# Two blocks sliding down an incline

1. Oct 15, 2013

### oneamp

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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

------
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

2. Oct 15, 2013

### NihalSh

you have not taken proper sign with F.

Draw and show, your free body diagram. If you check FBD, it will become clear that the direction of F is different in both the case but you have taken same direction for both mass. Balance forces again to clearly see the mistake.

3. Oct 15, 2013

### oneamp

I will try it out, thank you

4. Oct 15, 2013

okay!