You are trying to tip over a uniform rectangular box of mass 100kg, height 1.0m

Question

You are trying to tip over a uniform rectangular box of mass 100kg, height 1.0m and length 2.0m by pulling on a rope that is attached to the box as shown in the figure. The rope makes an angle of 40 degree with the vertical. The floor is rough and the box does not slip on the floor. Find the magnitude of the pulling force needed to just get the box to tip. In that situation, what is the minimum coefficient of static friction that will prevent the box from sliding? A physics professor of mass 58kg and height 1.68m is rappelling down a vertical cliff when she pauses for a moment. Her feet are touching the cliff, and she is leaning back so that her body makes an angle theta = 40degree with the vertical. She is tied into a harness that is connected to a rope that makes an angle of beta= 20 degree with the

Explanation / Answer

a) let F is the required force.

Apply net torque about left bottom = 0

F*1*sin(40) - m*g*(2/1)*sin(90) = 0

F = m*g/sin(40)

= 100*9.8/sin(40)

= 1524 N

b) Normal force, N = m*g + F*cos(theta)

= 100*9.8 + 1524*cos(40)

= 2147 N

let mue_s is coefficient friction for not to slip.

Apply, Fnetx = 0

N*mue_s - F*sin(40) = 0

mue_s = F*sin(40)/N

= 1524*sin(40)/2147

= 0.456

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