Question

A boy pushes a mass with a force F. Coefficient of friction between body and floor is μm and between boy shoe and floor is μB. There mass are M(block) and m(boy) respectively. What maximum force boy can apply without slipping

Answer 1

Answer:

good ques ....

let me know if I am correct or not...

Answer 2

Answer:

The maximum force to be applied to move without slipping is $(\mu_B m - \mu_m M)g$

Explanation:

Given a boy pushes a block with a force F.

The mass of the block is M and the mass of the boy is m.

Coefficient of friction between body and floor is $\mu_m$

And the coefficient of friction between boy shoe and floor is $\mu_B$.

The frictional force is given by

$f=\mu mg$

where $\mu$ is the coefficient of friction, m is the mass and g is the acceleration due to gravity.

In order to push without slipping, the force by boy must be greater than the frictional force between the block and floor.

i.e., $f_{boy} > f_{block}\implies\mu_B mg > \mu_m Mg$

Thus, the more force to be applied to move without slipping is

$F=\mu_B mg - \mu_m Mg=(\mu_B m - \mu_m M)g$.

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