A Rope Passes Over an Ideal Pulley Problem!?

Question

A crate of mass m1 on a frictionless inclined plane is attached to another crate of mass m2 by a massless rope. The rope passes over an ideal pulley so the mass m2 is suspended in air. The plane is inclined at an angle = 36.9°. Use conservation of energy to find how fast crate m2 is moving after m1 has traveled a distance of 1.4 m along the incline, starting from rest. The mass of m1 is 10.4 kg and the mass of m2 is 12.5 kg

Answer 1

The way to solve this is to look at energy lost by m2 falling versus the m1 sliding up the incline. Since there is no friction both masses will have the same acceleration and same speed because they are conneted by the rope. The balance of the energy will be kinetic.

for every distance, d, that m1 slides, m2 falls the same distance d.
IN that distance d, m2 loses potential energy equal to
m2*g*d

and m1 gains potential energy
m1*g*sin(36.9)*d

since both masses have the same speed:
(m1+m2)*v^2/2=
m2*g*d-
m1*g*sin(36.9)*d

do some algebra and plug in all the numbers to find v
I will use g=9.81
v=0.707 m/s

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