Question

Two blocks of masses 1 kg and 3 kg are connected by a string passing over a smooth pulley as shown by rest on a horizontal surface area stone be the coefficient of friction between a and b is same as that between b and the horizontal surface the minimum horizontal force f equal to face

Answer 1

The coefficient of friction between a and b is μ=0.625

Explanation:

Correct statement:

Two blocks A (1 kg) and B (2 kg) are connected by a string passing over a smooth pulley as shown in the figure. B rests on rough horizontal surface and A rest on B. The coefficient of friction between A and B is the same as that between B and the horizontal surface. The minimum horizontal force F required to move A to the left is 25 N. The coefficient of friction is:

Solution:

• Let f1 be the magnitude of limiting frictional force between the blocks
• f2 be the magnitude of limiting frictional force between the blocks and horizontal surface.
• The free body diagrams for both the blocks is as shown .
• Applying Newton's second low to both the blocks

F − f1 − T= m Aa -------(1)

F − f1 − f2 = m Ba ------(2)

For F to just pull the blocks, acceleration of blocks a=0.

Therefore from equation (1) and (2)

F = 2f1 + f2

25 = μ(2 × 1 × 10 + 2 × 10)

25 =  μ ( 20 + 20)

μ = 25 / 40

μ = 0.625

Thus the coefficient of friction between a and b is μ=0.625

Also learn more

Two masses a and b of 10 kg and 5 kg respectively are connected with a string passing over friction-less pulley fixed at the corner of a table as shown. the coefficient of static friction of a with table is 0.2. the minimum mass of c that must be placed on a to prevent it from moving is?

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