Turning effects of forces

1. Jul 3, 2009

Miri

1. The problem statement, all variables and given/known data
A uniform, horizontal 300N beam, 5.00m long, is attached to a wall by a hinge. Its far end is supported by a cable that makes an angle of 53.0° with the horizontal. A 600N person stands 1.50m from the wall. Find the tension in the cable (force).

2. Relevant equations
What do I have to do? I calculated the moment/torque of 600N*1.50m and than add it to 300N*3.5m. This gives me 1950Nm. But I don't know how to get the right result (413N).

2. Jul 3, 2009

Staff: Mentor

Since the beam is in equilibrium, set the net torque equal to zero.
That's the torque due to the person.
That's supposed to be the torque due to the weight of the beam--but why 3.5m?
Call the cable tension T. What torque does it produce?

3. Jul 3, 2009

Miri

ok, so this gives me the equation: 600N*1.50m+300N*5.0m=2400Nm but what do I have to do with the angle of 53.0°? And I can't just say 2400Nm=0, can I? I mean because you said that I have to set the net torque equal to zero, so I suppose that 2400Nm isn't the net torque...

4. Jul 3, 2009

Staff: Mentor

Here you just added two of the three torques, but ignored the torque due to the cable tension. Also, where did you get the 5.0m? (Hint: Where does the weight of the beam act?)
You need that angle to compute the torque due to the cable tension.
That wouldn't make sense, would it?
Right. You forgot about the cable tension.

5. Jul 3, 2009

RoyalCat

Be consistent about the point about which you're calculating your torques. What's the torque of the weight of the beam, relative to its center of mass, which is the point I'm assuming you're calculating with respect to?

6. Jul 3, 2009

Staff: Mentor

I presume that Miri is attempting to calculate torques with respect to the hinge. (But, as you say, all that matters is to be consistent.)

7. Jul 3, 2009

Miri

Is it 300N*2.5m because the force acts in the middle of the beam downwards? So we get 600N*1.50m+300N*2.5m+T=0 so for T we get -1650. Isn't there a mistake? :D And how do I have to use the angle??

8. Jul 3, 2009

Staff: Mentor

Good.
Assuming you are using T to stand for the cable tension, you need the torque not just T. Note that the torque from the cable tension goes in the opposite direction of the torques from the weight of person and beam, which means it has an opposite sign.
You'll need it to calculate the torque. Review such calculations here: http://hyperphysics.phy-astr.gsu.edu/hbase/torq2.html#tc"

Last edited by a moderator: Apr 24, 2017
9. Jul 4, 2009

Miri

So for T I take 300N*5.00m*sin(53.0°)=1197,95Nm. And as you said, it is +1650Nm when you solve it for T. But now I have two results and the last one is wrong, because I didn't use the formula like in the first one. Can you tell me what to do?

10. Jul 4, 2009

Staff: Mentor

No, the tension force is T, not 300N. You are trying to solve for T.

11. Jul 4, 2009

Miri

So what do I have to do instead of solving for T?

12. Jul 4, 2009

Staff: Mentor

What you do mean "instead"? Of course you must solve for T. The only question is how.

Add up the torques for all three forces. Two of them will be clockwise (say), while the other will be counterclockwise. The torque due to the tension will be in terms of the unknown tension, T.

Set the net torque = 0. Solve for T.