Question

# An object with mass M1M1 of 2.85 kg is held in place on an inclined plane...

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.

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

Comment in case any doubt please rate my answer ....

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