wiz-icon
MyQuestionIcon
MyQuestionIcon
7
You visited us 7 times! Enjoying our articles? Unlock Full Access!
Question

A skier starts from rest at point A and slides down the hill without turning or breaking. The friction coefficient is μ. When he stops at point B, his horizontal displacement is S. What is the height difference between points A and 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 on the velocity of the skier.)

A
h=μS
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
h=μS
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
h=2μS
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
h=μS2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B h=μS
According to question, the situation is shown in the figure.
For a sufficiently safe-horizontal displacement ΔS can be considered straight. If the corresponding length of path element is ΔL, the friction force is given by μmgΔSΔL and the work done by the friction force equals force times displacement.
μmgΔSΔLΔL=μmgΔS
Adding up, we find that along the whole path the total work done by the friction force is μmgS. By energy conservation this must equals the decrease mgh is potential energy of skier.
Hence, h=μS.
767631_741790_ans_97182971c4754c34bd4de236bf3bfb65.png

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Conservative Forces and Potential Energy
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon