A crate (weight 381 N) is lowered vertically a distance of 3.0 m by two ropes at a constant speed of 1.2 m/s. The tension in rope A is TA = 248 N; the rope makes an angle of ƒÆA = 63‹ with the horizontal. Rope B makes an angle of ƒÆB = 55‹ with the horizontal. What is the work that rope A does on the crate?

Question

A crate (weight 381 N) is lowered vertically a distance of 3.0 m by two ropes at a constant speed of 1.2 m/s. The tension in rope A is TA = 248 N; the rope makes an angle of ƒÆA = 63‹ with the horizontal. Rope B makes an angle of ƒÆB = 55‹ with the horizontal. What is the work that rope A does on the crate?

I thought no work was done in a vertical motion because cos90=0. I can determine the x and y components of tensionA but how do I find out its work on the crate?

drwls · Answer

The vertical component of the tension force in rope A, which is 248 sin 63 Newtons, performs equal to
-248 sin 63 N x 3.0 m
The answer is negative because it is being lowered.

You don't need information about rope B to answer the question. You also don't have to use the mass of the crate. They provide more data that you need.

Because the velocity stays the same, you don't have to consider addtional work needed to create kinetic energy.