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## Homework Statement

Ugh, rusty on my Newtonian Mechanics and need to refresh. I picked out this problem in my book:

Two boxes are on a 30 60 90 triangle. Box 1 is on the 60degree side and Box 2 on the 30degree side. The ramp has two different coefficient of static friction: u1 (for box 1) is 0.5 and u2 is 0.2. Both boxes are tied to a massless rope and a frictionless and massless pulley. Which way will the boxes slide?

Box 1 weighs 200lbs; Box 2 300 lbs.

Assume static initial conditions.

## Homework Equations

F = ma

f= uN

{del}E = rho/epsilon zero (im kidding!)

## The Attempt at a Solution

Ok, so I set up the 1st senario, the boxes slide with box 2 goign down first. Here's the work:

BOX 1)

E Fx = m1 a

T - fs1 - W1 sin(theta1) = m1 a

Box 2)

E Fx = -m2 a

T + fs2 - Wx2 = -m2 a

Combining the two equations (separating T and plugging it in the other):

[g * ( m1*cos(theta1)*u1 + m1*sin(theta1) + m2*cos(theta 2) -m2*sin(theta 2)]/[-(m1 + m2)] = a

a is -8.06 ft/s^2.

Checking my work, I do the complete opposite for the other scenario, where Box 1 goes down:

Box 1)

T + fs1 -W1*sin(theta 1) = -m1 a

Box 2)

T - W2*sin(theta 2) - fs2 = m2 a

Combining them and repeating, I get:

[g * ( m2sin(theta 2) + m2 g sin(theta 2)u2 + m1 cos(theta 1)u1 - m1sin(theta1))]/[-(m1+m2)] = a

a = 5.07 ft/s^2

Well...at least i got the signs to make sense from both accelerations...now where is my mistake as both magnitudes dont match? I cant find it :(

THANK YOU VERY MUCH!