1. A busy waitress slides a plate of apple pie along a counter to a hungry customer sitting near the end of the counter. The customer is not paying attention, and the plate slides off the counter horizontally at 0.84 m/s. The counter is 1.38 m high.
a. How long does it take the plate to fall to the floor?
b. How far from the base of the counter does the plate hit the floor?
2. The Moon revolves around Earth in a circular orbit with a radius of 3.84 108 m. It takes 27.3 days for the Moon to complete one orbit around Earth. What is the centripetal acceleration of the Moon?
3. A clown rides a small car at a speed of 15 km/h along a circular path with a radius of 3.5 m.
a. What is the magnitude of the centripetal force on a 0.18–kg ball held by the clown?
b. At the point where the car is headed due north, the clown throws the ball vertically upward with a speed of 5 m/s relative to the moving car. To where must a second clown run to catch the ball the same distance above the ground as it was thrown?
4. A 0.45–kg ball is attached to the end of a cord of length 1.4 m. The ball is whirled in a circular path in a horizontal plane. The cord can withstand a maximum tension of 57.0 N before it breaks. What is the maximum speed the ball can have without the cord breaking?
5. A marble rolls off the edge of a table that is 0.734 m high. The marble is moving at a speed of 0.122 m/s at the moment that it leaves the edge of the table. How far from the table does the marble land?
6. A car moving at 12.67 m/s rounds a bend in the road. The bend is semicircular and has a radius of 60 m. What is the centripetal acceleration of the car?
7. A town has a large clock on the hall in the town square. The clock has hands that show the hours, minutes, and seconds. A fly is sitting on the tip of the hand that shows the seconds. If the length of the hand is 1.2 m, what is the fly’s centripetal acceleration?
8. A rock is tied to a string and spun in a horizontal circle. The string is 1.8 m long and the rock has an acceleration of 3.4 m/s2. What is the tangential velocity of the rock?
9. The mass of Earth is 5.97 1024 kg, the mass of the Moon is 7.35 1022 kg, and the mean distance of the Moon from the center of Earth is 3.84 105 km. Use these data to calculate the magnitude of the gravitational force exerted by Earth on the Moon.
10. Two identical bowling balls are placed 1.00 m apart. The gravitational force between the bowling balls is 3.1 10–9 N. Find the mass of a bowling ball.
11. A plane drops a rescue capsule from an altitude of 8500 m.
a. How long does it take for the capsule to fall to Earth, assuming air resistance is negligible?
b. If the plane is traveling with a horizontal speed of 483 km/h when the capsule is released, what is the horizontal distance between the point at which the capsule is released and the point at which the capsule strikes the ground?
12. A satellite is placed in a circular orbit 100 km above Earth’s surface. Earth’s mass is 5.97 1024 kg and its average radius is 6.38 106 m.
a. What is the speed of the satellite?
b. How many minutes does it take the satellite to complete one orbit?
13. The asteroid Vesta has a mass of 3.0 1020 kg and an average radius of 510 km.
a. What is the acceleration due to gravity at its surface?
b. How much would a 95–kg astronaut weigh at the surface of Vesta?
14. The mass of Earth is 5.98 1024 kg and the mass of the Sun is 330,000 times greater than the mass of Earth. If the center of Earth is, on average, 1.495 1011 m from the center of the Sun, calculate the magnitude of the gravitational force the Sun exerts on Earth.
15. Two metal spheres, each weighing 24 kg are placed 0.05 m apart. Calculate the magnitude of the gravitational force the two spheres exert on each other.
16. A car and a truck are traveling side by side on the highway. The car has a mass of 1.37 103 kg and the truck has a mass of 9.92 103 kg. If the cars are separated by 2.1 m, find the force of gravitational attraction between the car and the truck.
17. A 5–kg mass weighs 8.1 N on the surface of the Moon. If the radius of the Moon is 1737 km, what is the mass of the Moon?
19. Acceleration due to gravity on Earth’s surface is 9.80 m/s2. Thus, a 1.00–kg mass weighs 9.80 N on the surface of Earth. If the radius of Earth was cut exactly in half but the mass of Earth remained unchanged, how much would a 1.00–kg mass weigh on the surface of Earth?
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It will take 1 s for the ball to return so it will go 4.17 m.
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If the radius was half, the force would increase by a factor of 4, thus a 1.00–kg mass would weigh 39.2 N
