How Are Forces Related When Lifting a Heavy Crate?

[Soaring Crane]

A woman is straining to lift a large crate, without success. It is too heavy. We denote the forces on the crate as follows: P is the upward force being exerted on the crate by the person, C is the contact force on the crate by the floor, and W is the crate’s weight. How are the magnitudes of these forces related, while the person is trying unsuccessfully to lift the crate?

a.P = C
b.P + C > W
c.P + C < W
d.P + C = W

Is it that P + C = W if in equilibrium? P + C - W = 0; P + C = W

Thanks.

 

[Chi Meson]

You are correct. It is still equilibrium since the normal contact force will automatically be lessened if another force is applied upward. The moment P is slightly more than W, then C goes to zero, and the crate accelerates slightly to move off the floor.