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

Respuesta :

The net torque is [tex]28.8 N \cdot m[/tex] in the counterclockwise direction

Explanation:

In order to find the net torque, we have to calculate the clockwise torque and the counterclockwise torque, and then evaluate their difference.

The clockwise torque is given by:

[tex]\tau_C = F_C r[/tex]

where

[tex]F_C = 43 N[/tex] is the force applied in the clockwise direction

r = 1.2 m is the distance between the point of application of the force and the axis of rotation (it is equal to half the diameter)

Substituting,

[tex]\tau_C = (43)(1.2)=51.6 N \cdot m[/tex]

Similarly, the counterclockwise torque is given by:

[tex]\tau_A = F_A r[/tex]

where

[tex]F_A = 67 N[/tex] is the force applied in the counterclockwise direction

r = 1.2 m

Substituting,

[tex]\tau_A = (67)(1.2)=80.4 N \cdot m[/tex]

Therefore, the net torque on the wheel is

[tex]\tau = \tau_A - \tau_C = 80.4-51.6=28.8 N \cdot m[/tex]

In the counterclockwise direction, since the counterclockwise moment is larger than the clockwise one.

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