Two masses m_1 (15 kg) and m_2 (25 kg) are shown in the figure below. Mass 1 sit

Question

Two masses m_1 (15 kg) and m_2 (25 kg) are shown in the figure below. Mass 1 sits on top of the table; mass 2 is hanging from a massless, inextensible tether over a non-rotating, frictionless pulley. The coefficient of static friction is given as mu_ and coefficient of kinetic friction given as mu_k. a. If the blocks are initially in equilibrium, determine the numerical value of mu_. b. In the case where block 1 is accelerating to the right at 2.5 m/s^2, determine the numerical value of mu_k. c. For the same scenario in part (c) determine the numerical value of T. A 12 kg box starts from rest and slides down a plane with a coefficient of kinetic friction of 0.23 and constant velocity of 6.5 m/s. Determine the angle of the incline?

Explanation / Answer

a) T = m2g = f = mues*n = mues*m1g

mues = m2/m1 = 25/15 = 1.67

b) m1a = T-muek*m1g

m2a = m2g-T

m1a = m2g-m2a-muek*m1g

2.5(40) = 9.8(25-muek*15)

muek = 0.987

c) T = 25(9.8-2.5) = 182.5 N

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