# Tension

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#### Mr. Z

##### Senior Member
7+ Year Member
15+ Year Member

For some reason I am having a hell of a time trying to figure out how to handle tension problems. Does anybody have any good "surefire" ways to handle them?

Here is a problem...

You have two masses, mass 1 = M, and mass 2 =2M, hanging across a massless, frictionless pulley. What is the tension in the rope?

#### rCubed

##### taiko master
10+ Year Member
15+ Year Member
did u try drawing a free body diagram, like they did back in physics class?

are both of the masses hanging down or is one on a table and the other hanging down?

#### Mr. Z

##### Senior Member
7+ Year Member
15+ Year Member
they are both hanging down, nothing is touching the system

#### rCubed

##### taiko master
10+ Year Member
15+ Year Member
hmmm...i'm not sure, but i think it goes something like this

the tension in the string should be enough so that the 2M mass can accelerate downwards and the smaller mass can go up.

the smaller mass will experience a force mg downwards and a force of T upwards. since it moves up, then T-mg= ma

the larger mass experiences T upwards but accelerates downwards due to gravity's force, 2mg, so ma= 2mg-T

solving these, i think u get something like 1.3mg=T

hope that helps

#### rCubed

##### taiko master
10+ Year Member
15+ Year Member
just remember,ma is the net force making a body move, so its the difference between the two forces acting on it, if they're acting in opposite directions

#### Mr. Z

##### Senior Member
7+ Year Member
15+ Year Member
that's the correct answer, thanks, i appreciate it.

#### limit

##### Molesting my inner-child
10+ Year Member
15+ Year Member
Always, when analyzing a free body diagram,
ma = (dominant force) - (resistive force)

For example, a 2 kg mass and 1 kg mass compete for who gets the right to slide down, and who gets hoisted into the air.

For the 2kg mass: ma = mg - T
(mg = pulling down, T = resisting the pull)

For the 1kg mass: ma = T - mg
(T = pulling up, mg = resisting)

The equations come out to be as follows:
(m2)a = (m2)g - T
(m1)a = T - (m1)g

Solving for a in one equation and plugging it into the other yields:
T = 4g/3 = 13N

Hope I didn't screw up anywhere