Question

The uniform crate has a mass of 150 kg. The coefficient of static friction between the crate and the floor is μs = 0.2. The coefficient of static friction between the man's shoes and the floor is μ′s = 0.4. Assume the man only exerts a horizontal force on the crate. Determine whether the 85-kg man can move the crate.

Answer 1

The man will be able to move the crate.

Step-by-step explanation:

`\mu_s` = Coefficient of static friction between the crate and the floor = 0.2

`\mu'_s` = Coefficient of static friction between the man's shoes and the floor = 0.4

`m_c` = Mass of crate = 150 kg

`m_p` = Mass of man = 85 kg

g = Acceleration due to gravity = 9.81 m/s²

Horizontal force in order to move the crate is given by

`F_h=\mu_sm_cg\\\Rightarrow F_h=0.2* 150* 9.81\\\Rightarrow F_h=294.3\ N`

Maximum force that the man can apply

`F_m=\mu'_sm_pg\\\Rightarrow F_m=0.4* 85* 9.81\\\Rightarrow F_m=333.54\ N`

Here it can be seen that
`F_m>F_h`.

So, the man will be able to move the crate.