A student is trying to push a desk of mass m = 65kg and horizontal width w = 0.8

Question

A student is trying to push a desk of mass m = 65kg and horizontal width w = 0.8m along the floor. The coefficient of friction between the desk and the floor is s = 0.69. The center of mass of the desk is at the geometric center of the rectangle shown. What is the minimum force necessary to move the desk? If the force that is applied is just barely less than the answer to the previous problem, what is the maximum height h so that the desk won't tip over?

Please give numerical answers so I may compare accordingly. Thank you in advance.

Explanation / Answer

A) minimum force requiredd is frictional force

so here

Fmin= u *m*g

Fmin = 0.69*65*9.81

Fmin = 440 N
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B) for desk tp not to tip over

Troque due to applied force = Torque due to weight

Fa*h = m*g*w/2

u*m*g*h = m*g*w/2

h = w/(2u)

h = 0.8/(2*0.69)

h = 0.58 m

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