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 perpendicular component of the force of the wall on the plank multiplied by the distance from the point of rotation (P) to the line of action of the force. In this case, the force of the wall is vertical and perpendicular to the plane of the plank, so the perpendicular component is equal to the magnitude of the force (80 N). The distance from P to the line of action of the force is the length of the plank (2 m) multiplied by the sine of the angle between the plank and the wall (60 degrees). Therefore, the torque is (80 N)(2 m)(sin 60) = 120 Nm. The correct answer is C.

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