# Balancing Beam

## Homework Statement

In the picture, m1 is 20kg, and the wedge pushes up with a force of 300 N. If the length L1 is 2 meters, solve for m2 and L2.

I'm not sure

## The Attempt at a Solution

The picture shows some sort of beam balancing on a fulcrum that is not centered. On the left side is a mass m1 hanging from the beam. The distance between the fulcrum and the mass is L1. Then on the other side of the fulcrum, the longer side of the beam remaining is L2, and on the other end is m2. The beam is perfectly balanced. I apologize for my lack of skill in physics, but this time, I really have no idea where to begin. I looked up some things about balance beams, but struggled to find anything that indicated how to find the length of the beam. Thanks in advance!

Andrew Mason
Homework Helper

## Homework Statement

In the picture, m1 is 20kg, and the wedge pushes up with a force of 300 N. If the length L1 is 2 meters, solve for m2 and L2.

I'm not sure

## The Attempt at a Solution

The picture shows some sort of beam balancing on a fulcrum that is not centered. On the left side is a mass m1 hanging from the beam. The distance between the fulcrum and the mass is L1. Then on the other side of the fulcrum, the longer side of the beam remaining is L2, and on the other end is m2. The beam is perfectly balanced. I apologize for my lack of skill in physics, but this time, I really have no idea where to begin. I looked up some things about balance beams, but struggled to find anything that indicated how to find the length of the beam. Thanks in advance!
What does the 300N upward force tell you about the total weight of the masses and beam? Is the beam mass given?

AM

What does the 300N upward force tell you about the total weight of the masses and beam? Is the beam mass given?

AM
I think that we're supposed to assume that the beam's mass is not enough to actually affect what's going on. I honestly don't know what the wedge pushing up with 300 N means. I figured that we'd have to have a value of force given with the masses hanging on the beam. I've never seen the wedge having an upward force like this in a problem.

Andrew Mason
Homework Helper
If the beam mass is negligible and the forces on the beam are balanced (the upward force by the wedge and the downward gravitational forces sum to 0) what does that tell you about m2?

AM

If the beam mass is negligible and the forces on the beam are balanced (the upward force by the wedge and the downward gravitational forces sum to 0) what does that tell you about m2?

AM
I know that it has to be lighter than M1 or else it would end up pulling the beam down...

Andrew Mason
Homework Helper
Why is the weight of m2 less than m1? All you are saying is that the torque due m2 has to be the same as that produced by m1.

AM

Why is the weight of m2 less than m1?

AM
Because since the length of the beam is longer on the side of m2, it cannot be heavier. Otherwise, the beam would pull down. If the fulcrum was centered over the beam, they'd be even then...

Andrew Mason
Homework Helper
There are two things you have to work out. First is total mass. Second is the torque. How are you determining each?

AM

There are two things you have to work out. First is total mass. Second is the torque. How are you determining each?

AM
That's the problem, I don't know how to do either. I know that the angle is 0 degrees, so that makes finding torque a little bit easier, maybe... sin(0) is 0, which would mean that the torque wouldn't exist, unless I'm missing something there. Other than that, I know that the distance from the fulcrum to m1 is 2m. I could plug that in for the radius and the 300 N for the force, but would that be right?

Andrew Mason
Homework Helper
To find the mass of m2 do a free-body diagram. What is the upward force?(hint:there is only one point where an upward force can be applied). Is the beam accelerating? So what is the total downward force? (Hint: what do all the forces sum to?). How much downward force is provided by m1? So how much is provided by m2?

Once you find m2, we can then look at torque about the pivot point. What do the torques sum to? (Hint: if there is a net torque what would happen to the beam?)

AM

To find the mass of m2 do a free-body diagram. What is the upward force?(hint:there is only one point where an upward force can be applied). Is the beam accelerating? So what is the total downward force? (Hint: what do all the forces sum to?). How much downward force is provided by m1? So how much is provided by m2?

Once you find m2, we can then look at torque about the pivot point. What do the torques sum to? (Hint: if there is a net torque what would happen to the beam?)

AM
Oh, I see what you're saying. The upward force is 300N, coming from the fulcrum. The downward force also has to be 300N, coming from the weights of both m1 and m2. Since m1 is 20kg, I would multiply gravity (our professor has us use 10) by 20. That would give me a force of 200N. Which means that the other mass needs a force of 100N, which means it must be 10kg. Is that correct so far? Then I could move on to finding the other length of the beam, which I'm still not sure how to do, but I'll feel more confident attempting it if I know I at least got the mass right.

Andrew Mason
Homework Helper
Good! Now you have to determine tbe torque (about the fulcrum) from each mass. Can you express the torque from each mass (hint: what is the net torque on the beam if it is balanced?).

AM

Good! Now you have to determine tbe torque (about the fulcrum) from each mass. Can you express the torque from each mass (hint: what is the net torque on the beam if it is balanced?).

AM
OHHHH! The angle at which they're acting to the beam is 90 degrees. Sin of 90 degrees is 1, which means I simply need to set them equal to something since the beam isn't moving. Isn't the net torque if the beam is balanced 0? If that was the case, I would get the answer that the radius equals zero, which I know cannot be right..

Andrew Mason