Solving Balancing Beam: m1, L1, m2, L2

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In summary, the picture shows a 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. The 300N upward force tells you about the total weight of the masses and beam. The weight of m2 is less than m1 because the length of the beam is longer on the side of m2. The upward force is provided by both m1 and m2, and the total downward force is provided by m
  • #1
EthanVandals
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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.

Homework Equations


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!
 
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  • #2
EthanVandals said:

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.

Homework Equations


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
 
  • #3
Andrew Mason said:
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.
 
  • #4
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
 
  • #5
Andrew Mason said:
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...
 
  • #6
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
 
  • #7
Andrew Mason said:
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...
 
  • #8
There are two things you have to work out. First is total mass. Second is the torque. How are you determining each?

AM
 
  • #9
Andrew Mason said:
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?
 
  • #10
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
 
  • #11
Andrew Mason said:
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.
 
  • #12
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
 
  • #13
Andrew Mason said:
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..
 
  • #14
??... What is the mathematical expression for torque? Express the torque from m1 about the fulcrum. What about m2? Be careful about signs.

AM
 

FAQ: Solving Balancing Beam: m1, L1, m2, L2

What is the purpose of solving a balancing beam with m1, L1, m2, L2?

The purpose of solving a balancing beam with m1, L1, m2, L2 is to determine the position and weight distribution of two objects on opposite ends of a beam in order to achieve equilibrium.

How do you calculate the center of mass for a balancing beam with m1, L1, m2, L2?

The center of mass can be calculated by multiplying the mass of each object by its respective distance from the fulcrum, and then dividing the sum of these values by the total mass of the system.

What is the equation for solving a balancing beam with m1, L1, m2, L2?

The equation for solving a balancing beam with m1, L1, m2, L2 is m1L1 = m2L2, where m1 and m2 are the masses of the objects and L1 and L2 are their respective distances from the fulcrum.

Can the balancing beam equation be used for objects with different masses?

Yes, the balancing beam equation can be used for objects with different masses as long as the distance from the fulcrum is taken into account. This equation works for any system where the sum of the moments on one side of the fulcrum is equal to the sum of the moments on the other side.

How does changing the distance from the fulcrum affect the balance of a beam with m1, L1, m2, L2?

Changing the distance from the fulcrum can greatly affect the balance of a beam with m1, L1, m2, L2. Increasing the distance from the fulcrum on one side and decreasing it on the other side will result in an unbalanced beam. However, if the distances are kept equal, the beam will remain balanced even if the masses are changed.

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