Answer to Question #84962 in Mechanics | Relativity for Udy

Question

A weightless rod CD, 1.0m long is acted upon by horizontal forces of 2N, 4N, 8N is shown in the figure. What force will be necessary to produce equilibrium?

2N..............................2N.....................8N
100 60. 4N. 0

Answer 1

It's quite difficult to solve the problem without a figure or detailed description.

For example, let us solve a similar problem for the vertical rod with force 2N acting to the right on the top of the rod (100 cm), force 2N acting to the right 60 cm below the top, and with force 8N acting to the left on the bottom of the rod (0 cm).

Q: What force will be necessary to produce equilibrium?

A: Since 2 forces of 2N act to the right and 1 force of 8N act to the left, that force is

$$2\cdot 2-8=-4\text{ N}.$$

Q: Where should it be applied?

A: Apply the principle of moments. Assume that we consider all moments relative to the bottom of the rod:

$$2\cdot 1+2\cdot 0.6-4\cdot y=0,$$ $$y=\frac{1}{4}(2+1.2)=0.8\text{ m}.$$