Students use compensation arguments to incorrectly solve conceptual problems.

Two blocks, one with twice the mass of the other, start from rest. They experience the same constant force for 1 s. Compare their kinetic energies after the force has been applied.

Since the two blocks experience the same force, the less massive block will accelerate at a greater rate. It will therefore cover more distance in the one second. Thus more work will have been done on the less massive block (same force, longer distance). By the work-energy theorem (work done is equal to the change in kinetic energy), the less massive block will have a greater kinetic energy. This can also be solved by realizing that the two blocks experienced the same impulse (same force, same time), so they must have the same final momenta (via the impulse-momentum theorem). However, kinetic energy is 1/2 mv ² = p ²/2m, so the less massive block must have a greater kinetic energy.

Two blocks, one with twice the mass of the other, start from rest. They experience the same constant force for 1 m. Compare their momenta after the force has been applied.

Since the two blocks experience the same force, the less massive block will accelerate at a greater rate. It will therefore take less time to cover the one meter. Thus the less massive block recieves a smaller impulse (same force, less time). The final momenta of the blocks are equal to the impulses they received (they started from rest), so the less massive block has a smaller momentum. This can also be solved by realizing that the two blocks had the same amount of work done on them (same force, same distance). So they must have the same final kinetic energies (via the work-energy theorem). However, kinetic energy is 1/2 mv ² = p ²/2m, so for the two blocks to have equal kinetic energies the less massive block must have a smaller momentum.