A block starts slipping on an inclined plane. It moves one metre in one second. What is the time taken ….

Illustration : A block starts slipping on an inclined plane. It moves one metre in one second. What is the time taken by block to cover next one metre ?

Solution :

The forces acting on the block at any moment are

(i) mg (ii) N, normal reaction

(iii) f , friction force

Let a = acceleration of the block (down the plane)

Applying $latex \displaystyle S = u t + \frac{1}{2}a t^2$

For path AB ,

1 = 0 + (1/2)a × 12

⇒ 1 = a/2 . . . (i)

for path AC ,

2 = 0 + (1/2)a t2

⇒ 2 = a t2/2 . . . .(ii)

From (i) & (ii), t2 = 2

⇒ t = √2 sec.

Time taken to cover the distance BC = (t – 1) sec = 0.41 sec

Exercise : A block of mass m = 2 kg is kept on a rough horizontal surface. A horizontal force F = 4.9 N is just able to slide the block. Find the coefficient of static friction. If F = 4 N, then what is the frictional force acting on the block ?

Illustration : Two blocks A & B are connected by a light inextensible string passing over a fixed smooth pulley as shown in the figure. The coefficient of friction between the block A & B the horizontal table is μ = 0.2; If the block A is just to slip, find the ratio of the masses of the blocks.

Solution : From F.B.D. of A, shown in fig

N + T Sin θ = mAg ……….(i)

T Cos θ = fmax = μ N. ………(ii)

From (i), N = mAg – T Sin θ ………(iii)

From (ii) and (iii), F.B.D. of A.

T Cos θ = μ mAg – μ T Sin θ

T (Cos θ + μ Sin θ) = μ mAg …………(iv)

From F.B.D. of B,

T = mBg ………(v)

Taking ratio of (iv) and (v)

Exercise : The block A is kept over a plank B. The maximum horizontal acceleration of the system in order to prevent slipping of A over B is a = 2m /sec2. Find the coefficient of friction between A & B.

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