Two people are pulling straight down on ropes attached to a wheel. The wheel has a radius of 2.42 m. One person pulls in a clockwise direction with a force of 43.2 N at the end of the wheel, while the other pulls in a counterclockwise direction with a force of 67.8 N only .522 m from the center of the wheel. What is the net torque on the wheel?

69.2 Nm

Explanation:

Since torque, τ = Fd where F = force and d = distance of force from center of wheel.

The torque due to the clockwise force F' = 43.2 N at a distance d' = radius of wheel = 2.42 m (since it is at the end of the wheel) is τ' = F'd' = 43.2 N × 2.42 m = 104.544 Nm. Since this force is counterclockwise, the torque is positive. So, τ' = 104.544 Nm

The torque due to the force F" = 67.8 N at a distance d" = 0.522 m from center of wheel is τ" = F"d" = 67.8 N × 0.522 m = 35.3916 Nm. Since this force is counterclockwise, the torque is negative. So, τ" = -35.3916 Nm

The net torque on the wheel  τ =  τ' +  τ"

= 104.544 Nm + (-35.3916 Nm)

= 104.544 Nm - 35.3916 Nm

= 69.1524 Nm

≅ 69.2 Nm