Figure caption: A diagram of a light cart and a heavy cart, both with a horizontal rightward force F applied to each.

A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest.

After the force is removed, how do the carts’ kinetic energy compare?

Question

Figure caption: A diagram of a light cart and a heavy cart, both with a horizontal rightward force F applied to each.

A light plastic cart and a heavy steel cart are both pushed with the same force for a distance of 1.0 m, starting from rest.

After the force is removed, how do the carts’ kinetic energy compare?

BlackTom AI · Accepted Answer

Work done by the force on each cart is W = F · d, so with the same constant horizontal force F applied through the same displacement d = 1.0 m each cart receives the same amount of work.

1) Relevant concepts
- Work (constant force): W = Fd (force times displacement in the direction of the force).
- Work–energy theorem: net work done on an object equals its change in kinetic energy, ΔKE = W.
- Mass affects acceleration and final speed but not the work done by a given force through a given displacement.

2) Step-by-step reasoning
- Both carts start from rest, so initial kinetic energy KE_i = 0 for each.
- The force does work W = F · d on each cart. Here d = 1.0 m, so W = F(1.0 m).
- By the work–energy theorem, ΔKE = W. Thus KE_final = KE_i + W = 0 + F(1.0 m) = F(1.0 m).
- This result is the same algebraic value for both carts because F and d are equal for both.

3) Intermediate calculation steps
- W_plastic = F × 1.0 = F J
- W_metal   = F × 1.0 = F J
- KE_final,plastic = 0 + F = F J
- KE_final,metal   = 0 + F = F J

4) Why the correct answer is correct
Because both carts receive identical work from the force over the same displacement, their increases in kinetic energy are identical regardless of their masses. Mass only changes the final speed: using 1/2 m v^2 = Fd gives v = sqrt(2Fd/m), so the lighter cart will have a larger speed but the same kinetic energy.

5) Why the other choices are incorrect
- "Plastic less than metal" / "Plastic greater than metal": incorrect because these compare KE as if mass determines KE for the same push-distance; here KE is fixed by work done and is independent of mass.
- "Can't say. It depends on how big the force is.": incorrect because whatever the value of F, both carts experience the same F and same d, so both get the same KE = Fd.

Conclusion: Both carts end up with the same kinetic energy. This matches the provided correct answer: "The KE of the plastic cart is equal to that of the metal cart."

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