Force, Momentum, Impulse, Gravitation, Work and Power
Solve the following problems on a separate sheet of paper, using proper problem-solving techniques. You must show all work, including equations, substitutions, calculations, and units. Consult your Reference Tables as necessary.
1. It takes a force of 50 N to give a body an acceleration of 10 meters per second per second. Calculate the mass of the body.
2. a. Calculate the weight of a 10-kilogram block of iron. b. Calculate the mass of an object that weighs 490 N.
3. An 8.0-kilogram rocket fired horizontally encounters a force of air resistance equal to 4.9 N. The force supplied by the rocket's engine is 60.9 N. a. Calculate the net force accelerating the rocket. b. Calculate the acceleration experienced by the rocket.
4. Assuming that at sea level the value of g is 9.8 meters per second per second, calculate the gravitational force exerted on a proton.
5. It requires a force of 300 N to keep a 500-N box sliding at constant speed across a floor. Calculate the coefficient of sliding (kinetic) friction.
6. A force acting on a 5.0-kilogram body increases its speed uniformly from 2.0 meters per second to 8.0 meters per second in 3.0 seconds. a. Calculate the initial momentum of the body. b. Calculate the final momentum of the body. c. Calculate the magnitude of the force acting on the body.
7. Calculate the length of time a 50-N force must act on a 400-kilogram cart to increase its speed from 10 meters per second to 12 meters per second.
8. When a car of mass 2.0 x 10exp3 kilograms moving at 9.0 meters per second collides head-on with second car possessing a mass of 1.5 x 10exp3 kilograms, the cars lock together and come to rest at the point of collision. a. Calculate the momentum of the second car just before the moment of collision. b. Calculate the speed of the second car just before the moment of collision. c. Calculate the momentum of both cars after the collision.
9. A ball of mass 0.20 kilograms is pitched to a batter at 30 meters per second. The ball is struck and hit back to the pitcher at a speed of 20 meters per second. If the ball and bat were in contact for 0.025 seconds, calculate the magnitude of the force exerted on the ball by the bat.
10. A 1-kilogram body moving forward at 5 meters per second collides directly with a second body at rest. After the collision, the 1-kilogram body reverses its direction and moves at 1 meter per second while the second body moves forward at 2 m/s. a. Calculate the direction and magnitude of the momentum of each body before collision. b. Calculate the direction and magnitude of the momentum of each body after the collision. c. Calculate the mass of the second body.
11. A satellite of 100-kilogram mass is put into orbit around the Earth at which point it weighs 920 N. The period of the satellite was observed to be 5.3 x 10exp3 seconds. a. Calculate the centripetal force exerted on the satellite by the Earth. b. Calculate the distance of the satellite from the Earth's surface (altitude).
12. a. Calculate the value of g at a point 400,000 meters above the Earth. b. Calculate the orbital speed which must be given to an Earth satellite to maintain it in orbit at this distance.
13. A 60.0-kilogram woman climbs a staircase to a level 11.0 meters above her starting point in 66.0 seconds. a. Calculate the minimum force she must exert to raise herself from step to step. b. Calculate the total amount of work done in climbing to the upper level. c. Calculate the power she generated in climbing to the upper level.
14. Calculate the power of a motor that does 700 joules of work in 35 seconds.
15. Calculate the amount of work done by a 250-watt motor in 20 seconds.
16. A boy applies a steady force of 32 N to a cart and pushes it 12 meters in 16 seconds. Calculate the power he generated.
17. A motor raises a 5000-N elevator 7.5 meters in 15 seconds. a. Calculate the work done by the motor. b. Calculate the power generated by the motor.
18. An airplane weighs 2.0 x 10exp5 N and is designed to gain altitude at the rate of 10 meters per second. Calculate the minimum power of its engines.