Question

2 rotational dynamics (continued)

1. net torque two people are pulling on ropes wrapped around the edge of a large wheel. the wheel has a mass of 12 kg and a diameter of 2.4 m. one person pulls in a clockwise direction with a 43-n force, while the other pulls in a counterclockwise direction with a 67-n force. what is the net torque on the wheel?

Explanation:

Step1: Find the radius of the wheel

The diameter \( d = 2.4\space m \), so the radius \( r=\frac{d}{2}=\frac{2.4}{2} = 1.2\space m \)

Step2: Calculate torque for each force

Torque is given by \( \tau = rF\sin\theta \). Since the forces are applied tangentially, \( \theta = 90^\circ \) and \( \sin\theta = 1 \).
For the clockwise force (\( F_1 = 43\space N \)): \( \tau_1 = rF_1 = 1.2\times43 \)
For the counter - clockwise force (\( F_2 = 67\space N \)): \( \tau_2 = rF_2 = 1.2\times67 \)

Step3: Determine the net torque

Let the counter - clockwise torque be positive and clockwise torque be negative.
Net torque \( \tau_{net}=\tau_2-\tau_1=r(F_2 - F_1) \)
Substitute \( r = 1.2\space m \), \( F_2 = 67\space N \) and \( F_1 = 43\space N \)
\( \tau_{net}=1.2\times(67 - 43)=1.2\times24 = 28.8\space N\cdot m \) (counter - clockwise direction)

Answer:

The net torque on the wheel is \( 28.8\space N\cdot m \) (counter - clockwise)