Physics quiz question: rope doing work on pulley and box

Physics 8A Quiz 9, Spring Semester 2004
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q9.2

[3.0 points.] Consider a pulley that turns without friction about a stationary horizontal axis through its center. A horizontal ideal massless, stretchless rope passes over the pulley, and has a 4.00 kg box suspended from its free end. There is no slipping between the rope and the rim of the pulley. The pulley is a uniform disk with radius 0.200 m and a moment of inertia of 0.700 kg*m^2. Initially this system is stationary, but a constant force pulls to the left on the rope, such that the box has a speed of 0.750 m/s after it has moved upwards by 0.100 m.

Which one of the following choices best describes the magnitude of the tension force in the rope?

(A) 39.2 N.
(B) 99.7 N.
(C) 127 N.
(D) 392 N.

(Cf. Young and Freeman, University Physics, 11/e, Problem 9.92.)

Correct answer: (B)
The external work done on this system is equal to the sum of the increase in gravitational potential energy of the box; increase in the translational kinetic energy of the box; and the increase in rotational kinetic energy of the pulley. Where d = +0.100 m, y_i = 0, w_f = v_f/r, and I_pulley = (1/2)*m_pulley*(r^2) then:

T_rope = ((m_box*g*y_f) + (1/2)*m_box*(v_f^2) + (1/2)*(I_pulley)*(w_f)^2)/d.

Somehow equating the tension in the rope to the weight of the box results in the incorrect response (A); the incorrect response (D) is the increase in gravitational energy of the box.

Student responses:
(A) : 17 students
(B) : 10 students
(C) : 1 student
(D) : 0 students