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QZ_02_S - Ph1a Solution to Quiz 2 Alejandro Jenkins Fall...

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Ph1a: Solution to Quiz 2 Alejandro Jenkins, Fall 2004 Problem 1 (4 points) - Incline Slipping An incline of mass M rests on a floor with a coefficient of static friction μ . A mass m 1 is suspended by a massless string that passes over a frictionless pulley of negligible mass, attached to the upper corner of the incline. The other end of the string is attached to a mass m 2 that slides without friction on the surface of the incline. The plane of the incline meets the horizontal at an angle θ , as shown in the figure. M rough floor m 1 m 2 θ Assume that the mass m 1 will move downward with respect to the pulley, and that the string can neither stretch nor break. (a) (2 points) For the case of very large μ , use Newton’s laws to determine the tension T of the string and the acceleration a of the masses. Express your answers in terms of M , m 1 , m 2 , θ , and the gravitational acceleration g . Solution : Figure 1 shows the force diagrams for both m 1 and m 2 . T N m g 1 T 2 m g 1 Figure 1: Forces acting on m 1 and m 2 Since the string cannot stretch or break, the acceleration of both these masses must be the same. By Newton’s second law:
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m 1 g - T = m 1 a T - m 2 g sin θ = m 2 a Solving for a : a = ( m 1 - m 2 sin θ ) g m
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