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

AI Thread Summary
The discussion focuses on calculating the acceleration and tension in a system involving two masses on an inclined plane with friction. The first mass is 4kg and the second is 5kg, with a friction coefficient of 0.24. The initial calculations for acceleration yielded 2.86 m/s², while the tension was calculated as 11.5 N, which were both found to be incorrect. The correct answers provided by the book are an acceleration of 2.4 m/s² and a tension of 37 N. A key point noted is the importance of considering the hanging mass in the calculations, which was initially overlooked.
Imuell1
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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


Fk= μkFnormal
Fnetx=Mg*Sinϑ-Fk=Ma
Fnormal=Mg*Cosϑ

Fnetx=Fk+Mg*Sinϑ-T=Ma ?

The Attempt at a Solution



a=(Sinϑ-μkCosϑ)g... a=9.8(Sin30-0.24*Cos30)=2.86m/s2
t=MgSinϑ-MgCosϑ*μk-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
 

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Imuell1 said:
Fnetx=Mg*Sinϑ-Fk=Ma
Fnetx=Fk+Mg*Sinϑ-T=Ma

How can this be?

a=(Sinϑ-μkCosϑ)g... a=9.8(Sin30-0.24*Cos30)=2.86m/s2
t=MgSinϑ-MgCosϑ*μk-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.
 
Last edited:
Awesome this helped me a lot. GOD bless you all.
 

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