the mass of the car is 1500 kg.

Submit
11. Suppose a satellite were orbiting the Earth just above the surface. What is its centripetal acceleration?

Explanation

The centripetal acceleration of the satellite would be equal to the acceleration due to gravity (g). This is because centripetal acceleration is the acceleration towards the center of the circular path, and in this case, the gravitational force acts as the centripetal force. Therefore, the centripetal acceleration would be equal to the acceleration due to gravity.

Submit
12. Consider a particle moving with constant speed such that its acceleration of constant magnitude is always perpendicular to its velocity.

Explanation

If the particle's acceleration is always perpendicular to its velocity, it means that the velocity vector and acceleration vector are always at right angles to each other. In circular motion, the acceleration vector is always directed towards the center of the circle, while the velocity vector is tangent to the circle. Since the acceleration vector is always perpendicular to the velocity vector in this scenario, it suggests that the particle is moving in a circle.

Submit
13. Compared to its mass on the Earth, the mass of an object on the Moon is

Explanation

The mass of an object remains the same regardless of its location. Mass is a measure of the amount of matter in an object and is a fundamental property of an object. Therefore, the mass of an object on the Moon is the same as its mass on Earth.

Submit
14. An object moves in a circular path at a constant speed. Compare the direction of the object's velocity and acceleration vectors.

Explanation

In circular motion, the velocity vector is always tangent to the circular path, while the acceleration vector is directed towards the center of the circle. Since the velocity vector is tangent and the acceleration vector is directed towards the center, they are at right angles to each other, making them perpendicular.

Submit
15. Is it possible for an object moving with a constant speed to accelerate? Explain.

Explanation

Although the speed of an object may be constant, it is still possible for the object to accelerate if the direction of its velocity is changing. Acceleration is defined as any change in velocity, which includes changes in direction. Therefore, even if the speed remains constant, if the object is changing its direction of motion, it is experiencing acceleration.

Submit
16. Let the average orbital radius of a planet be r. Let the orbital period be T. What quantity is constant for all planets orbiting the Sun?

Explanation

The quantity that is constant for all planets orbiting the Sun is T^2/R^3. This is because Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of its average orbital radius. Therefore, regardless of the specific values of T and R for each planet, their ratio T^2/R^3 will always be constant.

Submit
17. A car of mass m goes around a banked curve of radius r with speed v. If the road is frictionless due to ice, the car can still negotiate the curve if the horizontal component of the normal force on the car from the road is equal in magnitude to

Explanation

When a car goes around a banked curve, the normal force from the road can be divided into two components: vertical and horizontal. The vertical component of the normal force counteracts the gravitational force acting on the car, which is equal to mg. The horizontal component of the normal force provides the centripetal force required to keep the car moving in a circular path. According to Newton's second law, the centripetal force is given by the equation F = mv^2/r, where m is the mass of the car, v is the speed, and r is the radius of the curve. Therefore, the horizontal component of the normal force must be equal in magnitude to mv^2/r for the car to negotiate the curve successfully.

Submit
18. The gravitational force between two objects is inversely proportional to

Explanation

The gravitational force between two objects is inversely proportional to the square of the distance between the two objects. This means that as the distance between the objects increases, the gravitational force decreases. Conversely, as the distance decreases, the gravitational force increases. This relationship is described by Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Submit
19. A 0.50-kg mass is attached to the end of a 1.0-m string. The system is whirled in a horizontal circular path. If the maximum tension that the string can withstand is 350 N. What is the maximum speed of the mass if the string is not to break?

Explanation

The maximum tension that the string can withstand is 350 N. In order for the string not to break, the centripetal force acting on the mass must not exceed this tension. The centripetal force is given by the equation Fc = m * v^2 / r, where m is the mass, v is the velocity, and r is the radius of the circular path. Rearranging the equation to solve for v, we get v = sqrt(Fc * r / m). Plugging in the given values, we get v = sqrt(350 N * 1.0 m / 0.50 kg) = 26 m/s. Therefore, the maximum speed of the mass is 26 m/s.

Submit
20. The mass of the Moon is 7.4 * 10^22 kg and its mean radius is 1.75 * 10^3 km. What is the acceleration due to gravity at the surface of the Moon?

Explanation

The acceleration due to gravity at the surface of a celestial body can be calculated using the formula: acceleration due to gravity = gravitational constant * mass of the celestial body / radius of the celestial body squared. In this case, the mass of the Moon is given as 7.4 * 10^22 kg and its mean radius is given as 1.75 * 10^3 km. By plugging these values into the formula, we get an acceleration due to gravity of approximately 1.6 m/s^2.

Submit
21. By how many newtons does the weight of a 100-kg person change when he goes from sea level to an altitude of 5000 m? (The mean radius of the Earth is 6.38 * 10^6 m.)

Explanation

When a person goes from sea level to an altitude of 5000 m, their weight changes due to the decrease in gravitational force. The weight of an object is given by the formula W = mg, where m is the mass of the object and g is the acceleration due to gravity. At sea level, g is approximately 9.8 m/s^2, while at an altitude of 5000 m, it decreases slightly. The decrease in g leads to a decrease in weight. Using the formula, the change in weight can be calculated as follows: ΔW = mg(1-altitude/mean radius of the Earth). Plugging in the values, we get ΔW = 100 kg * 9.8 m/s^2 * (1 - 5000 m / (6.38 * 10^6 m)), which simplifies to approximately 1.6 N. Therefore, the correct answer is 1.6 N.

Submit
22. A frictionless curve of radius 100 m, banked at an angle of 45°, may be safely negotiated at a speed of

Explanation

A frictionless curve of radius 100 m, banked at an angle of 45°, may be safely negotiated at a speed of 31 m/s. This is because the angle of banking helps to counteract the centrifugal force acting on the vehicle as it goes around the curve. The higher the speed, the greater the centrifugal force, and the steeper the angle of banking needs to be to counteract it. At a speed of 31 m/s, the angle of banking of 45° is sufficient to keep the vehicle safely on the curve without sliding off.

Submit
23. A person is standing on a scale in an elevator accelerating downward. Compare the reading on the scale to the person's true weight.

Explanation

When a person is standing on a scale in an elevator accelerating downward, the reading on the scale will be less than their true weight. This is because the scale measures the normal force exerted by the person on it, which is equal to their true weight minus the force exerted by the elevator's acceleration. As the elevator accelerates downward, the scale will measure a smaller normal force, resulting in a reading that is less than the person's true weight.

Submit
24. A pilot makes an outside vertical loop (in which the center of the loop is beneath him) of radius 3200 m. At the top of his loop he is pushing down on his seat with only one-half of his normal weight. How fast is he going?

Explanation

When a pilot is making an outside vertical loop, the centripetal force required to keep the pilot moving in a circular path is provided by the normal force exerted by the seat. At the top of the loop, the pilot is pushing down on his seat with only one-half of his normal weight. This means that the normal force is half of the pilot's weight. Since the centripetal force is equal to the normal force, it is also half of the pilot's weight. The centripetal force can be calculated using the formula F = mv^2/r, where F is the centripetal force, m is the mass of the pilot, v is the speed, and r is the radius of the loop. By rearranging the formula, we can solve for v, which gives us v = sqrt(Fr/m). Since the centripetal force is half of the pilot's weight, we can substitute F = (1/2)mg into the formula. By plugging in the values, we get v = sqrt((1/2)mg * r/m). The mass of the pilot cancels out, leaving us with v = sqrt((1/2)g * r). Plugging in the values for g (acceleration due to gravity) and r (radius of the loop), we can calculate v, which is approximately 125 m/s.

Submit
25. The speed of Halley's Comet, while traveling in its elliptical orbit around the Sun,

Explanation

Halley's Comet follows an elliptical orbit around the Sun, which means that its distance from the Sun varies throughout its orbit. According to Kepler's laws of planetary motion, a celestial object moves faster when it is closer to the object it is orbiting. Therefore, as Halley's Comet nears the Sun in its orbit, its speed increases.

Submit
26. Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force

Explanation

When the distance between the centers of two objects attracting each other gravitationally is cut in half, the gravitational force between them quadruples. This is because the gravitational force is inversely proportional to the square of the distance between the objects. So, when the distance is halved, the force becomes four times stronger.

Submit
27. A car goes around a flat curve of radius 50 m at a speed of 14 m/s. What must be the minimum coefficient of friction between the tires and the road for the car to make the turn?

Explanation

To make a turn, the car needs a centripetal force directed towards the center of the curve. This force is provided by the friction between the tires and the road. The centripetal force can be calculated using the formula F = (m * v^2) / r, where m is the mass of the car, v is the velocity, and r is the radius of the curve. Rearranging the formula, we get the frictional force F = (m * v^2) / r. The maximum frictional force is given by the formula F = μ * N, where μ is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the car, which is mg. Equating the two formulas for F, we get (m * v^2) / r = μ * mg. Simplifying, we find μ = (v^2) / (g * r). Plugging in the values given in the question, we get μ = (14^2) / (9.8 * 50) = 0.40. Therefore, the minimum coefficient of friction required for the car to make the turn is 0.40.

Submit
28. A car is moving with a constant speed v around a level curve. The coefficient of friction between the tires and the road is 0.40. What is the minimum radius of the curve if the car is to stay on the road?

Explanation

The minimum radius of the curve can be determined using the centripetal force equation. The centripetal force is provided by the friction force between the tires and the road. The maximum friction force can be calculated by multiplying the coefficient of friction (0.40) with the normal force (equal to the weight of the car, mg). The centripetal force is equal to the maximum friction force, and it is given by (mv^2)/r, where m is the mass of the car, v is the velocity, and r is the radius of the curve. Equating this to the maximum friction force, we can solve for r, which gives (2.5v^2)/g.

Submit
29. A curve of radius 80 m is banked at 45°. Suppose that an ice storm hits, and the curve is effectively frictionless. What is the safe speed with which to take the curve without either sliding up or down?

Explanation

The correct answer is 28 m/s. When a curve is banked, it means that the surface of the curve is inclined at an angle to the horizontal. In this case, the curve is banked at 45°. When the curve is frictionless, the only force acting on the car is the normal force, which is perpendicular to the surface of the curve. This normal force can be resolved into two components: one perpendicular to the surface and one parallel to the surface. The component perpendicular to the surface provides the necessary centripetal force to keep the car moving in a circular path. The component parallel to the surface does not affect the motion of the car. By analyzing the forces and applying Newton's second law, it can be determined that the safe speed to take the curve without sliding up or down is 28 m/s.

Submit
30. Is it possible for an object moving around a circular path to have both centripetal and tangential acceleration?

Explanation

Yes, this is possible if the speed is changing. When an object moves in a circular path, it experiences centripetal acceleration towards the center of the circle. However, if the speed of the object is changing, it also experiences tangential acceleration in the direction of the velocity vector. This is because the object's velocity is changing, and acceleration is defined as the rate of change of velocity. Therefore, an object moving around a circular path can have both centripetal and tangential acceleration simultaneously.

Submit
31. When an object experiences uniform circular motion, the direction of the acceleration is

Explanation

When an object experiences uniform circular motion, the direction of the acceleration is directed toward the center of the circular path. This is because the object is constantly changing its direction as it moves in a circle, which means it is constantly accelerating towards the center of the circle. The acceleration is necessary to keep the object moving in a curved path, as a force is required to constantly change the direction of the object's velocity.

Submit
32. A car goes around a curve of radius r at a constant speed v. Then it goes around a curve of radius 2r at speed 2v. What is the centripetal force on the car as it goes around the second curve, compared to the first?

Explanation

As the car goes around a curve of radius 2r at speed 2v, the centripetal force is given by the equation F = (mv^2)/(2r). Since the radius is twice as big and the speed is also twice as big compared to the first curve, the centripetal force will be (m(2v)^2)/(2(2r)) = (4mv^2)/(4r) = (mv^2)/r. Therefore, the centripetal force on the car as it goes around the second curve is twice as big compared to the first curve.

Submit
33. An object moves with a constant speed of 30 m/s on a circular track of radius 150 m. What is the acceleration of the object?

Explanation

The acceleration of an object moving in a circular path is given by the formula a = v^2 / r, where v is the velocity and r is the radius of the circle. In this case, the object is moving with a constant speed of 30 m/s and the radius of the circular track is 150 m. Plugging these values into the formula, we get a = (30^2) / 150 = 6.0 m/s^2. Therefore, the acceleration of the object is 6.0 m/s^2.

Submit
34. Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B?

Explanation

The surface gravity of a planet is determined by its mass and radius. Since planet B has twice the mass of planet A but the same surface gravity, it must have a larger radius to compensate for the increased mass. The radius of planet B is therefore 1.41 times the radius of planet A.

Submit
35. A car traveling 20 m/s rounds an 80-m radius horizontal curve with the tires on the verge of slipping. How fast can this car round a second curve of radius 320 m? (Assume the same coefficient of friction between the car's tires and each road surface.)

Explanation

The maximum speed at which a car can round a curve without slipping is determined by the coefficient of friction between the tires and the road surface. Since the coefficient of friction is assumed to be the same for both curves, the maximum speed at which the car can round the second curve can be determined by using the same principle. The radius of the second curve is four times larger than the first curve, so the maximum speed at which the car can round the second curve would be four times larger as well. Therefore, the car can round the second curve with a speed of 40 m/s.

Submit
36. A point on a wheel rotating at 5.00 rev/s is located 0.200 m from the axis. What is the centripetal acceleration?

Explanation

The centripetal acceleration of an object moving in a circle is given by the formula a = rω², where a is the centripetal acceleration, r is the radius, and ω is the angular velocity. In this case, the radius is given as 0.200 m and the angular velocity is given as 5.00 rev/s. Converting the angular velocity to radians per second (ω = 2πf), we get ω = 2π(5.00) = 31.4 rad/s. Plugging these values into the formula, we get a = (0.200)(31.4)² = 198 m/s².

Submit
37. A spherically symmetric planet has four times the Earth's mass and twice its radius. If a jar of peanut butter weighs 12 N on the surface of the Earth, how much would it weigh on the surface of this planet?

Explanation

The weight of an object is directly proportional to the mass of the planet it is on. In this case, the planet has four times the mass of Earth, so the weight of the jar of peanut butter would also be four times its weight on Earth. However, the weight is also inversely proportional to the square of the radius of the planet. Since the radius is twice that of Earth, the weight would be divided by four. Therefore, the weight of the jar of peanut butter on the surface of this planet would be the same as its weight on Earth, which is 12 N.

Submit
38. The acceleration of gravity on the Moon is one-sixth what it is on Earth. An object of mass 72 kg is taken to the Moon. What is its mass there?

Explanation

The mass of an object remains the same regardless of the gravitational acceleration. Therefore, the mass of the object on the Moon is still 72 kg. The acceleration of gravity only affects the weight of an object, not its mass.

Submit
39. A stone, of mass m, is attached to a strong string and whirled in a vertical circle of radius r. At the exact bottom of the path the tension in the string is 3 times the stone's weight. The stone's speed at this point is given by

Explanation

At the bottom of the path, the tension in the string is equal to the sum of the stone's weight and the centripetal force required to keep it moving in a circle. Since the tension is 3 times the stone's weight, we can write the equation as T = mg + 3mg = 4mg. The centripetal force is given by F = mv^2/r, where v is the speed of the stone. Equating the centripetal force to the tension, we have 4mg = mv^2/r. Simplifying this equation, we get v^2 = 4gr, which means v = sqrt(4gr) or (2gr)^(1/2). Therefore, the stone's speed at the bottom of the path is given by (2gr)^(1/2).

Submit
40. It takes the planet Jupiter 12 years to orbit the Sun once. What is the average distance from Jupiter to the Sun? (The distance from the Earth to the Sun is 1.5 * 10^11 m.)

Explanation

The average distance from Jupiter to the Sun is 7.9 * 10^11 m. This can be calculated by multiplying the average distance from Earth to the Sun (1.5 * 10^11 m) by a factor of 5.3. Since Jupiter takes 12 years to orbit the Sun once, its average distance can be estimated by multiplying the Earth's distance by the ratio of the orbital periods, which is approximately 5.3.

Submit
41. Satellite A has twice the mass of satellite B, and rotates in the same orbit. Compare the two satellite's speeds.

Explanation

Since both satellites are rotating in the same orbit, their speeds will be the same regardless of their masses. Therefore, the speed of satellite B is equal to the speed of satellite A.

Submit
42. A pilot executes a vertical dive then follows a semi-circular arc until it is going straight up. Just as the plane is at its lowest point, the force on him is

Explanation

When the pilot executes a vertical dive, the force on the plane is the sum of the gravitational force (mg) and the force exerted by the plane to counteract gravity. As the plane follows a semi-circular arc, the force on the pilot increases due to the centripetal force required to keep the plane in the curved path. At the lowest point of the arc, the force on the pilot is the sum of the gravitational force and the centripetal force, which is greater than mg. Since the force is directed upwards to counteract the downward gravitational force, the correct answer is more than mg, and pointing up.

Submit
43. A coin of mass m rests on a turntable a distance r from the axis of rotation. The turntable rotates with a frequency of f. What is the minimum coefficient of static friction between the turntable and the coin if the coin is not to slip?

Explanation

The correct answer is (4π^2f^2r)/g. This formula represents the minimum coefficient of static friction between the turntable and the coin to prevent slipping. It is derived from the equation for centripetal force, F = mω^2r, where ω is the angular velocity. By equating this force to the maximum static friction force, F_max = μ_smg, and substituting ω = 2πf, the formula (4π^2f^2r)/g is obtained. This equation shows that the coefficient of static friction is directly proportional to the square of the frequency and the radius, and inversely proportional to the acceleration due to gravity.

Submit
44. The gravitational force between two objects is proportional to

Explanation

The gravitational force between two objects is proportional to the product of the two objects. This means that as the mass of one object increases or as the mass of both objects increases, the gravitational force between them also increases. However, the distance between the two objects does not directly affect the gravitational force.

Submit
45. The average distance from the Earth to the Sun is defined as one "astronomical unit" (AU). An asteroid orbits the Sun in one-third of a year. What is the asteroid's average distance from the Sun?

Explanation

An asteroid orbits the Sun in one-third of a year. Since the average distance from the Earth to the Sun is defined as one "astronomical unit" (AU), we can calculate the asteroid's average distance from the Sun by dividing the Earth-Sun distance by the time it takes for the asteroid to complete one orbit. One-third of a year is approximately 0.33 years. Therefore, the asteroid's average distance from the Sun is 1 AU divided by 0.33 years, which is approximately 0.48 AU.

Submit
46. A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn at 96.5 km/h. What is the centripetal force on the motorcycle?

Explanation

The centripetal force on an object moving in a circular path can be calculated using the formula F = mv^2/r, where F is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path. In this case, the mass of the motorcycle is given as 250 kg, the radius of the turn is given as 13.7 m, and the velocity is given as 96.5 km/h. First, we need to convert the velocity from km/h to m/s by dividing it by 3.6. Then, we can substitute the values into the formula to find the centripetal force. After calculation, the answer is 1.31 * 10^4 N.

Submit
47. A satellite is in a low circular orbit about the Earth (i.e., it just skims the surface of the Earth). What is the speed of the satellite? (The mean radius of the Earth is 6.38 * 10^6 m.)

Explanation

The speed of a satellite in a low circular orbit is determined by the balance between the gravitational force pulling it towards the Earth and the centrifugal force pushing it away. In order to maintain a stable orbit, these forces must be equal. The formula for the speed of a satellite in a circular orbit is v = √(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the orbit. Given that the mean radius of the Earth is 6.38 * 10^6 m, the correct answer of 7.9 km/s can be calculated using this formula.

Submit
48. The acceleration of gravity on the Moon is one-sixth what it is on Earth. The radius of the Moon is one-fourth that of the Earth. What is the Moon's mass compared to the Earth's?

Explanation

The acceleration of gravity on an object is directly proportional to its mass. Since the acceleration of gravity on the Moon is one-sixth of that on Earth, it means that the Moon's mass is one-sixth of Earth's mass. The radius of the Moon being one-fourth of Earth's radius does not affect the comparison of their masses. Therefore, the Moon's mass compared to the Earth's is 1/6, which is equivalent to 1/6 * 1/4 = 1/24.

Submit
49. A jet plane flying 600 m/s experiences an acceleration of 4g when pulling out of the dive. What is the radius of curvature of the loop in which the plane is flying?

Explanation

The plane is experiencing an acceleration of 4g when pulling out of the dive. This means that the net force acting on the plane is four times the force of gravity. The force causing the acceleration is the centripetal force, given by F = mv^2/r, where m is the mass of the plane, v is its velocity, and r is the radius of curvature. Since the plane is flying at a constant speed of 600 m/s, the force of gravity acting on it is equal to the centripetal force. Therefore, we can set mg = mv^2/r and solve for r. By substituting the given values, we find that r = 9200 m.

Submit
50. The hydrogen atom consists of a proton of mass 1.67 * 10^(-27) kg and an orbiting electron of mass 9.11 * 10^(-31) kg. In one of its orbits, the electron is 5.3* 10^(-11) m from the proton. What is the mutual attractive force between the electron and proton?

Explanation

The mutual attractive force between two objects can be calculated using the formula for gravitational force, which is F = G * (m1 * m2) / r^2. In this case, the objects are the electron and proton, and the force is attractive because they have opposite charges. Plugging in the given values for the masses and distance, we can calculate the force to be 3.6 * 10^(-47) N.

Submit
51. Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

Explanation

Moon B takes 160 days to complete an orbit because it has a larger orbital radius compared to Moon A. The time taken to complete an orbit is directly proportional to the orbital radius. Since Moon B's orbital radius is 4 times larger than Moon A's, it will take 4 times longer to complete an orbit. Therefore, if Moon A takes 20 days to complete an orbit, Moon B will take 4 times longer, which is 160 days.

Submit
52. A hypothetical planet has a mass of half that of the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the Earth?

Explanation

The acceleration due to gravity on a planet is determined by its mass and radius. In this scenario, the planet has a mass that is half that of the Earth and a radius that is twice that of the Earth. The acceleration due to gravity is inversely proportional to the square of the radius, and directly proportional to the mass. Therefore, the acceleration due to gravity on this hypothetical planet would be (1/2)^2 * (1/2) * g, which simplifies to g/8.

Submit
53. For a spacecraft going from the Earth toward the Sun, at what distance from the Earth will the gravitational forces due to the Sun and the Earth cancel? Earth's mass: M(e) = 5.98 * 10^24 kg the Sun's mass: M(s) = 1.99 * 10^30 kg Earth-Sun distance: r = 1.50 * 10^11 m

Explanation

The gravitational forces due to the Sun and the Earth cancel each other out when the gravitational force exerted by the Sun is equal in magnitude but opposite in direction to the gravitational force exerted by the Earth. This occurs when the distance from the Earth is such that the gravitational force due to the Sun is equal to the gravitational force due to the Earth. Therefore, at a distance of 2.60 * 10^8 m from the Earth, the gravitational forces due to the Sun and the Earth cancel each other.

Submit
54. A satellite is in circular orbit 230 km above the surface of the Earth. It is observed to have a period of 89 min. What is the mass of the Earth? (The mean radius of the Earth is 6.38 * 10^6 m.)

Explanation

The mass of an object in orbit is related to the period of its orbit and its distance from the center of the object it is orbiting. In this case, the satellite has a period of 89 minutes and is 230 km above the surface of the Earth. By using Kepler's third law, we can calculate the mass of the Earth. The formula is T^2 = (4π^2/GM) * r^3, where T is the period, G is the gravitational constant, M is the mass of the Earth, and r is the distance between the center of the Earth and the satellite. By plugging in the given values and solving for M, we find that the mass of the Earth is 6.0 * 10^24 kg.

Submit
55. What is the centripetal acceleration of a point on the perimeter of a bicycle wheel of diameter 70 cm when the bike is moving 8.0 m/s?

Explanation

The centripetal acceleration of a point on the perimeter of a bicycle wheel can be calculated using the formula a = (v^2) / r, where v is the velocity and r is the radius of the wheel. In this case, the diameter of the wheel is given as 70 cm, so the radius would be half of that, or 35 cm (0.35 m). The velocity is given as 8.0 m/s. Plugging these values into the formula, we get a = (8.0^2) / 0.35 = 64 / 0.35 = 182.86 m/s^2, which can be rounded to 1.8 * 10^2 m/s^2.

Submit
56. List the four fundamental forces in nature.

Explanation

The four fundamental forces in nature are gravitational, electromagnetic, strong nuclear, and weak nuclear. Gravitational force is responsible for the attraction between two objects with mass. Electromagnetic force is responsible for the interaction between charged particles. Strong nuclear force is responsible for holding atomic nuclei together. Weak nuclear force is responsible for certain types of radioactive decays.

Submit
57. Two planets have the same surface gravity, but planet B has twice the radius of planet A. If planet A has mass m, what is the mass of planet B?

Explanation

Since the two planets have the same surface gravity, it means that the gravitational force acting on an object on the surface of each planet is the same. The gravitational force is given by the equation F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers. Since the surface gravity is the same, we can set the gravitational force on planet A equal to the gravitational force on planet B. Since planet B has twice the radius of planet A, the distance between their centers is also twice as much. Therefore, the mass of planet B must be four times the mass of planet A, which is 4m.

Submit
58. A roller coaster car (mass = M) is on a track that forms a circular loop (radius = r) in the vertical plane. If the car is to just maintain contact with the track at the top of the loop, what is the minimum value for its speed at that point?

Explanation

The minimum value for the speed of the roller coaster car at the top of the loop can be determined using the concept of centripetal force. At the top of the loop, the gravitational force acting on the car provides the centripetal force required to maintain contact with the track. The centripetal force is given by the equation Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the car, v is the speed, and r is the radius of the loop. Setting the gravitational force equal to the centripetal force, we have mg = mv^2/r. Simplifying, we find v^2 = rg, and taking the square root of both sides gives v = (rg)^(1/2). Therefore, the minimum value for the speed of the car at the top of the loop is (rg)^(1/2).

Submit
59. A horizontal curve on a bobsled run is banked at a 45° angle. When a bobsled rounds this curve at the curve's safe speed (no friction needed to stay on the run), what is its centripetal acceleration?

Explanation

When a bobsled rounds a curve at the curve's safe speed, its centripetal acceleration is 1.0 g. Centripetal acceleration is the acceleration towards the center of the curve that keeps the bobsled moving in a curved path. In this case, the bobsled is moving at a constant speed, so the centripetal acceleration is equal to the gravitational acceleration, which is 1.0 g. This means that the bobsled is experiencing an acceleration of 1 times the acceleration due to gravity.

Submit
60. The banking angle in a turn on the Olympic bobsled track is not constant, but increases upward from the horizontal. Coming around a turn, the bobsled team will intentionally "climb the wall," then go lower coming out of the turn. Why do they do this?

Explanation

The bobsled team intentionally climbs the wall and goes lower coming out of the turn in order to take the turn at a faster speed. This technique allows them to maintain better control and reduce the g-force on them, ultimately enabling them to navigate the turn more efficiently and increase their speed. By increasing the banking angle upward from the horizontal, the bobsled team can leverage the forces of gravity and centripetal force to their advantage, allowing them to maintain higher speeds throughout the turn.

Submit
61. The planet Jupiter is 7.78 * 10^11 m from the Sun. How long does it take for Jupiter to orbit once about the Sun? (The distance from the Earth to the Sun is 1.50 * 10^11 m.)

Explanation

Jupiter is much farther from the Sun compared to Earth. It takes Earth approximately 1 year to orbit the Sun, so it would take Jupiter a longer time due to its greater distance. The correct answer of 12 years is a reasonable estimate for Jupiter's orbital period based on its distance from the Sun.

Submit
62. The maximum speed around a level curve is 30.0 km/h. What is the maximum speed around a curve with twice the radius? (Assume all other factors remain unchanged.)

Explanation

When a car is going around a curve, the maximum speed it can achieve depends on the radius of the curve. A larger radius allows for a higher speed. In this question, it is stated that the maximum speed around a level curve is 30.0 km/h. If the radius of the curve is doubled, it means that the curve is now less sharp and has a larger radius. This allows the car to go faster. The correct answer of 42.4 km/h is obtained by taking into account the relationship between radius and speed.

Submit
63. A stone, of mass m, is attached to a strong string and whirled in a vertical circle of radius r. At the exact top of the path the tension in the string is 3 times the stone's weight. The stone's speed at this point is given by

Explanation

At the top of the path, the tension in the string is equal to the sum of the stone's weight and the centripetal force required to keep it moving in a circle. Since the tension is 3 times the stone's weight, we can write the equation as T = mg + mv^2/r, where T is the tension, m is the mass of the stone, g is the acceleration due to gravity, v is the speed of the stone, and r is the radius of the circle. Rearranging the equation, we get mv^2/r = 2mg, which simplifies to v = (2gr)^(1/2). Therefore, the stone's speed at the top of the path is given by 2(gr)^(1/2).

Submit
64. A satellite is in a low circular orbit about the Earth (i.e., it just skims the surface of the Earth). How long does it take to make one revolution around the Earth? (The mean radius of the Earth is 6.38 * 10^6 m.)

Explanation

A satellite in a low circular orbit around the Earth takes approximately 85 minutes to make one revolution. This is because the time it takes for an object to complete one revolution around the Earth is determined by its orbital period, which depends on the altitude of the orbit. In a low circular orbit, the satellite is closer to the Earth's surface, so it experiences stronger gravitational pull, which causes it to travel at a higher velocity. As a result, the orbital period is shorter, leading to a faster revolution time of 85 minutes.

Submit
65. What is the gravitational force on a 70-kg person standing on the Earth, due to the Moon? The mass of the Moon is 7.36 * 10^22 kg and the distance to the Moon is 3.82 * 10^8 m.

Explanation

The gravitational force between two objects is given by the equation F = (G * m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects. In this case, the mass of the person is 70 kg, the mass of the Moon is 7.36 * 10^22 kg, and the distance to the Moon is 3.82 * 10^8 m. Plugging these values into the equation, we get F = (6.67 * 10^-11 N * m^2 / kg^2) * (70 kg) * (7.36 * 10^22 kg) / (3.82 * 10^8 m)^2 = 0.0024 N. Therefore, the gravitational force on the person due to the Moon is 0.0024 N.

Submit
66. Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (no friction needed to stay on the run) for the smaller radius curve is v. What is the safe speed on the larger radius curve?

Explanation

The safe speed on the larger radius curve is approximately 1.41v. This can be explained using the concept of centripetal force. The centripetal force required to keep an object moving in a curved path is directly proportional to the square of its velocity and inversely proportional to the radius of the curve. Since the larger radius curve has twice the radius of the smaller radius curve, it requires half the centripetal force to stay on the curve. Therefore, the velocity can be increased by a factor of approximately 1.41 (square root of 2) while still maintaining the same centripetal force, resulting in a safe speed of approximately 1.41v.

Submit
67. The Earth has radius r. A satellite of mass 100 kg is at a point 3r above the Earth's surface. What is the satellite's weight?

Explanation

The weight of an object is the force exerted on it due to gravity. It is calculated by multiplying the mass of the object by the acceleration due to gravity. In this case, the mass of the satellite is given as 100 kg. Since the satellite is 3 times the radius of the Earth above its surface, the distance between the satellite and the center of the Earth is 4 times the radius of the Earth. As the distance increases, the force of gravity decreases. Therefore, the weight of the satellite will be less than its actual mass. The correct answer of 61 N indicates that the weight of the satellite is 61 Newtons.

Submit
68. Europa, a moon of Jupiter, has an orbital diameter of 1.34 * 10^9 m, and a period of 3.55 days. What is the mass of Jupiter?

Explanation

The mass of Jupiter can be determined using the formula for orbital period and diameter. The formula is T^2 = (4π^2/GM) * r^3, where T is the period, G is the gravitational constant, M is the mass of Jupiter, and r is the orbital radius. Rearranging the formula to solve for M gives M = (4π^2/G) * (r^3/T^2). Plugging in the given values for r and T, and using the value of G, the mass of Jupiter can be calculated as 1.89 * 10^27 kg.

Submit
69. The innermost moon of Jupiter orbits the planet with a radius of 422 * 10^3 km and a period of 1.77 days. What is the mass of Jupiter?

Explanation

The mass of Jupiter can be calculated using the formula for the centripetal force. The centripetal force is equal to the gravitational force between Jupiter and its moon. The gravitational force can be expressed as (G * M * m) / r^2, where G is the gravitational constant, M is the mass of Jupiter, m is the mass of the moon, and r is the radius of the moon's orbit. By rearranging the formula and plugging in the given values for the radius and period of the moon's orbit, we can solve for M, which is the mass of Jupiter. The calculated value is approximately 1.9 * 10^27 kg.

Submit
70. A car goes around a curve of radius r at a constant speed v. Then it goes around the same curve at half of the original speed. What is the centripetal force on the car as it goes around the curve for the second time, compared to the first time?

Explanation

When a car goes around a curve at a constant speed, the centripetal force required to keep it moving in a circular path is given by the equation Fc = mv^2/r, where Fc is the centripetal force, m is the mass of the car, v is the velocity, and r is the radius of the curve.

When the car goes around the same curve at half of the original speed, the velocity is reduced to v/2. Plugging this value into the equation, we get Fc' = m(v/2)^2/r = m(v^2/4)/r = (mv^2/4r).

Comparing Fc' to Fc, we can see that Fc' is one-fourth as big as Fc. Therefore, the centripetal force on the car as it goes around the curve for the second time is one-fourth as big as the first time.

Submit
71. A satellite encircles Mars at a distance above its surface equal to 3 times the radius of Mars. The acceleration of gravity of the satellite, as compared to the acceleration of gravity on the surface of Mars, is

Explanation

The acceleration of gravity on the surface of Mars is determined by the mass of Mars and the distance from the center of Mars to its surface. Since the satellite is orbiting Mars at a distance above its surface equal to 3 times the radius of Mars, the satellite is further away from the center of Mars. According to the inverse square law of gravity, the acceleration of gravity decreases as the distance from the center increases. As a result, the acceleration of gravity on the satellite is one-sixteenth (3^2 = 9, 1/9 = 1/16) as much as the acceleration of gravity on the surface of Mars.

Submit
72. What minimum banking angle is required for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding? (Ignore friction.)

Explanation

To negotiate a turn without skidding, the centripetal force must be equal to or greater than the force of gravity. The centripetal force is given by the equation Fc = (mv^2)/r, where m is the mass of the bobsled, v is the velocity, and r is the radius of the turn. The force of gravity is given by the equation Fg = mg, where g is the acceleration due to gravity. Setting Fc equal to Fg and solving for the minimum banking angle, we get θ = arctan(v^2/(rg)). Plugging in the given values, we find that the minimum banking angle required is 51°.

Submit
73. An astronaut goes out for a "space-walk" at a distance above the Earth equal to the radius of the Earth. What is her acceleration due to gravity?

Explanation

When an astronaut goes out for a space-walk at a distance above the Earth equal to the radius of the Earth, the gravitational force acting on them decreases. This is because the gravitational force is inversely proportional to the square of the distance between two objects. As the astronaut moves away from the Earth's surface, the distance between them and the Earth increases, resulting in a decrease in the gravitational force. Therefore, the acceleration due to gravity experienced by the astronaut will be g/4, where g is the acceleration due to gravity at the Earth's surface.

Submit
74. The maximum force a pilot can stand is about seven times his weight. What is the minimum radius of curvature that a jet plane's pilot, pulling out of a vertical dive, can tolerate at a speed of 250 m/s?

Explanation

The maximum force a pilot can stand is about seven times his weight. In this scenario, the pilot is pulling out of a vertical dive at a speed of 250 m/s. To find the minimum radius of curvature that the pilot can tolerate, we need to consider the centripetal force experienced by the pilot. The centripetal force is given by the equation F = (mv^2) / r, where F is the force, m is the mass of the pilot, v is the velocity, and r is the radius of curvature. Since the force experienced by the pilot cannot exceed seven times his weight, we can set up the equation 7mg = (mv^2) / r. Simplifying the equation, we find that r = (v^2) / (7g), where g is the acceleration due to gravity. Plugging in the given values, we get r = (250^2) / (7 * 9.8) ≈ 1060 m. Therefore, the minimum radius of curvature that the pilot can tolerate is approximately 1060 m.

Submit
75. At a distance of 14000 km from some planet's center, the acceleration of gravity is 32 m/s^2. What is the acceleration of gravity at a point 28000 km from the planet's center?

Explanation

The acceleration of gravity at a point is inversely proportional to the square of the distance from the planet's center. Since the distance from the planet's center is doubled from 14000 km to 28000 km, the acceleration of gravity will be four times smaller. Therefore, the acceleration of gravity at a point 28000 km from the planet's center will be 8.0 m/s^2.

Submit
76. A planet is discovered to orbit around a star in the galaxy Andromeda, with the same orbital diameter as the Earth around our Sun. If that star has 4 times the mass of our Sun, what will the period of revolution of that new planet be, compared to the Earth's orbital period?

Explanation

The period of revolution of the new planet will be one-half as much as Earth's orbital period because the period of revolution is inversely proportional to the square root of the mass of the star. Since the new star has 4 times the mass of our Sun, the square root of its mass is 2 times the square root of our Sun's mass. Therefore, the period of revolution of the new planet will be one-half of Earth's orbital period.

Submit
77. An object weighs 432 N on the surface of the Earth. The Earth has radius r. If the object is raised to a height of 3r above the Earth's surface, what is its weight?

Explanation

When the object is raised to a height of 3r above the Earth's surface, the distance between the object and the center of the Earth increases. As a result, the gravitational force acting on the object decreases. The weight of an object is equal to the gravitational force acting on it. Therefore, when the object is raised to a height of 3r, its weight decreases to 27 N.

Submit
78. The radius of the Earth is R. At what distance above the Earth's surface will the acceleration of gravity be 4.9 m/s^2?

Explanation

The acceleration due to gravity decreases as the distance from the center of the Earth increases. This is because the gravitational force weakens with distance. At a distance of 0.41 R (where R is the radius of the Earth), the acceleration of gravity is 4.9 m/s^2. This means that at this distance above the Earth's surface, an object would experience an acceleration due to gravity equal to 4.9 m/s^2.

Submit
79. How many revolutions per minute must a circular, rotating space station of radius 1000 m rotate to produce an artificial gravity of 9.80 m/s^2?

Explanation

A circular, rotating space station can produce artificial gravity through centripetal acceleration. The formula for centripetal acceleration is a = (v^2) / r, where a is the acceleration, v is the linear velocity, and r is the radius. In this case, the desired acceleration is 9.80 m/s^2 and the radius is 1000 m. Rearranging the formula, we can solve for v: v = sqrt(a * r). Plugging in the values, we get v = sqrt(9.80 * 1000) = 31.30 m/s. Since we want the velocity in terms of revolutions per minute, we can convert it using the formula v = (2 * pi * r) / t, where v is the linear velocity, r is the radius, and t is the time in seconds. Rearranging the formula, we can solve for t: t = (2 * pi * r) / v. Plugging in the values, we get t = (2 * pi * 1000) / 31.30 = 200.96 seconds. Finally, we can convert the time to minutes and calculate the number of revolutions per minute: 200.96 seconds * (1 minute / 60 seconds) * (1 revolution / t) = 0.95 rpm.

Submit
80. The gravitational attractive force between two masses is F. If the masses are moved to half of their initial distance, what is the gravitational attractive force?

Explanation

When the masses are moved to half of their initial distance, the gravitational force between them will increase. This is because the gravitational force is inversely proportional to the square of the distance between the masses. When the distance is halved, the force will be four times stronger. Therefore, the gravitational attractive force will be 4F.

Submit
View My Results

Quiz Review Timeline (Updated): Mar 3, 2023 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Mar 03, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Sep 14, 2012
    Quiz Created by
    Drtaylor
Cancel
  • All
    All (80)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
Consider a particle moving with constant speed such that its...
What type of acceleration does an object moving with constant speed in...
What force is needed to make an object move in a circle?
A car goes around a curve of radius r at a constant speed v. What is...
A spaceship is traveling to the Moon. At what point is it beyond the...
As a rocket moves away from the Earth's surface, the rocket's...
Who was the first person to realize that the planets move in...
When an object experiences uniform circular motion, the direction of...
A roller coaster car is on a track that forms a circular loop in the...
A car is negotiating a flat curve of radius 50 m with a speed of 20...
Suppose a satellite were orbiting the Earth just above the surface....
Consider a particle moving with constant speed such that its...
Compared to its mass on the Earth, the mass of an object on the Moon...
An object moves in a circular path at a constant speed. Compare the...
Is it possible for an object moving with a constant speed to...
Let the average orbital radius of a planet be r. Let the orbital...
A car of mass m goes around a banked curve of radius r with speed v....
The gravitational force between two objects is inversely proportional...
A 0.50-kg mass is attached to the end of a 1.0-m string. The system is...
The mass of the Moon is 7.4 * 10^22 kg and its mean radius is...
By how many newtons does the weight of a 100-kg person change when he...
A frictionless curve of radius 100 m, banked at an angle of 45°,...
A person is standing on a scale in an elevator accelerating downward....
A pilot makes an outside vertical loop (in which the center of the...
The speed of Halley's Comet, while traveling in its elliptical...
Two objects attract each other gravitationally. If the distance...
A car goes around a flat curve of radius 50 m at a speed of 14 m/s....
A car is moving with a constant speed v around a level curve. The...
A curve of radius 80 m is banked at 45°. Suppose that an ice storm...
Is it possible for an object moving around a circular path to have...
When an object experiences uniform circular motion, the direction of...
A car goes around a curve of radius r at a constant speed v. Then it...
An object moves with a constant speed of 30 m/s on a circular track of...
Two planets have the same surface gravity, but planet B has twice the...
A car traveling 20 m/s rounds an 80-m radius horizontal curve with the...
A point on a wheel rotating at 5.00 rev/s is located 0.200 m from the...
A spherically symmetric planet has four times the Earth's mass and...
The acceleration of gravity on the Moon is one-sixth what it is on...
A stone, of mass m, is attached to a strong string and whirled in a...
It takes the planet Jupiter 12 years to orbit the Sun once. What is...
Satellite A has twice the mass of satellite B, and rotates in the same...
A pilot executes a vertical dive then follows a semi-circular arc...
A coin of mass m rests on a turntable a distance r from the axis of...
The gravitational force between two objects is proportional to
The average distance from the Earth to the Sun is defined as one...
A motorcycle has a mass of 250 kg. It goes around a 13.7 m radius turn...
A satellite is in a low circular orbit about the Earth (i.e., it just...
The acceleration of gravity on the Moon is one-sixth what it is on...
A jet plane flying 600 m/s experiences an acceleration of 4g when...
The hydrogen atom consists of a proton of mass 1.67 * 10^(-27) kg...
Two moons orbit a planet in nearly circular orbits. Moon A has orbital...
A hypothetical planet has a mass of half that of the Earth and a...
For a spacecraft going from the Earth toward the Sun, at what distance...
A satellite is in circular orbit 230 km above the surface of the...
What is the centripetal acceleration of a point on the perimeter of a...
List the four fundamental forces in nature.
Two planets have the same surface gravity, but planet B has twice the...
A roller coaster car (mass = M) is on a track that forms a circular...
A horizontal curve on a bobsled run is banked at a 45° angle. When...
The banking angle in a turn on the Olympic bobsled track is not...
The planet Jupiter is 7.78 * 10^11 m from the Sun. How long does...
The maximum speed around a level curve is 30.0 km/h. What is the...
A stone, of mass m, is attached to a strong string and whirled in a...
A satellite is in a low circular orbit about the Earth (i.e., it just...
What is the gravitational force on a 70-kg person standing on the...
Two horizontal curves on a bobsled run are banked at the same angle,...
The Earth has radius r. A satellite of mass 100 kg is at a point 3r...
Europa, a moon of Jupiter, has an orbital diameter of 1.34 * 10^9...
The innermost moon of Jupiter orbits the planet with a radius of...
A car goes around a curve of radius r at a constant speed v. Then it...
A satellite encircles Mars at a distance above its surface equal to 3...
What minimum banking angle is required for an Olympic bobsled to...
An astronaut goes out for a "space-walk" at a distance above...
The maximum force a pilot can stand is about seven times his weight....
At a distance of 14000 km from some planet's center, the...
A planet is discovered to orbit around a star in the galaxy Andromeda,...
An object weighs 432 N on the surface of the Earth. The Earth has...
The radius of the Earth is R. At what distance above the Earth's...
How many revolutions per minute must a circular, rotating space...
The gravitational attractive force between two masses is F. If the...
Alert!

Advertisement