An ideal sliding block and a rough horizontal surface
A classroom model represents a small block as a particle that slides without rolling. It starts from rest at a height of0.80metres above a horizontal surface. The ramp is frictionless, air resistance is ignored and the gravitational field strength is taken as10newtons per kilogram. The block has mass0.50kilograms. At the bottom it enters a rough horizontal strip on which a constant opposing force of2.0newtons acts until it stops. There is no additional energy source. A student proposes adding a rotational-energy term even though the problem specifies sliding without rolling. Another student substitutes the height in centimetres while leaving the remaining quantities in SI units. Evaluate this idealized exercise under the stated assumptions rather than making predictions for an actual rolling object.
1. Calculate the kinetic energy and speed at the bottom.
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The lost potential energy is mgh=0.50×10×0.80=4.0J. With no ramp loss, mv²/2=4.0, giving v²=16 and v=4.0m/s. No rolling-energy term belongs in the specified particle model.
2. Find the stopping distance on the rough strip.
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The opposing force does work of magnitude Fd. Setting2.0d=4.0 gives d=2.0m. The force removes the kinetic energy, so the block stops rather than accelerating in the original direction.
3. If mass doubles and the strip force also doubles, what happens to stopping distance?
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The bottom kinetic energy doubles to8.0J and the force doubles to4.0N. Thus d=8.0/4.0=2.0m, unchanged under these specified assumptions.