The drawing shows the top view of a door that is 1.68 m wide. Two forces are applied to the door as indicated. What is the magnitude of the net torque on the door with respect to the hinge?
A)0 N . m
B)4.4 N . m
C)8.3 N . m
D)9.1 N . m
E)11 N . m

Question

The drawing shows the top view of a door that is 1.68 m wide. Two forces are applied to the door as indicated. What is the magnitude of the net torque on the door with respect to the hinge? 
A)0 N . m 
B)4.4 N . m 
C)8.3 N . m 
D)9.1 N . m 
E)11 N . m

Quizplus · Accepted Answer

Torque is the product of force and the perpendicular distance from the line of action of the force to the hinge.

For the clockwise (CW) torque, we have:

τ_CW = F1 × d1 = 20 N × 0.4 m = 8 N·m

Similarly, for the counterclockwise (CCW) torque, we have:

τ_CCW = F2 × d2 = 10 N × 0.6 m = 6 N·m

The net torque is the difference between these torques (since they are in opposite directions):

τ_net = τ_CW - τ_CCW = 8 N·m - 6 N·m = 2 N·m

Note that we could have also used the perpendicular distances from the hinge to the lines of action of the forces (which are given as 0.8 m and 0.28 m) instead of the distances specified in the answer choices.

Therefore, the best choice is C: 8.3 N·m.

The Drawing Shows the Top View of a Door That