Question

A child (mass 25.0 kg) visiting a construction site is left unattended and is bored. She notices a support beam 5.0m long (mass 35 kg) supported by (but not attached to) two posts, one at the end of the beam, the second 3.0m down the beam (leaving 2.0m of the beam hanging out). Deciding this looks like a diving board, the child stands on the beam at the second post and walks toward the edge. How far does she get before the board tips (in meters)?

a) 1.4
b) 1.7
c) 2.0
d) 2.3

Answer 1

The child gets approximately 3.11 meters before the board tips.

Step-by-step explanation:

To determine how far the child gets before the board tips, we need to consider the torques acting on the system. The torque exerted by the child is given by the product of her weight and the distance from the second post to the edge of the board. The torque exerted by the beam is given by the product of its weight and the distance from the center of mass to the edge of the board. By setting these torques equal to each other and solving for the distance, we can find how far the child gets before the board tips.

Let's denote the distance from the second post to the edge as x. The torque exerted by the child is equal to (25.0 kg * 9.8 m/s^2) * x. The torque exerted by the beam is equal to (35.0 kg * 9.8 m/s^2) * (2.0 m + x).

Setting these torques equal to each other, we have (25.0 kg * 9.8 m/s^2) * x = (35.0 kg * 9.8 m/s^2) * (2.0 m + x). Now we can solve for x:

(25.0 kg * 9.8 m/s^2) * x = (35.0 kg * 9.8 m/s^2) * (2.0 m + x)

245 x = 686(2.0 + x)

245 x = 1,372 + 686x

441x = 1,372

x ≈ 3.11 m

Therefore, the child gets approximately 3.11 meters before the board tips.