Page 67 - Physics - XI

In actual practice, however, some friction is always present. By its nature, force of friction f will act
downwards when roller moves upwards and f will act upwards when roller moves downwards. Let the total
weight W = M g move the roller upwards, we have
1 1
mg sin θ + f = W = M g …(i)
1 1
Similarly, if total weight W = M g makes the roller move downwards, we have
2
2
mg sin θ – f = W = M g
2 2
Adding both the equations, we get
2 mg sin θ = W + W = (M + M )g
1 2 1 2
W W ( M M g)
mg sin θ = 1 2 1 2
2 2
which gives the corrected value of downward force acting on the roller kept on an inclined plane.

Let W = W W 2 ( M M g)
2
1
1
2 2
then, we have W = mg sin θ
For same roller, m = constant, hence for the motion of a roller along an inclined plane

W = mg sin θ, i.e. W ∝ sin θ

If we plot a graph between W and sin θ, the graph must be a straight line.

Procedure
1. Check the pulley of the inclined plane and see whether it is free from friction. Grease or oil it, if
necessary.
Pulley

Roller
Inclined Plane
Weight Pan
Protractor

θ

Fig. 10.2: Experimental Set-up
2. Make the base of the inclined plane horizontal with the help of a spirit level.
3. Find the least count of the spring balance. Find the zero error if any of the spring balance.
4. Find the weight of the roller and pan with the help of a spring balance after applying the appropriate

zero correction.
5. Tie one end of the thread to the roller placed on the inclined plane and pass it over the pulley and tie
the other end of the thread to the pan. See that the pan is hanging freely and it is not touching either the
base of the plane or the table.
6. Fix the inclined plane at an angle of 30° after raising it. The roller may start rolling down with some

acceleration.
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