# Finding Acceleration and Tension, With Friction

1. Sep 28, 2011

### VACA

1. The problem statement, all variables and given/known data
In figure P4.52 (below), the coefficient of kinetic friction between two blocks shown is 0.30. The surface of the table and the pulleys are frictionless. (a) Draw a free-body diagram for each block. (b) Determine the acceleration of each block. (c) Find the tension in the strings.

2. Relevant equations
Since all accelerations are equal:
-a2 = a3 = -a10

Also, a = F/m
And for gravity: Fg=m (in kg)*9.8

3. The attempt at a solution

For the force diagram I know that the 2kg block will have T1 pulling it to the left and friction pulling it to the right. The 3kg block will have T2 pulling it to the right and friction and T1 pulling to the left. And the 10kg ball, sphere, whatever, has T2 pulling upward and gravity pulling downward.

Fk is 5.88N since Fn is 19.6N (0.3*19.6).
And Fg is 98N.

- (5.88N - T1) / 2kg = (T2 - T1 - 5.88N) / 3kg = - (T2 - 98N) / 10kg Got rid of my fractions, LCD of 30...

15T1 - 88.2N = 10T2 - 10T1 -58.8N = 294N - 3T2 Used the first two equations to solve for T2

2.5T1 - 2.94N = T2 Plugged in to the last 2 equations and ended up getting...

25T1 - 29.4N - 10T1 - 58.8N = 294N - 7.5T1 + 88.2N

T1 = 20.906N

The correct answer for T1 is 17N. I've looked over my work and couldn't find a mistake in my math, though I'm sure there is. I need help figuring out where I messed up.

I hope this isn't just some dumb mistake because I've spent so long on this single problem.