Question

Use the worked example above to help you solve this problem. Two disgruntled businessmen are trying to use a revolving door, as shown in the figure. The door has a diameter of 2.60 m. The businessman on the left exerts a force of 634 N perpendicular to the door and 1.3 m from the hub's center, while the one on the right exerts a force of 791 N perpendicular to the door and 0.634 m from the hub's center. Find the net torque on the revolving door. (Indicate the direction with the sign of your answer.)

Answer 1

To calculate the net torque on the revolving door, we apply the torque formula taking into account the perpendicular forces and their distances from the pivot. The net torque is 322.706 N·m, indicating a counterclockwise rotation.

Step-by-step explanation:

To find the net torque on the revolving door exerted by the two businessmen, we should use the formula τ = rF sin θ, where τ is the torque, r is the distance from the pivot point at which the force is applied, F is the magnitude of the force, and θ is the angle between the force direction and the line from the pivot point to the point of force application. Since the forces are applied perpendicular to the door, the angle θ is 90 degrees, and sin θ is 1.

The first businessman exerts a torque given by:

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The second businessman exerts a torque given by:

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To find the net torque, we consider the direction of each force. If they cause rotation in opposite directions, one torque will be positive and the other will be negative. Assuming the businessman on the left causes a counterclockwise rotation (positive torque) and the one on the right causes a clockwise rotation (negative torque), the net torque is:

τnet = τ1 - τ2 = 824.2 N·m - 501.494 N·m = 322.706 N·m

The positive value of the net torque indicates that the net effect is counterclockwise rotation.