# Homework Help: Inclined plane work

1. Oct 12, 2012

### oreosama

1. The problem statement, all variables and given/known data
A block of mass m1 is placed on an inclined plane with slope angle a and is connected to a second hanging block of mass m2 by a cord passing over a small frictionless pulley the coefficient of kinetic friction is uk the system is released from rest with block m2 dropping a distance h.

given m1, a, h, m2, uk
calc the work due to each of the forces on block 1 in moving h
calc the work due to each of the forces on block 2 in moving h
calc the total work on the sys and final speed of the blocks

2. Relevant equations

w = F*d

3. The attempt at a solution

http://i.imgur.com/IxtPw.png

for block1

Wg = -h*mg*sin a

Wt1 = hT

Wn=0

Wff = -h*uk*mg*cos a

Wtot = hT - *mg*sin a - h*uk*mg*cos a

for block2

Wg = mgh

Wt = -hT

Wtot = mgh - hT

hT - *mg*sin a - h*uk*mg*cos a + mgh - hT = 1/2*m*Vf^2 + 1/2*m2*Vf^2 - 0 (start from rest)

sqrt( 2/(m1+m2) * (mg*sin a - h*uk*mg*cos a + mgh)) = Vf

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blocks a, b, c are connected as shown. block a,b,c have same mass m and coefficient of kinetic friction between each block and the surface is uk. block c descends with constant velocity. use 30 for angle of incline. given m h uk determine

work due to forces on A moving h
work due to forces on B moving h
work due to forces on C moving h
solve for uk in terms of the other givens for the system to move at constant speed

http://i.imgur.com/DtwxJ.png

block A

Wff= -uk*mg*h

Wt= T1*h

block B

Wt2 = T2*h
Wg = -mg*sin a*h
Wff= -uk*mg*cos a * h
Wt1 = -T1*h

wtot = T2*h - mg*sin a * h - uk*mg*cos a * h - T1* h

block C

Wg = mg*h
Wt2 = -T2*h

Wtot = mg*h - T2*h

T1*h - uk*mg*h + T2*h - mg*sin a * h - uk* mg* cos a * h - T1*h + mg*h - T2*h = 0(constant speed implies vf v0 are the same meaning no change in kinetic energy right??)

-uk*mg*h - uk*mg*cos a * h = mg*sin a * h - mg*h

-uk - uk*cos a = sin a - 1

-uk(1 + cos a) = sin a - 1
uk = - (sin a - 1/ (1+cos a))

uk = 1/2 / (2+sqrt(3))/2

uk = 1/(2+sqrt(3))

want to be sure im not doing anything horribly wrong thanks for any help.

2. Oct 12, 2012

### SammyS

Staff Emeritus
Wow! A little bit of punctuation, etc. sure helps ! ...along with a few other changes.

3. Oct 14, 2012

### oreosama

didnt seem to be an issue on other posts, sorry

4. Oct 14, 2012

### SammyS

Staff Emeritus
Do you mean, in your other posts?

In many of those you did, at least, use periods.

You probably should take a bit of time to read rules for posting in this Forum. Here are two short excerpts.
General Posting Guidelines
...Pay reasonable attention to written English communication standards. This includes the use of proper grammatical structure, punctuation, capitalization, and spelling. ...