# Velocity of two identical masses over a frictionless pulley

## Homework Statement

"Consider the following arrangement of masses. Mass 1 is connected to mass 2 by a very light string and moves over a frictionless pulley so that both masses move with the same speed and move the same distances (m2 to the right and m1 down).
Assume m1 = 15 kg, m2 = 15 kg and the coef. of kinetic friction is 0.73. The masses start with an initial velocity of 1.00 m/s. What is their speed after moving 0.0100 m?"

## Homework Equations

dE = E1 + E2 = dU1 + dK1 + dU2 + dK2

E1 = dU1 + dK1 (0) = m*g*dH

E2 = dU2 (0) + dK2 = m/2 * (vxf^2 - vxi^2) - friction?????

Friction = - 0.73 * mg * d

## The Attempt at a Solution

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This is where I'm getting stuck.
So do I set

m*g*dH = m/2 * (vxf^2 - vxi^2) - friction

and solve for vf through this equation?

or do I use m/2 * (vxf^2 - vxi^2) - m*g*dH = - friction?

I'm just not sure how to set up the final equation in order to solve for velocity.

In my humble opinion, the best way of solving this (and many similar) problems is not to throw a number of equations on the table and then trying to make sense with them...

I suggest, first of all, to make a clear sketch, with the masses and forces. Then, and in the case of this problem, you should calculate the acceleration by using f = m * a, plugging in the equation the total mass and the net force. And then you can easily find the solution with one of the equations of uniformly accelerated motion...

Unfortunately this is how we're expected to solve these for the time being

I also realized I was missing KE for one of the masses,so now....

I believe that dE = dE1 + dE2

and E1 = dU = mgHf - mGHi and dK = m/2 (vf^2 - vi^2)

and E2 = dU = 0 and that dK = m/2 (vf^2 - vfi^2)

also friction = -(coef friction)*mgd

BiGyElLoWhAt
Gold Member
Here's my honest opinion:
I honestly can't make sense of your equations. It looks like you're trying to use energy's, which you should be able to do, but I don't know what your equations mean. What is E1? What is E2? what is dE? is dE differential energy, whereas E1 and E2 are total energy? If so, how do you get dE = E1 + E2?
I'm assuming mghf is final GPE and mghi is initial GPE, which works, but there's a significant lack of organization IMHO.
Also, forces definitely work in this situation as well, as NTW said.