M1 30° M2 9) The figure below shows a block with mass M1 20 kg, sitting on a smo

Question

M1 30° M2 9) The figure below shows a block with mass M1 20 kg, sitting on a smooth incline plane that makes a 45 degree angle with the horizontal. The mass M1 is attached to a light cord that runs over a frictionless pulley, that routes the string to a second block, with mass M2, with unknown mass, hanging vertically, as shown. When the masses are released, the mass M2 descends 12 meters in 3 seconds. Calculate the magnitude of M2 required to cause the motion described. Choose from the closest answer bellow. A) M2 27 kg; B) M2 54 kg; C) M2 14 kg; or D) M2 81 kg M1

Explanation / Answer

s = 1/2at^2

12 = 1/2 x a x 3^2

a = 2.67 m/s^2

By FBD

net pulling force is (m1 + m2)a

M2*g - M1*g*sin(45) = (M1 + M2)*a

M2*(g - a) = M1*(a + g/sqrt(2))

M2 = (2.67 + 6.93) / (9.81 - 2.67)

M2 = 26.93 kg

Ans :- A)

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