# Balancing Act: Forces on See-Saws in a Square Arrangement

• cmcd
In summary, a team of Mexican acrobats is developing a new act where four see-saws are arranged in a square and each member of the team has a mass of 50kg. The contact forces between the see-saws were calculated using the equations \sum{V_{forces}}=0 and \sum{M_{pivotPoint}}=0. By symmetry, the reactions between see-saws are all the same, resulting in a reaction force of 50g/3 for each see-saw in part (a). In part (b), it was determined that the system can be seen as a set of two x two see-saw balancing acts, where the reaction force is 0 at the meeting point. The reaction
cmcd

## Homework Statement

A team of Mexican acrobats are developing a new act. Four see-saws are arranged in a square so that the ends of the see-saws overlap as shown in the plan view below. Each member of the team has a mass of exactly 50kg.

(a) Calculate the contact forces between the see-saws when the acrobats, under the sombreros are positioned as shown in the digram - {linked}

(b) What will happen if one member of the team over-eats and becomes heavier than the three others?
Can the other three acrobats position themselves such that the system is balanced?

## Homework Equations

$$\sum{V_{forces}}=0$$

$$\sum{M_{pivotPoint}}=0$$

## The Attempt at a Solution

[/B]
$$R_A=\text{ Force exerted on see-saw in question on the left}$$
$$R_B=\text{ Force exerted on see-saw in question on the right}$$
$$N=\text{ The reaction force due to the fulcrum in the middle of the see-saw}$$
$$L =\text{ The length of the see-saw}$$

$$\sum{M_{Fulcrum}} =+R_A*L/2 - 50*g*L/3 +R_B*L/2$$

This is just for one of the four see-saws. For part (a) I suppose each see-saw should be the same. Is this right? Or do I have to include the forces the see-saw in question exerts on the other see-saws?

#### Attachments

• Mech2011-page-4.jpg
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Yes, by symmetry you can deduce the reactions between see-saws are all the same.

Can the system be seen as a set of two x two see-saw balancing acts, where the reaction force = 0 where they meet? N must be equal to 50g Newtons right? Can the reaction forces = 0?

Last edited:
cmcd said:
Can the system be seen as a set of two x two see-saw balancing acts, where the reaction force = 0 where they meet? N must be equal to 50g Newtons right? Can the reaction forces = 0?
Sure, but by the symmetry you can reduce it to a single see-saw with equal and opposite forces applied at the ends.

cmcd
That's great thanks!
I got the reaction force = $$50g/3$$
for part (a)

Last edited:
cmcd said:
That's great thanks!
I got the reaction force = $$50g/3$$
for part (a)
Looks right.

## 1. How does a see-saw work in a balancing act?

In a see-saw balancing act, the two ends of the see-saw act as the fulcrum and the load. The weight of the load on one end causes it to tilt downwards, while the weight of the person on the other end causes it to tilt upwards. When the two weights are balanced, the see-saw remains in equilibrium.

## 2. What factors affect the balance of a see-saw in a balancing act?

The balance of a see-saw in a balancing act is affected by the weight and distance from the fulcrum of each load and person on the see-saw. The heavier the load or the further away it is from the fulcrum, the greater its effect on the balance.

## 3. Can a see-saw ever be perfectly balanced?

Yes, a see-saw can be perfectly balanced when the weights and distances from the fulcrum on each end are equal. This means that both ends of the see-saw are at the same height and there is no movement.

## 4. What happens if one person on the see-saw moves closer to the fulcrum?

If one person on the see-saw moves closer to the fulcrum, it decreases their weight and distance from the fulcrum, making their side lighter. This causes the see-saw to tilt downwards on their side and upwards on the other side, creating an imbalance.

## 5. How can you adjust the balance of a see-saw in a balancing act?

The balance of a see-saw in a balancing act can be adjusted by changing the weight or distance from the fulcrum on each side. Adding or removing weights or moving closer or further away from the fulcrum can help achieve a balance. Additionally, having people of similar weight on each side can also help in balancing the see-saw.

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