Where Should the Pivot Be Placed to Balance a See-Saw?

  • #1
panda02
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0
Homework Statement
If Sara (100kg) and Jim (200kg) are 1m from the edge of opposite sides of a 13m long, 100kg see-saw, where does the pivot point need to be in order to balance the see-saw?
Relevant Equations
Ts=Tj
Torque_left = 100 kg * 1 m = 100 kg·m
Torque_right = 200 kg * (13 - x) m = 200(13 - x) kg·m
100 kg·m = 200(13 - x) kg·m
100 = 200(13 - x)
x = 12.5 meters

pivot = 12.5 m
 
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  • #2
panda02 said:
Homework Statement: If Sara (100kg) and Jim (200kg) are 1m from the edge of opposite sides of a 13m long, 100kg see-saw, where does the pivot point need to be in order to balance the see-saw?
Relevant Equations: Ts=Tj

Torque_left = 100 kg * 1 m
It should be 100 kg times the distance from the pivot point, but 1 m is the distance from the edge.
 
  • #3
Please make the title of your thread more informative. We already know that it is in the Homework Help forum.
 
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  • #4
Hill said:
Please make the title of your thread more informative. We already know that it is in the Homework Help forum.
Looks like the OP has fixed it up a little now. Thanks.
 
  • #5
panda02 said:
Homework Statement: If Sara (100kg) and Jim (200kg) are 1m from the edge of opposite sides of a 13m long, 100kg see-saw, where does the pivot point need to be in order to balance the see-saw?
Relevant Equations: Ts=Tj

Torque_left = 100 kg * 1 m = 100 kg·m
How do you know that Sara is 1 m away from the pivot point?
 
  • #6
panda02 said:
Homework Statement: If Sara (100kg) and Jim (200kg) are 1m from the edge of opposite sides of a 13m long, 100kg see-saw, where does the pivot point need to be in order to balance the see-saw?
Relevant Equations: Ts=Tj

Torque_left = 100 kg * 1 m = 100 kg·m
Torque_right = 200 kg * (13 - x) m = 200(13 - x) kg·m
100 kg·m = 200(13 - x) kg·m
100 = 200(13 - x)
x = 12.5 meters

pivot = 12.5 m
Hello @panda02 ,
:welcome: ##\qquad## !​

hehe, at least this thread got out of the starting block.

I advise you to stop using torque_left and _right. Just torque and a position for the axis of rotation..

Torque contributions are positive if going counterclockwise, negative if clockwise.

And a picture ! (edit: updated pic)
1698072687329.png

Force balance: The support has to compensate 400 g
Torque:
If we choose the left end of the board as axis of rotation, we have
from Sara ##\ \ -## 100 g x 1 m
from the board weight ##\ \ -## 100 g x 6.5 m
from Jim ##\ \ -## 200 g x 12 m
and from the supporting pivot point ##\ \ +## 400 g x X m

with X the distance from the left end of the board to the pivot point.

##\ ##
 

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FAQ: Where Should the Pivot Be Placed to Balance a See-Saw?

1. What is the principle behind balancing a see-saw?

The principle behind balancing a see-saw is the concept of torque. Torque is the rotational equivalent of force and is calculated as the product of the force and the distance from the pivot point. For a see-saw to balance, the torques on either side of the pivot must be equal. This means that the product of the weight and distance from the pivot must be the same on both sides.

2. How do you determine the pivot point for two people of different weights?

To determine the pivot point for two people of different weights, you can use the formula \( W_1 \times D_1 = W_2 \times D_2 \), where \( W_1 \) and \( W_2 \) are the weights of the two people, and \( D_1 \) and \( D_2 \) are their respective distances from the pivot. Rearrange the equation to solve for the unknown distance or position the pivot so that the torques are balanced.

3. Can the see-saw be balanced if the pivot is not at the center?

Yes, the see-saw can be balanced even if the pivot is not at the center, as long as the torques on both sides are equal. This means the heavier person needs to sit closer to the pivot, and the lighter person should sit further away. The exact position can be calculated using the torque balance equation.

4. What happens if the see-saw is not balanced?

If the see-saw is not balanced, one side will be heavier and will tip downward, while the lighter side will rise upward. This occurs because the torques on either side of the pivot are not equal, causing a rotational imbalance.

5. How does the length of the see-saw affect the pivot placement?

The length of the see-saw affects the pivot placement because it determines the maximum possible distances \( D_1 \) and \( D_2 \) from the pivot. A longer see-saw allows for greater leverage, meaning smaller differences in weight can be balanced by adjusting the distance more precisely. The pivot should be placed such that the product of the weight and distance is equal on both sides for balance.

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