posted by Elizabeth .
Blocks of mass m1 and m2 are connected by a massless string that passes over a frictionless pulley. Mass m1 slides on a frictionless surface. Mass m2 is released while the blocks are at rest. The pulley is a solid disk with a mass mp and a radius R. Use conservation of energy to find the speed of mass m1 after it has traveled a distance x.
I don't understand what to do here. I know conservation of energy is E=K +U...so Ki + Ui = Kf + Uf but I have no idea how to use the rest of the information to do this. I'm also assuming that you need to get the moment of inertia and use it for something...but I don't know what...
The kinetic energy of the system is the sum of the translational energies of the two masses,
(1/2) m1 V^2 + (1/2) m2 V^2
PLUS the rotational energy of the pulley, which is (1/2) I w^2.
The pulley angular speed is w = V/R and the moment of inertia of the pulley is I = (1/2) mp*R^2 Therefore the pulleyrotational energy is
(1/4) mp V^2
After m2 falls a distance x, the system potential energy is reduced by m2 g x
Set m2 g x equal to the total kinetic energy (derived above) to get the velocity as a function of x.