Question
A block of mass 5 kg is placed on an inclined plane making an angle of 37° with the horizontal. The block is given a velocity of 10m/s up the slope. The coefficient of friction between block and the inclined plane is 0.5. Find how far the block goes up the slope. Take g = 10m/s2.
Solution
Given,
Mass of the block, m = 5 kg
Angle of inclination with the horizontal,
= 370
Velocity with which the block is moving, v = 10 m/s
Coefficient of friction = 0.5
See the fig. given above,
Mass of the block, m = 5 kg
Angle of inclination with the horizontal,
= 370Velocity with which the block is moving, v = 10 m/s
Coefficient of friction = 0.5
See the fig. given above,
Component of weight acting parallel and down the inclined plane is,
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Component of weight normal to inclined plane is,
The force of friction between block and the inclined plane is,
Since the body is projected up the inclined plane, therefore the force of friction will act on the block down the inclined plane.
Thus the total force acting on the block down the inclined plane is,
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The retardation of block is,
Now,
and
Therefore, the distance by which the block goes up the inclined plane is,
Component of weight normal to inclined plane is,
The force of friction between block and the inclined plane is,
Since the body is projected up the inclined plane, therefore the force of friction will act on the block down the inclined plane.
Thus the total force acting on the block down the inclined plane is,
The retardation of block is,
Now,
and Therefore, the distance by which the block goes up the inclined plane is,
