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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.

For a, this is what I did:

Fapp = Fs + Fg sin theta

= Usmgcos theta + mg sin theta

= mg (Uscos theta + sin theta)

= (22kg) (9.8m/s^2)(0.78 cos 45 degrees + sin 45 degrees)

= 270N

The largest force that can be applied upward if the box is to stay at rest is 270N.

For b..i'm not totally sure but this is what I got:

Fs = Fg sin theta

= mg sin 45 degrees

= (22) (9.8) (0.707)

= 152N

Fn = Fs * Us

= 152 * 0.78

= 118N

Fapp = Fn - Fg cos theta

= 118 - mg cos 45 degrees

= 118 - (22) (9.8) (0.707)

= 118 - 152

= -34N

Could that be right?