Question

An object with mass M1M1 of 2.85 kg is held in place on an inclined plane that makes an angle θθ of 40.0° with the horizontal (see figure below). The coefficient of static friction between the plane and the object is 0.566. A second object that has a mass M2M2 of 4.75 kg is connected to the first object with a massless string over a massless, frictionless pulley.

Calculate the initial acceleration and tension once objects are released.

Answer 1

Given,

Mass, M1 = 2.85 kg, M2 = 4.75 kg

Angle = 40 degrees

A)

Suppose T be the tension in the string and mass M2 is moving downward with an acceleration a

M2 x g - T = M2 x a

Tension, T = M2 (g - a) ...........(1)

T - M1 g sin(theta) - u x M1 g cos(theta) = M1 a

put value of T from (1)

M2 (g - a) - M1 g sin(theta) - u x M1 g cos(theta) = M1 a

M2 g - M1 g sin(theta) - u x M1 g cos(theta) = (M1+M2) a

4.75 x 9.8 - 2.85 x 9.8 x sin(40) - 0.566 x 2.85 x 9.8 x cos(40) = (2.85 + 4.75) a

Acceleration, a = 2.17 m/s^2

b) T = M2 (g - a) = 4.75 ( 9.8 - 2.17) = 36.246 N

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