Final answer:
The net torque about the pivot is calculated by finding the individual torques caused by each force and then subtracting the clockwise torque from the counterclockwise torque, resulting in a positive net torque of 8.58 N·m. So the correct option is c.
Step-by-step explanation:
The student is asking to calculate the net torque about the pivot on a rod being acted upon by two forces causing opposing torques. To find the net torque, we need to calculate each torque and then subtract the clockwise (cw) torque from the counterclockwise (ccw) torque. Torque (τ) can be calculated using the formula τ = rFsin(θ), where r is the distance from the pivot, F is the force applied, and θ is the angle at which the force is applied relative to the rod.
Step-by-step calculation:
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- Calculate the torque due to the 7.80 N force acting at 1.60 m from the pivot: τ1 = 7.80 N × 1.60 m × sin(90°) = 12.48 N·m
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- Calculate the component of the 2.60 N force acting perpendicular to the rod using the sine function: Fperpendicular = 2.60 N × sin(30°) = 1.30 N
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- Calculate the torque due to this force acting at 3.00 m from the pivot: τ2 = 1.30 N × 3.00 m × sin(90°) = 3.90 N·m
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- Since the 2.60 N force causes a clockwise (cw) torque, it will have a negative value, so subtract τ2 from τ1 to get the net torque: Net τ = τ1 - τ2 = 12.48 N·m - 3.90 N·m = 8.58 N·m
Since the counterclockwise (ccw) torque is the positive direction, the net torque of 8.58 N·m is positive, giving us option c) 8.58 N·m as the correct answer.