# Static Equilibrium and tension of a beam

1. Oct 29, 2009

### G-reg

1. The problem statement, all variables and given/known data
In the figure below, a uniform beam of weight 520 N and length 3.4 m is suspended horizontally. On the left it is hinged to a wall; on the right is it supported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N.

What value of D corresponds to that tension?

2. Relevant equations
$$\Sigma\tau$$ = 3.4m(520N) + ???

3. The attempt at a solution
I'm not really sure what to put in after what I have put in already.
I know it's conservation of torque but that's about it..

2. Oct 29, 2009

### kuruman

At what point on the beam does gravity act? Draw a free body diagram and put in all the forces. Then say that the sum of all the torques is zero.

3. Nov 3, 2009

### G-reg

I know that gravity acts on the beam at 1.7m but I'm not seeing how I'm supposed to set the sum of the torques equal to zero..but that's probably because I'm not sure what forces are acting upon the beam besides gravity and the tension from the cable.

4. Nov 4, 2009

### kuruman

There is a force at the hinge that has horizontal and vertical components Fx and Fy. If you calculate torques about the hinge, they do not contribute to the net torque. However gravity and the tension must exert equal and opposite torques about the hinge if this beam is to be in equilibrium.