Two masses M1 and M2 (where M1 > M2) are connected by a rope through a frictionl

Question

Two masses M1 and M2 (where M1 > M2) are connected by a rope through a frictionless pulley. They are placed on two slopes, each with the same angle to the horizontal, which are connected at the top to make a triangle. The total angle between the two slopes at the top is . The pulley is located at the top. M2 MI The right slope with M2 is frictionless, while the left slope with MI has coefficients , and . The two masses are initially at rest due to the static friction on MI. The angle is reduced (equally between each side) until the masses just start sliding, at which point is held constant If ,-0.8, .-0.1, M,-5.3, and M2=1.6, what is the magnitude of the acceleration experienced by the masses?

Explanation / Answer

on M2 : T - M2 g cos(theta/2) = 0

T = m2 g cos(theta/2)

on m1: M1 g cos(theta/2) - us M1 g sin(theta/2) - T = 0

M1 cos(theta/2) - 0.8 M1 sin(theta/2) - M2 cos(theta/2) = 0

3.7 cos(theta/2) - 4.24 sin(theta/2) = 0

tan(theta/2) = 0.87

theta = 82.2 deg

T - 1.6 g cos41.1 = 1.6 a

5.3 g cos41.1 - 0.53 g sin41.1 -T = 5.3 a

adding both,

a = 3.47 m/s^2

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