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## Homework Statement

Two packages at UPS start sliding down a 20 degree incline. Package A has a mass of 5kg and a coefficient of friction of 0.20. Package B has a mass of 10kg and a coefficient of 0.15. Package A is in front of Package B according to a diagram given. The distance between Package A and the bottom of the ramp is 2m. How long does it take for Package A to reach the bottom?

## Homework Equations

Kinematics Equations and Free-Body Diagrams yielded the following breakdown of all the forces, given in this form:

(Force), (x hat) +/- (y hat)

uk_(box) is the kinetic friction coefficient.

Ff is the friction force

Fg/Fn are obvious

X_Y is the force X on Y

## The Attempt at a Solution

The very first thing I did was make a table of forces symbolically:

For package A, assume a tilted axis of 20 degrees, with +x in the direction of the packages' motion.

Fn, 0 + Fn

Fg, mg sin 20 - mg cos 20

Ff, -uk_A(Fn) + 0

B_A, B_A + 0

Fnet, (M_a)(A_a) + 0

For package B, assume an identical axis.

Fn, 0 + Fn

Fg, mg sin 20 - mg cos 20

Ff, -uk_B(Fn) + 0

A_B, -A_B + 0

Fnet, (M_b)(A_b) + 0

The acceleation is constrained by A_a = A_b, allowing us to use one acceleration "a".

I then get these final equations for:

Package A X: mg sin 20 - uk_a(Fn) + B_A = M_a(a)

Package A Y: Fn = mg cos 20

Package B X: mg sin 20 - uk_b(Fn) - A_B = M_b(a)

Package B Y: Fn = mg cos 20

Now, I haven't the foggiest idea what to do. All I see are endless streams of unsolvable equations with two unknowns.

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