How Do You Solve This Pulley and Friction Problem?

[AcecA]

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
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.

 

[tiny-tim]

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.

 

[nlightner]

I would like to point out that there seems to be some confusion in the given problem. The values provided for the hypotenuse and the vertical leg of the triangle do not match the given information of the block A's motion. Additionally, the given values for the friction coefficient and the mass of the blocks do not align with the calculated values.

Assuming that the given values are correct, I would suggest double-checking your calculations and equations. It is also important to consider the direction of the forces and the motion of the blocks. The block A is moving down the plane, which means the friction force will act in the opposite direction. The tension in the rope should also be considered in the equation for block A's acceleration.

Furthermore, it is important to consider the pulley and cable system in the problem. The mass of the pulleys and cables should also be taken into account, as they will affect the overall motion and acceleration of the blocks.

In conclusion, it is important to carefully analyze the given problem and consider all the relevant factors in order to accurately solve the problem. Double-checking calculations and equations is also crucial in order to avoid errors.