13.3.A.1Multiple Choice
Which of the following systems has a well-defined potential energy?
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 five essential knowledge statements of Topic 3.3 — which systems have potential energy, potential energy as a scalar tied to positions, choosing where U = 0, the spring and gravitational forms of U, and adding up the pairs in a larger system. Use g = 10 m/s² and G = 6.67 × 10−11N·m²/kg². Round decimals to the nearest hundredth unless noted otherwise.
Which of the following systems has a well-defined potential energy?
Select A, B, C, or D to check your answer.
A 4 kg block slides 5.0 m down a ramp that drops 2.0 m in height. A constant 6 N kinetic friction force acts between the block and the ramp. (a) Find the change in gravitational potential energy of the block–Earth system. (b) Find the energy dissipated by friction. (c) Can a potential energy be assigned to the friction force? Explain.
Which of the following interactions has an associated potential energy?
Select A, B, C, or D to check your answer.
Two identical 3 kg blocks start on the floor. Block 1 is lifted straight up 2.0 m. Block 2 is pushed up a frictionless ramp to the same 2.0 m height. Take U = 0 at the floor. (a) Find the gravitational potential energy of each block–Earth system at the end. (b) Find the total potential energy of the two systems. (c) Does the potential energy depend on the path or direction of travel?
Which statement about potential energy is correct?
Select A, B, C, or D to check your answer.
An ideal spring has a spring constant of 300 N/m. (a) Find its elastic potential energy when it is stretched 0.20 m. (b) Find its elastic potential energy when it is compressed 0.20 m. (c) Find its elastic potential energy when it is stretched only 0.10 m.
A 2 kg ball is 3 m above the floor. Student A defines U = 0 at the floor. Student B defines U = 0 at a table top that is 1 m above the floor. The ball is then lowered to the table top. Which statement is correct?
Select A, B, C, or D to check your answer.
A 4 kg box sits on a shelf 2.0 m above the floor. A table top is 0.75 m above the floor, and the ceiling is 3.0 m above the floor. Find the gravitational potential energy of the box–Earth system when U = 0 is defined at (a) the floor, (b) the table top, and (c) the ceiling. (d) Find ΔU when the box is lowered from the shelf to the table top.
A student calculates the gravitational potential energy of a box–Earth system and gets −40 J. Is this possible?
Select A, B, C, or D to check your answer.
A 0.4 kg pendulum bob hangs from a 0.8 m string. It is pulled aside until it is 0.25 m above its lowest point. (a) Find Ug at the raised position if U = 0 is at the lowest point. (b) Find Ug at the lowest point and at the raised position if U = 0 is at the pivot (0.8 m above the lowest point). (c) Find ΔU between the two positions for each choice of zero.
An ideal spring stores 2 J of elastic potential energy when it is stretched 0.10 m. How much does it store when it is stretched 0.30 m?
Select A, B, C, or D to check your answer.
An ideal spring has k = 250 N/m. (a) Find the elastic potential energy when it is compressed 0.12 m. (b) How far must it be stretched to store 5.0 J? (c) A second spring is twice as stiff (k = 500 N/m). How much energy does it store when compressed 0.12 m?
For which of the following is the approximation ΔUg = mgΔh appropriate?
Select A, B, C, or D to check your answer.
A 500 kg satellite moves from a distance of 1.0 × 107 m to 2.0 × 107 m from the center of Earth. Use GMEarth = 3.98 × 1014 m³/s². (a) Find Ug at 1.0 × 107 m. (b) Find Ug at 2.0 × 107 m. (c) Find ΔUg. (d) Why are both values negative?
A 50 kg student climbs a flight of stairs that rises 12 m. What is the change in the gravitational potential energy of the student–Earth system?
Select A, B, C, or D to check your answer.
A 1500 kg car drives up a hill. The road is 400 m long and rises 25 m in elevation. (a) Find the change in the car's gravitational potential energy. (b) A different road to the same spot winds back and forth for 800 m. What is ΔUg for that road? (c) The car then drives 10 m downhill. Find ΔUg for that stretch.
Four objects interact gravitationally. How many pairs of objects must be included when the total gravitational potential energy of the system is calculated?
Select A, B, C, or D to check your answer.
Three identical 2.0 kg masses lie along a line at x = 0, x = 1.0 m, and x = 3.0 m. (a) Find the potential energy of each of the three pairs. (b) Find the total gravitational potential energy of the system. (G = 6.67 × 10−11 N·m²/kg²)
A ball rests on a compressed vertical spring. Take the system to be the ball, the spring, and Earth. The ball–Earth gravitational potential energy is 20 J, and the elastic potential energy of the spring is 5 J. What is the total potential energy of the system?
Select A, B, C, or D to check your answer.
A 0.30 kg ball sits on top of a vertical spring (k = 150 N/m) that is compressed 0.10 m. The ball is 0.40 m above the floor, and Ug = 0 at the floor. The system is the ball, the spring, and Earth. (a) Find the gravitational potential energy. (b) Find the elastic potential energy. (c) Find the total potential energy. (d) The spring then returns to its relaxed length, raising the ball by 0.10 m. Find the new total potential energy and the change in potential energy.