A block with mass mi and a cylinder with mass m2 are connected by a string that

Question

A block with mass mi and a cylinder with mass m2 are connected by a string that passes over a pulley. See figure on bottom right. At the instant shown, both objects have a speed of 2.00 m/s. As they move, the block has a displacement of 50.0 cm up the incline and the cylinder has a dowaward displacment of 50.0 cm. After these displacements, both objects have a speed of 3.00 m/s. During the motion, the friction force removes 0.150 J of mechanical energy from the block and the tension force adds 1.50 J of mechanical energy to the block. Find mi, and m2. Solve by using the energy equation. Do not solve by finding acceleration values. 2.00 m/s block, m friction cylinder, mm 30.0° 2.00 m/s

Explanation / Answer

given block mass = m1
cylinder mass = m2
speed og both objects at the given instant, u = 2 m/s
displacement of block, d = 50 cm up the incline
displacement of cylinder, d = 50 cm downwards
after the displacement, v = 3 m/s

considering the block
energy lost to friction, Ef = 0.15 J
energy gained by tension, Et = 1.5 J
theta = 30 deg
hence energy lost to gravity = m1*g*d*sin(30)
hence
from conservation of energy
1.5 - m1*g*d*sin(30) - 0.15 = 0.5*m1*(v^2 - u^2)
1.5 - 2.4525m1 - 0.15 = 2.5m1
m1 = 0.272589601 kg

now, work done by tension on m2 = -1.5 J
work done by gravity = m2*g*0.5
from work energy theorem
0.5gm2 - 1.5 = 2.5m2
m2 = 1.5/(0.5g - 2.5) = 0.6237 kg

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