Physics quiz question: pivoting triangle

Physics 8A Quiz 6, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q6.1

[3.0 points.] Consider a horizontal metal right triangle plate, 0.400 m on each leg, pivoted about a vertical axis through point "O" at its 90.0° corner. Two forces are exerted as shown, resulting in a net counterclockwise torque of magnitude 0.600 N*m, and a counterclockwise acceleration of 1.90 rad/s^2. The plate and the forces are in the plane of this page.

If F_1 has a magnitude of 8.00 N, which one of the following choices best corresponds to the magnitude of F_2?
(A) 5.00 N.
(B) 8.00 N.
(C) 11.0 N.
(D) 16.0 N.

(Cf. Young and Freeman, University Physics, 11/e, Exercise 10.3.)

Correct answer: (C)
Applying Newton's second law, where net torque = +0.600 N*m = -F_1*(0.400 m) + F_2*(0.400 m), and thus F_2 = 11.0 N. Be careful in setting up all torques in the proper rotation direction (+ = ccw, - = cw), and note that the "perpendicular" lever arm for the force F_1 is the same as the lever arm for the perpendicular force F_2.

Student responses:
(A) : 2 students
(B) : 6 students
(C) : 23 students
(D) : 3 students