Solving Balance Scale Math: X vs Y Weight Difference

In summary, the conversation discusses the mechanics behind an old fashioned balance scale and how it maintains equilibrium when there is a difference in weight between the two sides. The speaker mentions the role of torque and different theories for how the system returns to equilibrium, such as friction or a spring-like force. They are seeking help understanding the math and physics behind this phenomenon.
  • #1
jackrabbit
12
0
I was trying to figure out the following - assume you have an old fashioned balance scale, with two pans hanging from a lever with a fulcrum in the middle of the lever. On one side you have a weight of X, and on the other side you have a weight Y. If Y is big enough, that side of the scale will fall until it hits the desk holding the scale. But if Y is only slight more than X, the scale will only tip in Y's direction a small amount. That seems intuitive enough, but how does the math work? As long as there is any difference in weight between the two sides, which doesn't side Y fall the same amount in both cases?

I thought it had something to do with torque, but I can't get the calculations to work. For example, assume X is 5 lbs and Y is 5.5 lbs, and they are hanging from pans that are each 4 units from the fulcrum. The torque from X is (5*4* the sine of the angle between the force vector and the lever). The torque from Y is (5.5*4*the sine of the angle between the force vector and the lever). I thought that the differential between the two torques would equilibrate as the angles changed. However, as the angles are always supplementary to each other, the relevant sines are always the same, so the torque never ends up in equilibrium.

So, clearly my math and/or physics is wrong. Can someone help?
 
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  • #2
There must be something else that forces the system back to equilibrium when it is displaced a small amount. I would guess it is because friction (at the connection between lever and fulcrum) increases slightly when the lever moves slightly from its initial position. Another possibility is that there is some kind of spring-like force (at the fulcrum connection) that returns the system to steady when there is only a small displacement. For example, maybe the connection gets slightly tighter when the lever rotates, so a small displacement is negated.
 

1. How do I solve a balance scale math problem?

To solve a balance scale math problem, you need to first identify the known weight on one side of the scale and the unknown weight on the other side. Then, use the balance principle to determine the weight difference between the two sides. This can be done by adding or subtracting weights from each side until the scale is balanced.

2. What is the balance principle in math?

The balance principle in math states that the weight on one side of a balance scale is equal to the weight on the other side. This means that if you add or subtract weights from one side, you must also add or subtract the same amount of weight from the other side in order to maintain balance.

3. How do I determine the weight difference in a balance scale math problem?

The weight difference in a balance scale math problem can be determined by comparing the weights on each side of the scale. If one side is heavier than the other, the weight difference is the amount needed to be added to the lighter side to balance the scale. If one side is lighter than the other, the weight difference is the amount needed to be subtracted from the heavier side to balance the scale.

4. Can I solve a balance scale math problem without using numbers?

Yes, it is possible to solve a balance scale math problem without using numbers. Instead, you can use letters or variables to represent the weights on each side of the scale. This method is often used in algebraic equations to find the value of an unknown variable.

5. Are there any tips for solving balance scale math problems?

One helpful tip for solving balance scale math problems is to always keep the scale balanced by adding or subtracting equal weights from each side. Another tip is to start with the larger weights and work your way down to the smaller ones. It can also be helpful to write out the weights on each side of the scale and keep track of your calculations to avoid errors.

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