Question

A box with a mass of 22kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficient of friction between the box and the ramp are mu static = 0.78 mu kinetic = 0.65.

a) Determine the magnitude of the largest force that can be applied upward, parallel to the ramp, if the box is to remain at rest.

b) Determine the magnitude of the smallest force that can be applied onto the top of the box, perpendicular to the ramp, if the box is to remain at rest.

My work:
a. M*g = 22*9.8 = 215.6 N. = Wt. of box.
F = 215.6*sin45 = 152.5 N.

b. F = 215.6*cos45 = 152.45

is my work correct?

Answer 1

..... but where is your friction force?
It is to remain at rest both times, so use static coef = mu = 0.78
max friction force = mu m g cos 45 = mu *152.5 = 119
(because cos 45 = sin 45 = 0.707)
1. Push up
F = 152.5 + 119
2. push down adding to weight
152.5 = mu (m g).707 + .78 F = 119 + (.78) F

Answer 2

I agree.