13.4.A.1Multiple Choice
A system consists of a single object. Which forms of energy can that system have?
Select A, B, C, or D to check your answer.
Directions:Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions mix the main ideas of Topic 3.4 — which energies a system has, mechanical energy, balancing energy changes inside a system, energy transferred by work, and what happens when friction dissipates energy. Always decide what your system is first. Use g = 10 m/s². Round decimals to the nearest hundredth unless noted otherwise.
A system consists of a single object. Which forms of energy can that system have?
Select A, B, C, or D to check your answer.
A 4 kg ball is 2.5 m above the ground and moving at 3 m/s. Take U = 0 at the ground. (a) Find the energy of the system if the ball alone is the system. (b) Find the kinetic energy, the potential energy, and the mechanical energy if the system is the ball and Earth. (c) Why does the ball-alone system have no potential energy?
Which of the following systems may have both kinetic energy and potential energy?
Select A, B, C, or D to check your answer.
A 0.5 kg block is attached to an ideal spring (k = 50 N/m) on a frictionless table. The spring is stretched 0.40 m and the block is released from rest. (a) Find the energy stored in the system at release. (b) Find the block's kinetic energy as it passes the relaxed position. (c) Find its speed there.
What is the mechanical energy of a system?
Select A, B, C, or D to check your answer.
A 3 kg cart is 2.0 m above the ground and moving at 4 m/s. A platform is 0.5 m above the ground. (a) Find the mechanical energy of the cart–Earth system if U = 0 is at the ground. (b) Find it if U = 0 is at the platform. (c) Is one of these answers wrong?
A 2 kg ball is 4.0 m above the ground and moving at 3.0 m/s. Take U = 0 at the ground. What is the mechanical energy of the ball–Earth system?
Select A, B, C, or D to check your answer.
A 0.4 kg block on a frictionless table is attached to an ideal spring (k = 100 N/m). At one instant the spring is stretched 0.20 m and the block is moving at 1.5 m/s. (a) Find the mechanical energy of the system. (b) Find the block's speed when the spring is relaxed. (c) Find the greatest stretch of the spring.
A ball falls toward the ground with negligible air resistance. The system is the ball and Earth. As the ball falls, the gravitational potential energy of the system decreases by 40 J. Which statement is correct?
Select A, B, C, or D to check your answer.
A 3 kg block starts from rest at the top of a frictionless curved track and slides down a vertical drop of 1.8 m. (a) Find ΔUg of the block–Earth system. (b) Find the block's kinetic energy at the bottom. (c) Find its speed at the bottom. (d) What would the speed be for a 6 kg block?
A compressed ideal spring launches a block across a frictionless table. For which choice of system is the total mechanical energy constant during the launch?
Select A, B, C, or D to check your answer.
A 0.25 kg cart on a frictionless track is pushed against an ideal spring (k = 100 N/m), compressing it 0.20 m, then released from rest. (a) With the cart and spring as the system, find the total energy. (b) Find the cart's speed when the spring is relaxed. (c) With the cart alone as the system, how much work does the spring do on it?
The total energy of a system increases by 100 J. Which of the following must be true?
Select A, B, C, or D to check your answer.
A person lifts an 8 kg box 1.5 m straight up at constant speed. The box and Earth are the system. (a) Find the work done on the system by the person. (b) Find the change in the system's mechanical energy. (c) Find ΔK and ΔUg.
A car skids to a stop on a level road. Its kinetic energy decreases to zero. Which statement is consistent with the conservation of energy?
Select A, B, C, or D to check your answer.
A 500 kg roller coaster car starts from rest at the top of a 20 m hill. Ignore friction and air resistance. Take U = 0 at the bottom. (a) Find the car's speed at the bottom. (b) Find its speed when it is 15 m above the bottom on the way down. (c) Does either answer depend on the car's mass?
A 1 kg ball is dropped from rest from a height of 20 m. Ignore air resistance. What is the ball's speed just before it hits the ground?
Select A, B, C, or D to check your answer.
A 4 kg block slides from rest down a rough ramp that is 5.0 m long and drops 2.5 m in height. It reaches the bottom moving at 4 m/s. Take U = 0 at the bottom. (a) Find the initial mechanical energy. (b) Find the final mechanical energy. (c) How much mechanical energy was dissipated, and where did it go? (d) Find the average friction force on the block.
A student pushes a crate across a frictionless floor. The crate is the system, and the student does +50 J of work on it. Which statement is correct?
Select A, B, C, or D to check your answer.
A 900 kg car moving at 10 m/s brakes to a stop on level ground. The car is the system. (a) Find the car's initial kinetic energy. (b) Find the work done on the car by the road. (c) If the braking force is a constant 5000 N, how far does the car travel?