An 80-N uniform plank leans against a frictionless wall as shown. The torque (about point P) applied to the plank by the wall is:
A) 40 N.m
B) 60 N.m
C) 120 N.m
D) 160 N.m
E) 240 N.m

Question

An 80-N uniform plank leans against a frictionless wall as shown. The torque (about point P) applied to the plank by the wall is: 
A) 40 N.m 
B) 60 N.m 
C) 120 N.m 
D) 160 N.m 
E) 240 N.m

Quizplus · Accepted Answer

The torque applied to the plank by the wall is equal to the force applied by the wall multiplied by the perpendicular distance from the point of rotation (point P) to the line of action of the force. In this case, the perpendicular distance is the length of the plank (3 meters), and the force applied by the wall is equal and opposite to the component of the weight of the plank that is perpendicular to the wall. This weight can be found using trigonometry:

sin(60°) = opposite/hypotenuse
opposite = sin(60°) x 80 N
opposite = 69.28 N

Therefore, the torque is:

torque = force x distance
torque = 69.28 N x 3 m
torque = 207.84 Nm

Converting to newton-meters, we get:

torque = 207.84 NF1F1F1S1F1F1F10m

The closest answer choice is C, 120 NF1F1F1S1F1F1F10m.

An 80-N Uniform Plank Leans Against a Frictionless Wall as Shown