How Does the Tension Equation Differ with Inclined Planes and Multiple Masses?

[ThatGermanDude]

[SOLVED] Tension Equation Question

Hi, this is my first post here.

i came across an equation for tension in my textbook that i have never seen before and wanted to ask if someone could explain it to me.

Tension = g * (m$$^{1}$$ * m$$^{2}$$) / (m$$^{1}$$ + m$$^{2}$$) * (1 + sin$$\Theta$$)


i always thought Tension is equal to the sum of the forces applied to the rope.


the context is following problem:

a block of mass m$$_{1}$$ is at rest on an inclined plane at $$\Theta$$ degrees with the horizontal. it is connected with a block of mass m$$_{2}$$ that is hanging of the inclined plane hrough a massless rope.


so the way i thought about tension it would just be

Tension = m$$_{1}$$ * g * sin$$\Theta$$ + m$$_{2}$$ * g

but that gives me a different answer and i don't know what's wrong.

so any help is appreciated.

 

[Doc Al]

i always thought Tension is equal to the sum of the forces applied to the rope.

The tension is the force exerted on each end of the rope (and exerted by each end of the rope). Note that for a massless rope, the force at each end is the same--the tension is the same throughout the rope.

so the way i thought about tension it would just be

Tension = m$$_{1}$$ * g * sin$$\Theta$$ + m$$_{2}$$ * g

Realize the the weights are forces that act directly on the masses, not the rope. To find the tension in the rope, analyze the forces on each mass: On m1 there is gravity and the rope tension; on m2 there is also gravity and rope tension. Apply Newton's 2nd law to each mass and solve for the tension.

 

[Dick]

Draw a force diagram for the two blocks with the blocks having an acceleration 'a' and a tension 'T'. Then actually solve for T and a. Assuming it's the sum of the two gravitational forces is just jumping to conclusions.

 

[ThatGermanDude]

i did all that and then end up with the equation i stated before.
in this case the only acting forces are th weights since the slope is frictionless.

 

[Doc Al]

Specify the forces acting on each mass and the resulting equations you got from applying Newton's 2nd law.

 

[ThatGermanDude]

i figured it out. the mistake i made was using gravity instead of acceleration, like i should have, to find tension.

thanks