Circular Motion & Gravity Challenge: Physics Quiz

1. What is the centripetal force that holds planets in orbit?

Inertia

Gravitational force

Planetary force

Kepler's force

The centripetal force that holds planets in orbit is the gravitational force. This force is generated by the mass of the planet and the mass of the object it is orbiting, such as the Sun. The gravitational force pulls the planet towards the center of its orbit, causing it to continuously change direction and maintain a circular or elliptical path around the object it is orbiting. This force is responsible for keeping planets in their orbits and preventing them from flying off into space.

Explanation

The centripetal force that holds planets in orbit is the gravitational force. This force is generated by the mass of the planet and the mass of the object it is orbiting, such as the Sun. The gravitational force pulls the planet towards the center of its orbit, causing it to continuously change direction and maintain a circular or elliptical path around the object it is orbiting. This force is responsible for keeping planets in their orbits and preventing them from flying off into space.

2. What term describes a force that causes an object to move in a circular path?

Circular force

Centripetal acceleration

Centripetal force

Centrifugal force

Centripetal force is the correct answer because it is the force that acts towards the center of a circular path, keeping an object moving in that path. It is necessary to counteract the tendency of the object to move in a straight line and ensures that the object maintains its circular motion. Centripetal force is responsible for keeping planets in orbit around the sun, cars moving around a curve, and even a ball on a string swinging in a circle.

Explanation

Centripetal force is the correct answer because it is the force that acts towards the center of a circular path, keeping an object moving in that path. It is necessary to counteract the tendency of the object to move in a straight line and ensures that the object maintains its circular motion. Centripetal force is responsible for keeping planets in orbit around the sun, cars moving around a curve, and even a ball on a string swinging in a circle.

3. A 45 kg child riding a Ferris wheel has a tangential speed of 8.5 m/s. Find the magnitude of the centripetal force on the child if the distance from the child to the axis of the wheel is 18 m.

180.6 N

8128.1 N

120 N

21.3 N

The centripetal force acting on an object moving in a circle is given by the formula F = m * v^2 / r, where F is the force, m is the mass, v is the tangential speed, and r is the distance from the object to the center of the circle. In this case, the mass of the child is 45 kg, the tangential speed is 8.5 m/s, and the distance from the child to the axis of the wheel is 18 m. Plugging these values into the formula, we get F = 45 kg * (8.5 m/s)^2 / 18 m, which simplifies to F = 180.6 N. Therefore, the magnitude of the centripetal force on the child is 180.6 N.

Explanation

The centripetal force acting on an object moving in a circle is given by the formula F = m * v^2 / r, where F is the force, m is the mass, v is the tangential speed, and r is the distance from the object to the center of the circle. In this case, the mass of the child is 45 kg, the tangential speed is 8.5 m/s, and the distance from the child to the axis of the wheel is 18 m. Plugging these values into the formula, we get F = 45 kg * (8.5 m/s)^2 / 18 m, which simplifies to F = 180.6 N. Therefore, the magnitude of the centripetal force on the child is 180.6 N.

4. A model airplane with a mass of 3.2 kg moves in a circular path with a radius of 12 m. If the airplane's speed is 45 m/s, how large is the force that the control line exerts on the plane to keep it moving in a circle?

12 N

540 N

3.6 N

1728 N

The force that the control line exerts on the plane to keep it moving in a circle can be calculated using the centripetal force formula, which is F = (m * v^2) / r. In this case, the mass of the airplane is given as 3.2 kg, the speed is 45 m/s, and the radius is 12 m. Plugging these values into the formula, we get F = (3.2 kg * (45 m/s)^2) / 12 m = 540 N. Therefore, the force that the control line exerts on the plane is 540 N.

Explanation

The force that the control line exerts on the plane to keep it moving in a circle can be calculated using the centripetal force formula, which is F = (m * v^2) / r. In this case, the mass of the airplane is given as 3.2 kg, the speed is 45 m/s, and the radius is 12 m. Plugging these values into the formula, we get F = (3.2 kg * (45 m/s)^2) / 12 m = 540 N. Therefore, the force that the control line exerts on the plane is 540 N.

5. The law of universal gravitation states that

Two objects always exert gravitational forces on each other.

The force of gravity depends on the mass and the distance between the two objects

All objects fall at different rates on earth.

Both a and b.

The law of universal gravitation states that two objects always exert gravitational forces on each other, which is represented by option a. Additionally, the force of gravity between two objects depends on their masses and the distance between them, as stated in option b. Therefore, both options a and b are correct explanations of the law of universal gravitation.

Explanation

The law of universal gravitation states that two objects always exert gravitational forces on each other, which is represented by option a. Additionally, the force of gravity between two objects depends on their masses and the distance between them, as stated in option b. Therefore, both options a and b are correct explanations of the law of universal gravitation.

6. Because of the conditions that give rise to them, tornadoes do not have the widespread destructive effects of hurricanes. Nevertheless, the winds encountered in some tornadoes are even greater than those at the eyewall of a hurricane. Suppose a small pebble is swept up in a tornado. The pebble is 3.81 m from the center of the tornado and has a tangential speed equal to that of the surrounding wind: 124 m/s. What is the magnitude of the centripetal acceleration of the pebble?

32.5 m/s2

8.54 m/s2

1059.2 m/s2

4035.7 m/s2

The centripetal acceleration of an object moving in a circular path can be calculated using the formula a = v^2/r, where v is the tangential speed and r is the distance from the center of the circle. In this case, the tangential speed of the pebble is given as 124 m/s and the distance from the center of the tornado is 3.81 m. Plugging these values into the formula, we get a = (124 m/s)^2 / 3.81 m = 4035.7 m/s^2. Therefore, the magnitude of the centripetal acceleration of the pebble is 4035.7 m/s^2.

Explanation

The centripetal acceleration of an object moving in a circular path can be calculated using the formula a = v^2/r, where v is the tangential speed and r is the distance from the center of the circle. In this case, the tangential speed of the pebble is given as 124 m/s and the distance from the center of the tornado is 3.81 m. Plugging these values into the formula, we get a = (124 m/s)^2 / 3.81 m = 4035.7 m/s^2. Therefore, the magnitude of the centripetal acceleration of the pebble is 4035.7 m/s^2.

7. When calculating the gravitational force between two extended bodies, you should measure the distance

From the closest points on each body

From the most distant points on each body

From the center of each body

From the center of one body to the closest point on the other body

When calculating the gravitational force between two extended bodies, it is necessary to measure the distance from the center of each body. This is because the gravitational force between two objects depends on the distance between their centers of mass. By measuring from the center of each body, we can accurately determine the distance at which the gravitational force acts.

Explanation

When calculating the gravitational force between two extended bodies, it is necessary to measure the distance from the center of each body. This is because the gravitational force between two objects depends on the distance between their centers of mass. By measuring from the center of each body, we can accurately determine the distance at which the gravitational force acts.

8. Deimos, a satellite of Mars, has an average radius of 6.3 km. If the gravitational force between Deimos and a 3.0 kg rock at its surface is 2.5 ´10^-² N, what is the mass of Deimos?

4.96 x 10^15 kg

7.87 x 10^11 kg

4.96 x 10^25 kg

4.96 x 10^-21 kg

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 objects, and r is the distance between the centers of the objects. In this case, we are given the force, the mass of the rock, and the radius of Deimos. We can rearrange the equation to solve for the mass of Deimos: m2 = (F * r^2) / (G * m1). Plugging in the given values, we get m2 = (2.5 * 10^-2 N * (6.3 km)^2) / (G * 3.0 kg). Using the value of G, we can calculate m2 to be approximately 4.96 x 10^15 kg.

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 objects, and r is the distance between the centers of the objects. In this case, we are given the force, the mass of the rock, and the radius of Deimos. We can rearrange the equation to solve for the mass of Deimos: m2 = (F * r^2) / (G * m1). Plugging in the given values, we get m2 = (2.5 * 10^-2 N * (6.3 km)^2) / (G * 3.0 kg). Using the value of G, we can calculate m2 to be approximately 4.96 x 10^15 kg.

9. Which of the following is due to inertia?

A ball whirled in a circular motion stays in one plane.

A ball whirled in a circular motion experiences centripetal acceleration directed toward the center of motion.

A ball whirled in a circular motion experiences a centripetal force directed toward the center of motion.

A ball whirled in a circular motion will move off in a straight line if the string breaks.

When a ball is whirled in a circular motion, it experiences centripetal force that keeps it moving in a circular path. This force acts towards the center of the motion, preventing the ball from moving off in a straight line. However, if the string holding the ball breaks, the centripetal force is no longer present, and the ball continues to move in a straight line due to its inertia. Inertia is the tendency of an object to resist changes in its motion, so when the string breaks, the ball will keep moving in the same direction and speed as before.

Explanation

When a ball is whirled in a circular motion, it experiences centripetal force that keeps it moving in a circular path. This force acts towards the center of the motion, preventing the ball from moving off in a straight line. However, if the string holding the ball breaks, the centripetal force is no longer present, and the ball continues to move in a straight line due to its inertia. Inertia is the tendency of an object to resist changes in its motion, so when the string breaks, the ball will keep moving in the same direction and speed as before.

10. The most violent part of a hurricane is at the edge of the hurricane's eye. This region, called the eyewall, can have winds with speeds of more than 300 km/h. Suppose winds in a hurricane's eyewall have a tangential speed of 82.2 m/s. If the eyewall is 25 km from the center of the hurricane, what is the magnitude of the centripetal acceleration of particles in the eyewall?

0.27 m/s2

270.3 m/s2

0.003 m/s2

3.3 m/s2

The centripetal acceleration of particles in the eyewall can be calculated using the formula: a = v^2 / r, where v is the tangential speed and r is the distance from the center. Plugging in the given values, we get a = (82.2 m/s)^2 / 25000 m = 0.27 m/s^2.

Explanation

The centripetal acceleration of particles in the eyewall can be calculated using the formula: a = v^2 / r, where v is the tangential speed and r is the distance from the center. Plugging in the given values, we get a = (82.2 m/s)^2 / 25000 m = 0.27 m/s^2.

11. A ball is whirled on a string, then the string breaks. What causes the ball to move off in a straight line?

Centripetal acceleration

Centripetal force

Centrifugal force

Inertia

When the string breaks, the ball continues to move off in a straight line due to its inertia. Inertia is the tendency of an object to resist changes in its motion. Since there is no longer a force acting on the ball to keep it moving in a circular path, it moves in a straight line according to Newton's first law of motion. The other options, centripetal acceleration, centripetal force, and centrifugal force, are not applicable in this scenario as they are all related to circular motion.

Explanation

When the string breaks, the ball continues to move off in a straight line due to its inertia. Inertia is the tendency of an object to resist changes in its motion. Since there is no longer a force acting on the ball to keep it moving in a circular path, it moves in a straight line according to Newton's first law of motion. The other options, centripetal acceleration, centripetal force, and centrifugal force, are not applicable in this scenario as they are all related to circular motion.

12. When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car?

Centripetal acceleration

Centripetal force

Centrifugal force

Inertia

When a car makes a sharp left turn, the passengers tend to move toward the right side of the car due to inertia. Inertia is the tendency of an object to resist changes in its state of motion. As the car turns left, the passengers' bodies want to continue moving forward in a straight line due to their inertia. This causes them to move toward the right side of the car, which is the opposite direction of the car's turn.

Explanation

When a car makes a sharp left turn, the passengers tend to move toward the right side of the car due to inertia. Inertia is the tendency of an object to resist changes in its state of motion. As the car turns left, the passengers' bodies want to continue moving forward in a straight line due to their inertia. This causes them to move toward the right side of the car, which is the opposite direction of the car's turn.

13. The sun has a mass of 2.0 x 10³⁰ kg and a radius of 7.0 x 10⁵ km. What mass must be located at the sun's surface for a gravitational force of 470 N to exist between the mass and the sun?

1.73 x 10 ^-23 kg

1.73 kg

1.73 x 10^-6 kg

1.73 x 10^-34 kg

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 question, we are given the mass of the sun (2.0 x 10^30 kg), the radius of the sun (7.0 x 10^5 km), and the gravitational force (470 N). We need to find the mass that must be located at the sun's surface for this gravitational force to exist. Since we are given the mass and radius of the sun, we can rearrange the equation to solve for the mass of the second object (m2). Rearranging the equation gives m2 = (F * r^2) / (G * m1). Plugging in the values, we get m2 = (470 N * (7.0 x 10^5 km)^2) / (G * 2.0 x 10^30 kg). Using the given values for G (gravitational constant), we can calculate the value of m2 to be approximately 1.73 kg.

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 question, we are given the mass of the sun (2.0 x 10^30 kg), the radius of the sun (7.0 x 10^5 km), and the gravitational force (470 N). We need to find the mass that must be located at the sun's surface for this gravitational force to exist. Since we are given the mass and radius of the sun, we can rearrange the equation to solve for the mass of the second object (m2). Rearranging the equation gives m2 = (F * r^2) / (G * m1). Plugging in the values, we get m2 = (470 N * (7.0 x 10^5 km)^2) / (G * 2.0 x 10^30 kg). Using the given values for G (gravitational constant), we can calculate the value of m2 to be approximately 1.73 kg.

14. A centripetal force acts

In the same direction as tangential speed

In the direction opposite tangential speed

Perpendicular to the plane of motion

Perpendicular to the tangential speed but in the same plane

A centripetal force acts perpendicular to the tangential speed but in the same plane because it is responsible for continuously changing the direction of an object moving in a circular path. The force is directed towards the center of the circle and is perpendicular to the velocity vector at any given point. This force is necessary to keep the object moving in a curved path and prevent it from moving in a straight line.

Explanation

A centripetal force acts perpendicular to the tangential speed but in the same plane because it is responsible for continuously changing the direction of an object moving in a circular path. The force is directed towards the center of the circle and is perpendicular to the velocity vector at any given point. This force is necessary to keep the object moving in a curved path and prevent it from moving in a straight line.

15. The force that Earth exerts on the moon

Is greater than the force the moon exerts on Earth

Is less than the force the moon exerts on Earth

Is equal in magnitude to the force the moon exerts on Earth

Causes tides

The force that Earth exerts on the moon is equal in magnitude to the force the moon exerts on Earth because of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The gravitational force between two objects depends on their masses and the distance between them, but the forces they exert on each other are always equal in magnitude. Therefore, the force that Earth exerts on the moon is equal to the force the moon exerts on Earth.

Explanation

The force that Earth exerts on the moon is equal in magnitude to the force the moon exerts on Earth because of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The gravitational force between two objects depends on their masses and the distance between them, but the forces they exert on each other are always equal in magnitude. Therefore, the force that Earth exerts on the moon is equal to the force the moon exerts on Earth.

16. How does the gravitational force between two objects change if the distance between the objects doubles?

The force decreases by a factor of 4

The force decreases by a factor of 2

The force increases by a factor of 2

The force increases by a factor of 4

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that if the distance between the objects doubles, the force will decrease by a factor of 4. This is because doubling the distance will result in the denominator of the inverse square relationship being multiplied by 4, causing the force to decrease by a factor of 4.

Explanation

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that if the distance between the objects doubles, the force will decrease by a factor of 4. This is because doubling the distance will result in the denominator of the inverse square relationship being multiplied by 4, causing the force to decrease by a factor of 4.