Two Masses, a Pulley, and an Inclined Plane (Figure 1) Block 1, of mass m1, is c

Question

Two Masses, a Pulley, and an Inclined Plane

(Figure 1) Block 1, of mass m1, is connected over an ideal (massless and frictionless) pulley to block 2, of mass m2, as shown. Assume that the blocks accelerate as shown with an acceleration of magnitude a and that the coefficient of kinetic friction between block 2 and the plane is .

Part A

Find the ratio of the masses m1/m2.

Express your answer in terms of some or all of the variables a, , and , as well as the magnitude of the acceleration

due to gravity g.

Explanation / Answer

m1 g is the pulling force.
The other pulling force is m2g sin along the plane downward.
Since m2 is moving up frictional force
m2g cos is also acting along with m2g sin

The net pulling force of the system is
m1g - m2g sin - m2g cos and this pulls the two masses
m1 and m2 with an acceleration a.

m1g - m2g sin - m2g cos = (m1 +m2) a
Dividing by m2 and expressing m1/m2 as K
Kg - g sin - g cos = (K + 1) a = Ka + a
K ( g- a) = a +g (sin + cos)
m1/m2 = {a +g (sin + cos) } / ( g- a)

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