Centripetal Force And Big G Quiz

Explanation
The magnitude of the centripetal acceleration of the stone is 20 m/s2 because centripetal acceleration 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 stone is moving at a constant speed of 4.0 m/s and the radius of the circle is 0.80 m. Plugging these values into the formula, we get a = (4.0 m/s)^2 / 0.80 m = 20 m/s2.

Explanation
The centripetal acceleration of an object moving in a circular path is always directed towards the center of the circle. In this case, the car is moving clockwise around the circular track, so the center of the circle is towards the east (E). Therefore, the car's centripetal acceleration is directed towards E.

Explanation
If the circular track were to suddenly become frictionless, the car would continue to move in the direction it was moving before. Since the car was initially moving in a clockwise direction, it would continue moving in that direction. Therefore, the car's direction of travel would be toward the north (N).

Explanation
At the instant shown in the diagram, the car is moving in a clockwise direction around the circular track. The centripetal force is the force that keeps an object moving in a circular path. According to the right-hand rule, the centripetal force always points towards the center of the circle. Since the car is moving clockwise, the center of the circle is towards the east (E). Therefore, the centripetal force acting on the car is directed towards E.

Explanation
The centripetal force experienced by a passenger in the car can be calculated using the formula F = (mv^2)/r, where F is the centripetal force, m is the mass of the car, v is the speed of the car, and r is the radius of the circular track. In this case, the mass of the car is 1000 kg, the speed of the car is 5.00 m/s, and the radius of the track is 25.0 meters. Plugging these values into the formula, we get F = (1000 kg * (5.00 m/s)^2) / 25.0 m = 1000 N. Therefore, the passenger in the car is experiencing a centripetal force of 1000 N.

Explanation
The force due to gravity on an object is inversely proportional to the square of its distance from the center of the Earth. This means that as the distance from the center of the Earth increases, the force due to gravity decreases. In this case, when the distance from the center of the Earth is 3R, it is three times farther away than when it was at distance R. Since the force due to gravity is inversely proportional to the square of the distance, the force will be 1/9 of the original force, which is represented by 1/9 F.

Explanation
The magnitude of the gravitational force of attraction between satellite B and the planet is one-fourth as great compared to the magnitude of the gravitational force of attraction between satellite A and the planet. This is because the gravitational force is inversely proportional to the square of the distance between two objects. Since both satellites are in circular orbits around the planet, they have the same distance from the planet. Therefore, the force of attraction between satellite B and the planet is one-fourth of the force of attraction between satellite A and the planet.

Explanation
As the astronaut travels further away from the center 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. Since weight is the force experienced by an object due to gravity, and weight is directly proportional to mass, the weight of the astronaut will decrease as they travel further away. Therefore, the correct answer is D. weight remains the same.

Explanation
Doubling the mass of both objects would increase the gravitational force of attraction between them. According to Newton's law of universal gravitation, the force of attraction between two objects is directly proportional to the product of their masses. Therefore, increasing the mass of both objects would result in a stronger gravitational force. Doubling the distance between the objects, on the other hand, would decrease the gravitational force of attraction. This is because the force of attraction is inversely proportional to the square of the distance between the objects. Therefore, option A is the correct answer.

Explanation
The magnitude of the gravitational force between two objects can be calculated using the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers. In this case, the masses of the spheres are given as 15.0 kilograms each, and the distance between their centers is given as 3.00 meters. Plugging these values into the formula, we can calculate the magnitude of the gravitational force.

Explanation
The mass of the spacecraft remains the same at a distance of one Earth radius above Earth's surface. Therefore, the correct answer is C. 2.00 × 104 kg.

Explanation
The magnitude of the gravitational force of attraction between two objects is inversely proportional to the square of the distance between them. Therefore, if the distance between Earth and the Moon is halved from 3.84 × 108 meters to 1.92 × 108 meters, the magnitude of the gravitational force of attraction would be four times greater. So, the correct answer is B. 4.0 × 1020 N.

Explanation
As the distance between the meteor and the center of the Earth decreases from 16 Earth radii to 2 Earth radii, the magnitude of the gravitational force between them becomes 64 times as great. This is because the gravitational force is inversely proportional to the square of the distance between two objects. Therefore, when the distance is reduced by a factor of 8 (from 16 Earth radii to 2 Earth radii), the gravitational force increases by a factor of 8^2, which is 64.

Explanation
The magnitude of the object's acceleration can be found using the formula for centripetal acceleration, which is given by a = v^2/r, where v is the velocity and r is the radius. Plugging in the values, we have a = (4.0 m/s)^2 / 0.25 m = 16 m/s^2. Therefore, the correct answer is C. 16 m/s^2.

Explanation
A. smaller. The acceleration due to gravity is directly proportional to the mass of the planet and inversely proportional to the square of the radius. Since Mars has a smaller mass and radius compared to Earth, the acceleration due to gravity on the surface of Mars is smaller than that on Earth.

Explanation
The magnitude of the centripetal force acting on the car as it travels around the circular path is approximately 1.1 X 104 N. This can be calculated using the formula for centripetal force, F = (m * v^2) / r, where m is the mass of the car, v is the velocity of the car, and r is the radius of the circular path. Plugging in the given values, we get F = (1200 kg * (9.0 m/s)^2) / 25 m = 1.1 X 104 N.

Explanation
The car will continue to move in a circular path with a radius of 25 meters on the ice. The absence of frictional force on the tires does not affect the car's ability to turn, as the centripetal force required for circular motion is provided by the car's inertia.