Question

a man is pushing a box on a level surface. he is walking at constant speed and pushing with constant force. the surface is very slippery so the box slides easily, and he is wearing special shoes so he won’t slip and fall. could the box move faster than the man is walking? a yes, but only if he didn’t walk fast. b yes, but only if he pushed the box harder and harder. c yes, but only if the force of the push on the box was greater than the force of friction on the box. d no, because if he was pushing with constant force, the box would have to move at constant speed.

Explanation:

To determine if the box can move faster than the man, we analyze the forces and motion:

1. The man walks at constant speed, pushing the box with constant force. The surface is slippery (low friction).
2. For the box to accelerate (move faster than the man’s constant speed), the net force on it must be non - zero. By Newton’s second law ($F_{net}=ma$), if the pushing force ($F_{push}$) exceeds the friction force ($F_{friction}$), the box will accelerate ($a=\frac{F_{push}-F_{friction}}{m}$) and can move faster than the man (who has constant speed, so his acceleration is zero).
3. Option A is incorrect because the man’s walking speed doesn’t directly limit the box’s speed if net force exists. Option B is incorrect—“pushing harder and harder” implies changing force, but the problem states “constant force.” Option D is incorrect because if $F_{push}>F_{friction}$, the box accelerates (doesn’t move at constant speed). Only Option C correctly links the box’s acceleration to the push force exceeding friction.

Answer:

C. Yes, but only if the force of the push on the box was greater than the force of friction on the box.