Two blocks sliding down an incline

[oneamp]

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

------
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

 

[NihalSh]

sum of x for A: -7.55 + F = ma = (5)(a)
for B: -19.7 + F = ma = (10)(a)

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.

 

[oneamp]

I will try it out, thank you

 

[NihalSh]

I will try it out, thank you

okay!

 

[Nickie]

for providing your solution and explanation. However, I am unable to determine why your answer is incorrect without seeing your calculations and assumptions. Please review your work and make sure all equations and variables are correct. Additionally, it may be helpful to double check the units and make sure they are consistent throughout your calculation. If you are still having trouble, please provide more information so I can assist you further.