Objects of masses m_1=4.00 kg and m_2 = 9.00 kg are connected by a light string

Question

Objects of masses m_1=4.00 kg and m_2 = 9.00 kg are connected by a light string that passes over a frictionless pulley as in the figure below. The object m_1 is held at rest on the floor, and m_2 rests on a fixed incline of theta - 42.0 degree. The objects are released from rest, and m_2 slides 1.60 m down the slope of the incline in 4.10 s. (a) Determine the acceleration of each object. (Enter the magnitude only.) m/s^2 (b) Determine the tension in the string. (Enter the magnitude only.) N (c) Determine the coefficient of kinetic friction between m_2 and the incline.

Explanation / Answer

a) d = 1/2at^2

a = 2*1.6/4.1^2 = 0.19 m/s^2

b) T - m1 g = m1 a
T = m1(g + a) = 4(0.19+9.8) = 39.96 N

c) m2gsin42-f-T = m2a

m2gsin42-f(m1a+m1g) = m2a

f = mue*m2gcos42

so mue = (m2gsin42-m1a-m1g-m2a)/m2gcos42 = (59.02-39.96-1.71)/65.54

mue = 0.265

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