Question

The child with weight w has an identical twin also of weight w. The two twins now sit on the same side of the seesaw, with one twin a distance L2 from the pivot and the other a distance L3. (Figure 2)

Part D
Where should the mother position the child of weight W to balance the seesaw now?
Express your answer in terms of L2, L3, W, and w. L=????
Bad news! When the mother finds the distance L from the previous part it turns out to be greater than Lend, the distance from the pivot to the end of the seesaw. Hence, even with the child of weight W at the very end of the seesaw the twins exert more torque than the heavier child does. The mother now elects to balance the seesaw by pushing sideways on an ornament (shown in red) that is a height h above the pivot. (Figure 3)
Part E
With what force in the rightwards direction, Fx, should the mother push? Note that if you think the force exerted by the mother should be toward the left, your final answer Fx should be negative.
Express your answer in terms of W, Lend, w, L2, L3, and h.
Fx= ????

Answer 1

To balance the seesaw, the mother should exert a force, Fx, in the rightwards direction on the ornament. The force should create a torque that balances the torques exerted by the twins. The equation for torque balance shows that the force should be proportional to the distances and weights involved.

Step-by-step explanation:

To balance the seesaw with the twins and the child of weight W, the mother should push sideways on the ornament. The force, Fx, should be such that it creates a torque that is equal in magnitude but opposite in direction to the torque exerted by the twins. The equation for torque is given by:

Torque = Force x Distance

Since the twins are at distances L2 and L3 from the pivot, and the child of weight W is at distance Lend from the pivot, the mother's force should create a torque that balances the torques exerted by the twins. Thus, the equation for torque balance is:

Fx x h = (w x L2) + (w x L3) - (W x Lend)

Therefore, the force in the rightwards direction, Fx, that the mother should exert is:

Fx = [(w x L2) + (w x L3) - (W x Lend)] / h

Answer 2

The problem involves calculating the sideways force the mother should exert at a certain height to balance the seesaw using two identical twins and static equilibrium. The force Fx that balances the torques is found using the equation Fx = (w * L2 + w * L3) / h.

Step-by-step explanation:

The problem at hand deals with static equilibrium and requires applying the principles of torques on a seesaw system. Since no specific numbers are given, the answers must be provided in algebraic form, in terms of the given variables W (weight of the mother), w (weight of each twin), L2 (distance of one twin from pivot), L3 (distance of the second twin from pivot), Lend (distance from pivot to end of seesaw), and h (height of the ornament from pivot).

For part D, assume the seesaw is initially balanced with the two twins on one side. Because the solution to the position L turned out to be greater than Lend, we can say the seesaw cannot be balanced by merely placing the child W (mother) at the end. The system is still in static equilibrium, though, with regard to horizontal torques, by placing the child at Lend.

For part E, we need to apply the principles of torque and equilibrium when the mother applies a sideways force. To calculate the force Fx the mother should push with, we would normally use the equation:

Torque due to mother + Torque due to twins = 0

The torque due to the twins is w * L2 + w * L3 (since they have the same weight and are at different distances from the pivot). The torque due to the mother's push is Fx * h. To solve for Fx, we set up the equation as follows:

Fx * h = w * L2 + w * L3

Thus, Fx = (w * L2 + w * L3) / h

We assume this force acts in the rightward direction; if it acted in the leftward direction the sign of Fx would be negative.