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## Homework Statement

The figure shows two packages that start sliding down a 20 degree ramp from a rest a distance d=6.6m along the ramp from the bottom. Package A has a mass of 5.0kg and a coefficient of friction 0.20. Package B has a mass of 10kg and a coefficient of friction of 0.15. How long does it take package A to reach the bottom?

Illustration shows A closer to the ground on the ramp, with B directly behind (and in contact with) it.

## Homework Equations

## The Attempt at a Solution

I made a free body diagram for each block.

A

---

m = 5kg

mu_k = 0.20

f_k = 9.21 N

n = 46.04 N

F_G_x = -16.76 N

F_G_y = -46.04 N

B

---

m = 10kg

mu_k = 0.15

f_k = 13.82 N

n = 92.1 N

F_G_x = -33.52 N

F_G_y = -92.1 N

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Third law stuff:

F_(a on b) = F_(b on a) = simply 'F' below.

a_a = a_b (acceleration constraint)

---

sum of x for A: -7.55 + F = ma = (5)(a)

for B: -19.7 + F = ma = (10)(a)

solve the system of equations:

a = -2.43 m/s^2

kinematics:

t = 2.335

But -- my answer is wrong. Why?

Thank you