Physics quiz question: two-box system, frictionless table, ideal pulley

Physics 8A Quiz 7, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q7.2

[3.0 points.] Consider a 4.00 kg box on a frictionless table, connected by an ideal cable to a box of unknown mass. The pulley has negligible mass, and is frictionless. The system is released from rest, and after the 4.00 kg box has moved 0.155 m, it has a speed of 1.08 m/s. Neglect air resistance. Which one of the following choices best corresponds to the mass of the unknown box?

(A) 1.11 kg.
(B) 1.54 kg.
(C) 2.49 kg.
(D) 26.5 kg.

(Cf. Young and Freeman, University Physics, 11/e, Problem 6.82.)

Correct answer: (C)
The decrease in gravitational potential energy of the unknown mass box is equal to the sum of the increases in kinetic energies of the 4.00 kg box and the unknown mass box. Thus if y_f = 0, then:

m_unknown = ((4.00 kg)*v_f^2)/(2*g*y_i – v_f^2) = 2.49 kg.

Note that setting the decrease in gravitational potential energy of the unknown mass box equal to the increase in kinetic energies of the 4.00 kg box only, where again y_f = 0, results in the incorrect response (B):

m_unknown = ((4.00 kg)*v_f^2)/(2*g*y_i) = 1.54 kg.

Student responses:
(A) : 2 students
(B) : 20 students
(C) : 9 students
(D) : 0 students