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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Laws of Motion

JIPMER 2017 · Physics · Laws of Motion

A skier starts from rest at point A and slides down the hill...

A skier starts from rest at point AA and slides down the hill without turning or breaking. The friction coefficient is μ\mu. When he stops at point BB, his horizontal displacement is SS. What is the height difference between points AA and B?B ? (The velocity of the skier is small so that the additional pressure on the snow due to the curvature can be neglected. Neglect also the friction of air and the dependence of μ\mu on the velocity of the skier.)A skier starts from rest at point A and slides down the hill without turning or breaking. The friction coefficient is μ

Options

  1. Ah=μSh=\mu S
  2. Bh=μSh=\frac{\mu}{S}
  3. Ch=2μSh=2 \mu S
  4. Dh=μS2h=\mu S^2

Correct answer

A. h=μSh=\mu S

Step-by-step solution

According to question, the situation is shown in the figure A skier starts from rest at point A and slides down the hill without turning or breaking. The friction coefficient is μ For a sufficiently safe-horizontal displacement ΔS\Delta S can be considered straight. If the corresponding length of path element is ΔL\Delta L, the friction force is given by μmgΔSΔL\mu_{m g} \frac{\Delta S}{\Delta L} and the work done by the friction force equals force times displacement μmgΔSΔLΔL=μmgΔS\mu_{m g} \frac{\Delta S}{\Delta L} \Delta L=\mu_{m g} \Delta S Adding up, we find that along the whole path the total work done by the friction force is μmgs\mu_{m g} s. By energy conservation this must equals the decrease mgh in potential energy of skier. Hence, h=μSh=\mu S
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