Solving a Pulley Problem: Finding Rope Tension

AI Thread Summary
The discussion centers on calculating the tension in a rope connected to two masses, 10 kg and 2.5 kg, over a frictionless pulley. The user correctly identifies the acceleration of the system as 1.962 m/s² using the formula A=F/M, where F is the force acting on the masses. There is confusion regarding the application of tension formulas, specifically whether to use T = m(g + a) or T = m(g - a), and which mass to apply. Clarification is provided that the force of gravity on the 2.5 kg mass is indeed 24.525 N, and that tension can be determined using T = ma for the top mass. Understanding these principles is crucial for solving the pulley problem effectively.
Oliviam12
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I have a question on a pulley problem; the problem looks like this:

M (10) ...O
------------|...
xxxxxxxxxxxx|...
xxxxxxxxxxxx|m (2.5)
xxxxxxxxxxxx|...
With the: O being a frictionless pulley
- being solid ground
. Being a rope
M a mass of 10 kg
m a mass of 2.5 kg

I need to find the tension in the rope.

I have found the acceleration of the masses by:
FM=ma
=10*0
=0 N

Fm=2.5 *9.81
Fm= 24.525 N

A=F/M
A=(24.525 N)/ (10+2.5)
A= 1.962 m/s^2

I know I need to use the equation T= m(g+a) or T=m(g-a) but, I am not sure which one or what mass I am supposed to use. (maybe 2.5 kg?)
 
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I don't understand these parts:

"FM=ma
=10*0
=0 N"

"Fm=2.5 *9.81
Fm= 24.525 N"

24.525 is the force of gravity on m... is that what you meant here?

You have the right acceleration... The top mass has only one force acting on it.. tension... so Tension = ma
 

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