Homework Help: Finding tension between two objects with different fs

1. Nov 25, 2014

Potatochip911

1. The problem statement, all variables and given/known data
What is the tension in the strap which the boy uses to hold onto the pack?
Mass of Boy=45kg
Mass of Pack=25kg
θ=42°
Coefficient of kinetic friction between boy and incline=0.35
Coefficient of kinetic friction between pack and incline=0.48
Acceleration of boy=4m/s^2

2. Relevant equations
Fnet=F1+F2+F3...+Fn
F=ma

3. The attempt at a solution
Mass of boy=M
Mass of pack=m
Fpb=parallel force of boy
etc...

Fpb=Mgsinθ
Fpp=mgsinθ
fsb=0.35Mcosθ
fsp=0.48mcosθ

a(M+m)=Fpb+Fpp-fsb-fsp-T

I'm really confused as to how to solve this since both acceleration and tension are unknowns. I've tried doing a lot of things to try and get a value for acceleration but none of them have given me the correct answer which is T=15N.

2. Nov 25, 2014

Simon Bridge

Draw free body diagrams for the boy and the pack separately.
Apply $\sum \vec F = m\vec a$, and you'll end up with four equations with four unknowns which have to be true simultaneously.

Last edited: Nov 26, 2014
3. Nov 26, 2014

Potatochip911

Thanks so much! Can't believe I messed that up haha. If anyone wants the solution

1. Fpb-T-Fsb=Ma
2. Fpp+T-Fsp=ma

FpB+Fpp-Fsb-Fsp=Ma+ma
a=(FpB+Fpp-Fsb-Fsp)/(M+m)
After putting values in
a=3.67m/s^2

Rearranging first equation

T=Fpb-fsb-Ma
T=15N