Torque Physics Example 2

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Example 2

medium
A 3 m3 \text{ m} seesaw has a pivot at its center. A 30 kg30 \text{ kg} child sits at one end. How far from the center must a 45 kg45 \text{ kg} child sit to balance the seesaw? Use g=9.8 m/s2g = 9.8 \text{ m/s}^2.

Solution

  1. 1
    For rotational equilibrium, the net torque must be zero: τ1=τ2\tau_1 = \tau_2.
  2. 2
    The 30 kg30 \text{ kg} child sits 1.5 m1.5 \text{ m} from the pivot: τ1=30×9.8×1.5=441 N m\tau_1 = 30 \times 9.8 \times 1.5 = 441 \text{ N m}.
  3. 3
    For the 45 kg45 \text{ kg} child: τ2=45×9.8×d=441  ⟹  d=441441=1 m\tau_2 = 45 \times 9.8 \times d = 441 \implies d = \frac{441}{441} = 1 \text{ m}.

Answer

d=1 m from the centerd = 1 \text{ m from the center}
A seesaw balances when the torques on both sides are equal. The heavier child must sit closer to the pivot to produce the same torque as the lighter child sitting farther away.

About Torque

The rotational equivalent of force; a measure of how much a force tends to cause an object to rotate about an axis.

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