Solving a Pulley Problem: Finding Rope Tension

[Oliviam12]

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?)

 

[learningphysics]

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

 

[ogb p]

I would approach this problem by first identifying all the known information and variables. From the given information, we know that there are two masses, 10 kg and 2.5 kg, connected by a rope passing over a frictionless pulley. We also know that the mass of the rope itself can be ignored in this problem. The only unknown in this problem is the tension in the rope.

To solve for the tension, we can use Newton's Second Law, which states that the net force on an object is equal to its mass times its acceleration. In this problem, we can apply this law to both masses separately.

For the 10 kg mass, we know that the net force acting on it is 0 N, since it is not accelerating. Therefore, the tension in the rope pulling on this mass must also be 0 N.

For the 2.5 kg mass, we can use the equation F=ma to calculate the net force acting on it. From the given information, we know that the mass is 2.5 kg and the acceleration is 1.962 m/s^2. Plugging these values into the equation, we get:

F = (2.5 kg)(1.962 m/s^2) = 4.905 N

Since this is the net force acting on the 2.5 kg mass, it must also be the tension in the rope pulling on this mass.

Therefore, the tension in the rope in this problem is 4.905 N. It is important to note that the tension in the rope is the same throughout the entire length of the rope, regardless of where we measure it. In this case, we can measure it at either end of the rope or at any point in between and still get the same value of 4.905 N.

In summary, to solve for the tension in a pulley problem, we can use Newton's Second Law and apply it to each mass separately. The net force acting on each mass will be equal to the tension in the rope pulling on that mass. By identifying all the known information and variables, we can determine the correct equation to use and solve for the unknown tension in the rope.