Acceleration and Tension of two masses on an inclined plane with friction.

[Imuell1]

Homework Statement

In the attachment there is a drawing of the situation.
Mass one = 4kg and Mass two = 5kg
The coefficient of friction between mass one and the inclined plane = 0.24
Find the magnitude of the acceleration of the masses and the tension in the cord.

Homework Equations

F_k= μ_kF_normal
Fnet_x=Mg*Sinϑ-F_k=Ma
F_normal=Mg*Cosϑ

Fnet_x=F_k+Mg*Sinϑ-T=Ma ?

The Attempt at a Solution

a=(Sinϑ-μ_kCosϑ)g... a=9.8(Sin30-0.24*Cos30)=2.86m/s²
t=MgSinϑ-MgCosϑ*μ_k-Ma... t=33.9481-8.1476-14.3=11.5NI'm not sure if the equation I ended up with for acceleration is correct and I am pretty sure that my equation for tension is completely wrong.

The book is giving me the answers a=2.4m/s/s and t=37N

 

[Kruum]

Fnet_x=Mg*Sinϑ-F_k=Ma
Fnet_x=F_k+Mg*Sinϑ-T=Ma

How can this be?

a=(Sinϑ-μ_kCosϑ)g... a=9.8(Sin30-0.24*Cos30)=2.86m/s²
t=MgSinϑ-MgCosϑ*μ_k-Ma... t=33.9481-8.1476-14.3=11.5N

What you're doing here is calculating an acceleration of a system that has a gravity towards sky. And using the acceleration from that to determine the tension of a completely different system.

Hint: Your completely ignoring the hanging mass. You can use it to your advantage.

 

[Phyzicslearn]

Awesome this helped me a lot. GOD bless you all.