Question

M1 has a mass of 6.090 kg. It is on a horizontal surface, connected by a massless string to a hook where mass M2 can be increased smoothly. The pulley has a negligible mass and no friction. When M2 = 3.325 kg it begins to accelerate downwards at a rate of 2.100 m/s2. Calculate μs - μk between M1 and the surface.

Answer 1

Calculation for mu_s

Tension in the string will be equal to weight of M2.

T = M2 * g

T = 3.325 * 9.8

T = 32.585 N

now as the block M1 is not moving till T = 32.585 so

friction force will be equal to T.

mu_s * M1 * g = T

mu_s = 32.585 / ( 6.09 * 9.8 )

mu_s = 0.546

Calculation for mu_k

now the block is moving with acceleration 2.1 m/s2

so equation of motion will become

T - Fk = M1 * a where Fk is the friction force .

Fk = T - M1 * a

Fk = 32.585 - ( 6.09 * 2.1 )

Fk = 19.796

mu_k * M1 *g = Fk

mu_k = 19.796 / ( 6.09 * 9.8 )

mu_k = 0.332