Rotational Equilibrium and Newton's First Law in Rotational Form

AP Physics 1· difficulty 3/5

A 20 kg20~\text{kg} board of length 4.0 m4.0~\text{m} rests on a single pivot at its center. A 30 kg30~\text{kg} child sits at the left end. To balance, a 20 kg20~\text{kg} child must sit at distance from pivot

  • A

    3.0 m3.0~\text{m} on the right

  • B

    2.0 m2.0~\text{m} on the right

  • C

    Cannot balance

    check_circle
  • D

    1.0 m1.0~\text{m} on the right

Explanation

The board's CM is at the pivot, so it contributes no torque. Balance requires 302.0=20dd=3.0 m30 \cdot 2.0 = 20 \cdot d \Rightarrow d = 3.0~\text{m}. But the 4-m board has only 2 m on each side of the pivot, so the 20-kg child would have to sit beyond the right end — which is physically impossible. The system cannot be balanced with the 20-kg child alone.

Want 10 more like this — adaptive to your weak spots?

Related questions