Force Relationships: P + C = W

[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.

 

[kyle8921]

This equation, P + C = W, represents the concept of equilibrium, where all forces acting on an object are balanced and the object is not accelerating. In this scenario, the woman is trying to lift the crate, but is unable to do so. This means that the upward force she is exerting on the crate (P) is not enough to overcome the weight of the crate (W). The contact force (C) from the floor is also acting on the crate, but it is not enough to counteract the weight either. Therefore, in this situation, the magnitude of the forces are not equal and the equation P + C = W does not hold. In order for the woman to successfully lift the crate, the magnitude of the upward force (P) must be greater than the weight (W) of the crate, and the contact force (C) from the floor must also be enough to support the weight. So, the correct answer is b. P + C > W.