13.4.A.1–2Multiple Choice
A ball is in freefall near Earth's surface. Which choice of system has both kinetic energy and potential energy, rather than kinetic energy alone?
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 threads of Topic 3.4 — what energies a chosen system can have, how mechanical energy balances internally versus transfers externally, choosing a system so that energy is constant, the two conditions for conservation of mechanical energy, and what happens energetically when those conditions fail. Use g = 10 m/s² unless a problem gives you other values to use. Round decimals to the nearest hundredth unless noted otherwise.
A ball is in freefall near Earth's surface. Which choice of system has both kinetic energy and potential energy, rather than kinetic energy alone?
Select A, B, C, or D to check your answer.
A 3 kg ball moves at 8 m/s, 5 m above the ground. (a) Find the ball's kinetic energy. (b) If the system is defined as “ball and Earth,” find the gravitational potential energy (taking the ground as U = 0). (c) Explain why defining the system as “ball alone” would mean this potential energy term doesn't exist for that system.
Two carts on a frictionless track collide and permanently latch together, like Velcro (a perfectly inelastic collision). Which best describes what happens to the kinetic energy lost in the collision?
Select A, B, C, or D to check your answer.
A spring is compressed and held in place (a reversible deformation), while separately, a lump of clay is squashed flat between two plates (an irreversible deformation). (a) Which of these two, upon release, can return its stored energy as kinetic energy? (b) For the clay, where does the work done to squash it actually go? (c) Explain the energetic difference between the two cases in terms of potential energy.
A system is defined as “pendulum bob and Earth.” As the bob swings from its highest point to its lowest point (no air resistance), which statement correctly describes K and U?
Select A, B, C, or D to check your answer.
A pendulum bob and Earth have total mechanical energy Emech = 8 J. At the highest point of the swing, K = 0. (a) Find U at the highest point. (b) At the lowest point, U = 0. Find K at the lowest point. (c) Explain, in terms of internal vs. external forces, why Emech stays the same between those two points.
The system is defined as “block alone” (Earth is not included). An external agent does 24 J of work pushing the block across a frictionless floor, starting from rest. Which statement correctly describes the energy change?
Select A, B, C, or D to check your answer.
A 2 kg block, initially at rest, is pushed by an external horizontal force doing 40 J of work on a frictionless floor. The system is defined as “block alone.” (a) Find the block's final kinetic energy. (b) Find its final speed. (c) If instead the system were defined as “block and Earth,” would U change during this horizontal push? Explain.
A box is pushed up a frictionless ramp by an external force doing +150 J of work. The system is defined as “box and Earth,” which has ΔU = +100 J for this motion. What is ΔK for this system?
Select A, B, C, or D to check your answer.
A pendulum (bob + Earth system), released from rest, has total Emech = 10 J throughout its swing. (a) If instead we define the system as “bob alone” (excluding Earth), explain why K alone is not constant as the bob swings. (b) For the bob-alone system, is gravity internal or external? (c) Explain how your answer to (b) connects to your answer in (a).
Which choice of system is most useful for showing that mechanical energy is constant for a ball thrown straight up and caught at the same height, under gravity alone (no air resistance)?
Select A, B, C, or D to check your answer.
An external agent does 90 J of work on a box–Earth system (frictionless ramp) as the box rises, with ΔU = +130 J for that rise. The box's final kinetic energy is 25 J. (a) Use ΔEmech = Wext to find ΔK. (b) Find the box's initial kinetic energy. (c) Explain in words what the 90 J of external work physically represents.
Which pair of conditions must both hold for a system's mechanical energy to be conserved?
Select A, B, C, or D to check your answer.
A 4 kg block slides down a frictionless ramp (system = block + Earth), starting from rest at height h = 3 m. (a) Find Emech initially, taking U = 0 at the bottom. (b) Use conservation of Emech to find the block's speed at the bottom. (c) State the two conditions that justify using conservation of energy here.
A box slides across a rough horizontal floor, decelerating, with the system defined as “box and Earth.” Why does mechanical energy conservation fail here?
Select A, B, C, or D to check your answer.
Consider three scenarios, each analyzed with the system “object and Earth”: (i) a ball in free fall with no air resistance, (ii) a box sliding across a rough floor, (iii) a rocket accelerating upward under its engine's thrust. For each, state whether Emech is conserved, and justify briefly using the two conditions for conservation.
A crane's motor does 6000 J of work lifting a load (system = load and Earth), with no friction anywhere in the lift. Which equation correctly relates this to the change in mechanical energy?
Select A, B, C, or D to check your answer.
A crane motor does 8800 J of work lifting a 400 kg load from rest to rest (system = load and Earth, no friction anywhere). (a) Since the load starts and ends at rest, what is ΔK? (b) Use ΔEmech = Wext to find ΔU. (c) Find the height the load was raised.
A sled is pulled across a rough horizontal surface by a person's rope, while friction also acts between the sled and the ground. For the system “sled and Earth,” which best describes how the sled's mechanical energy changes?
Select A, B, C, or D to check your answer.
A 1500 kg car moving at 20 m/s brakes to a stop on a level road (system = car and Earth; friction from the brakes and tires is internal to this system). (a) Find the car's initial kinetic energy. (b) Since the car ends at rest and at the same height, find ΔEmech. (c) Explain what happened to that energy, referencing the system boundary.