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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.

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Answer:

The man will be able to move the crate.

Explanation:

[tex]\mu_s[/tex] = Coefficient of static friction between the crate and the floor = 0.2

[tex]\mu'_s[/tex] = Coefficient of static friction between the man's shoes and the floor = 0.4

[tex]m_c[/tex] = Mass of crate = 150 kg

[tex]m_p[/tex] = 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

[tex]F_h=\mu_sm_cg\\\Rightarrow F_h=0.2\times 150\times 9.81\\\Rightarrow F_h=294.3\ N[/tex]

Maximum force that the man can apply

[tex]F_m=\mu'_sm_pg\\\Rightarrow F_m=0.4\times 85\times 9.81\\\Rightarrow F_m=333.54\ N[/tex]

Here it can be seen that [tex]F_m>F_h[/tex].

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

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