Question
A block slides down a rough inclined plane (making an angle 45° with the horizontal) in the time twice the time it takes in a smooth inclined plane of same inclination. Find the coefficient of friction of rough inclined plane.
Solution
Acceleration of block on smooth inclined plane is,
The acceleration of block on rough inclined plane is,
where,
p is the coefficient of friction of rough inclined plane.
Let, t1 and t2 be the time taken by the block to slide down the smooth inclined plane and rough inclined plane respectively.
If s is the distance moved by the block on the inclined plane then,
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, is the coefficient of friction of rough inclined plane.
The acceleration of block on rough inclined plane is,
where,
p is the coefficient of friction of rough inclined plane.
Let, t1 and t2 be the time taken by the block to slide down the smooth inclined plane and rough inclined plane respectively.
If s is the distance moved by the block on the inclined plane then,
Here
∴
, is the coefficient of friction of rough inclined plane.
