Equilibrium: A 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam?
A) 2.12 m
B) 1.98 m
C) 1.93 m
D) 2.07 m
E) 2.20 m

Question

Quizplus · Accepted Answer

To find the length of the beam, we can use torque equilibrium. Since the beam is in equilibrium, we know that the sum of the clockwise torques around the fulcrum must equal the sum of the counterclockwise torques. We can choose the fulcrum as the point around which we calculate the torques. Let's take the torque due to the 30.0 kg child as positive (counterclockwise) and the torque due to the 40.0 kg child as negative (clockwise). Then we have:

$(30.0	ext{ kg})(g)(1.10	ext{ m}) - (40.0	ext{ kg})(g)(L - 1.10	ext{ m}) = 0$

where $g$ is the acceleration due to gravity and $L$ is the length of the beam. Solving for $L$, we get:

$L = \frac{(30.0	ext{ kg})(g)(1.10	ext{ m})}{(40.0	ext{ kg})(g)} + 1.10	ext{ m} = 1.98	ext{ m}$

Therefore, the best choice is (B) 1.98 m.

Equilibrium: a 30