# Pulley and friction problem

## Homework Statement

At the instant shown the 100-lb block A is moving down the plane at 5 ft/s while being attached to the 50-lb block B. If the coefficient of friction is µk = 0.2, determine the acceleration of A and the distance A slides before it stops. Neglect the mass of the pulleys and cables.
http://0pcode.ath.cx/photo.jpg [Broken]
The picture was taken with my phone, so the triangle under A is kinda hard to see. Its hypoteneuse is 5, the vertical leg is 3, and the horizontal leg is 4.

## Homework Equations

F = ma
m = W/g (slug)
F(friction) = µ*N
V$$^{2}$$ = V$$^{2}_{0}$$ + 2ad

## The Attempt at a Solution

I tried finding the frictional force of block A first, which I calculated to be 16-lb. I then found the tension force in the rope at A, which I calculated to be 12.5-lb. I then took those two values and added them together, and got an acceleration value of 9.12ft/s^2. And I found the distance the block slides to be 1.37 feet.
The answers are supposed to be 1.29ft/s^2, and 9.70 feet. I don't know where I went wrong, any help would be appreciated :) Thanks.

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tiny-tim
Homework Helper
Hi AcecA! … I tried finding the frictional force of block A first, which I calculated to be 16-lb. I then found the tension force in the rope at A …
Nooo … to find the friction force, you first need to find the normal force, and that will depend on the acceleration.

In this sort of problem, everything depends on everything else you can't "start at one end and work your way across" (the way we do in most mechanics problems )

Hint: call the tensions T1 and T2, and the distance along the slope x, and then use good ol' Newton's second law twice, once for A and once for B. 