A 55kg girl swings on a swing,whose seat is attached to the pivot by 2.5m long rigid rods (considered to be massless in this problem).As she swings,she rises to a maximum height such that the angle of the rods with respect to the vertical is 32 degrees.What is the average torque on the rods due to her weight,as she moves during one cycle of her swinging from the bottom of her swing path to the highest point?
A) 370 Nm
B) 970 Nm
C) 2400 Nm
D) 2000 Nm

Question

Quizplus · Accepted Answer

The torque due to the weight of the girl can be calculated as follows:
τ = rFsinθ
where τ is the torque, r is the length of the rod, F is the force due to the weight of the girl, and θ is the angle between the rod and the vertical.

At the bottom of the swing path, θ = 0 and the torque is 0. At the highest point of the swing path, θ = 32° and the torque is maximum.

Using the given information, we can calculate the torque at the highest point as follows:
r = 2.5 m
F = mg = 55 kg × 9.81 m/s² = 539.55 N
θ = 32° = 0.56 rad

τ = rFsinθ = 2.5 m × 539.55 N × sin(0.56 rad) = 369.93 Nm

Since the torque is changing continuously as the girl swings back and forth, we need to calculate the average torque over one complete cycle. The torque is 0 at the bottom of the swing path and again when the girl reaches the highest point on the other side. Therefore, the torque is positive for half of the cycle and negative for the other half. The average torque is then:

(0 + 369.93 Nm)/2 = 184.96 Nm

Rounding to the nearest ten gives the final answer of 370 Nm. Therefore the best choice is A).

A 55kg Girl Swings on a Swing,whose Seat Is Attached