a)What mass of m2 will just barely set the system in motion? b)After the system

Question

a)What mass of m2 will just barely set the system in motion?

b)After the system begins to move, what is the acceleration?

Unless otherwise stated, all objects are located near the Earth?s surface, where g = 980 m/s^2 . In the apparatus shown in the figure (Figure 1) , m1 = 10 kg and the coefficients of static and kinetic friction between m1 and the table are 0.57 and 0.45, respectively. a)What mass of m2 will just barely set the system in motion? b)After the system begins to move, what is the acceleration?

Explanation / Answer

a) Consider a free-body diagram of the string. m2 pulls in one direction and friction pulls in the other. I'll call uk and us the coefficients of kinetic and static friction, respectively. Then F(friction) = F(m2).

(us)m1g = m2g therefore m2 = (us)m1 = (0.57)(10 kg) = 5.7 kg will just barely set the system in motion.

b) After the system is in motion the net force Fnet = F(m2) - F(friction). Then

(m1 + m2)a = m2g - (uk)m1g, yielding a= g(m2 - (uk)m1) / (m1 + m2) = 0.74 m/s^2

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