# AP Physics C Mechanics: Conservation of Energy Problem

SHawking

## Homework Statement

A block of mass m hangs on the end of a cord and is connected to a block of mass M by a pulley arrangement. (m hangs freely, M is attached to the string, and is on a table top. (So m is attached to a string which goes therough a pulley changing the strings direction 90 degrees where it goes through a pulley attached to M and back to a block on the table. So, for every unit m moves M moves two, sorry this is hard to explain without a diagram.) Using energy considerations,
a.) find an expression for the speed m as a function of the distance fallen,
b.) repeat the previous assuming that a friction of µ acts on the block on the table. Assume everything is at rest.

I don't think it is pertinant, but, it has a few latter parts which are calculus based that I was able to get using what I know to be the answer to a and b.

## Homework Equations

U=mgh
K=.5mv^2
F=µN (N=mg)
MAybe some kinematics equations for part B?)

## The Attempt at a Solution

I think I got part a, just a math error.

Using the formula K(m)+K(M)+U2(m)=U(m) U2 being the new potential energy after a change in distance, and then
1/2mv^2+1/2m(v/2)^2(It will be half the speed of m)+mgh2=mgh
and solving for M, I think I am getting the correct answer

For B, that is including coefficient of friction I think I am having a lot more trouble. My first attempt was to attempt to factor in the friction into the velocity, but that got an incorrect answer. I then tried tog et force, and integrate (integral of NetForce dx=∆K)

Can anyone point me in the right direction?