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

Question

An object with mass M1M1 of 2.85 kg is held in place on an inclined plane that makes an angle of 40.0° with the horizontal (see figure below). The coefficient of kinetic friction between the plane and the object is k=0.542k=0.542. 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.

a)Calculate the initial acceleration of the system once the objects are released. (Express your answer to three significant figures.)

b)Calculate the tension in the string once the objects are released. (Express your answer to three significant figures.)

Explanation / Answer

M1 has a downslope component of weight

F1 = mgsin

F1= 2.85 kg x 9.8 m/s^2 x sin40º

F1= 18 N

M2 weighs,

F2 = mg = 4.75 kg x 9.8 m/s^2 = 46.6 N

The friction force points downslope with magnitude

Ff = µmgcos

Ff = 0.542 x 2.85 kg x 9.8 m/s^2 x cos40º

Ff = 11.6 N

Net motive force Fnet = 46.6 N - 11.6 N - 18 N = 17 N

acceleration a = Fnet / mtotal = 17N / 7.60 kg

a = 2.24 m/s^2

tension T = m(g - a) = 4.75kg x (9.8 - 2.24)m/s^2

T = 35.9 N

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