Simple Tension Problem: Calculating Tension and Acceleration

[physicsnewb7]

Homework Statement

Two masses are suspended by a frictionless string on a frictionless pulley, one with mass 75 kg and the other 100 kg.
What is the tension of the string and the acceleration of the masses

The Attempt at a Solution

My attempt was to say since mass A, 75 kg, was 75 percent of mass B, then the acceleration of mass B would be 25 percent of the acceleration of gravity 9.8 m/s^2.
so it would be roughly 2.5 m/s^2. Since the acceleration was 2.5 m/s^2, I thought the tension would be equivelant to the force of the mass of both A and B times the acceleration 2.5 m/s^2 ie. F=ma. Clearly there is something wrong with this approach. What is it that I'm missing? is there a generalized formula for tension of a string?

 

[tiny-tim]

Two masses are suspended by a frictionless string on a frictionless pulley, one with mass 75 kg and the other 100 kg.
What is the tension of the string and the acceleration of the masses

Hi physicsnewb7!

Call the tension T, and then apply good ol' Newton's second law twice (to each mass separately) …

since the acceleration, a, of each mass is the same (in opposite directions), you can solve for T and a

 

[physicsnewb7]

so if a I say a100kg=100g-T and a75=T-75g, where a is the acceleration, g is gravitational acceleration and T is tension, then add the two equations together to get a=25/175g=1/7g and then solve for T by plugging a in the equations. Is that right? would the acceleration be 1/7g? any help would be greatly appreciated!

 

[tiny-tim]

so if a I say a100kg=100g-T and a75=T-75g, where a is the acceleration, g is gravitational acceleration and T is tension, then add the two equations together to get a=25/175g=1/7g and then solve for T by plugging a in the equations. Is that right? would the acceleration be 1/7g? any help would be greatly appreciated!

Hi physicsnewb7!

Yes, that's right!

Another way of doing it is to imagine that the string is straight …

there's 100g of force pulling it left, and 75g pulling it right, making a total of 25g … since the total mass is 175, that makes a = 175g/25 = g/7.

(or, if you're not interested in the tension, you could even use conservation of energy and a = dv/dt = v dv/dh = 1/2 d(v²)/dh)

 

[physicsnewb7]

Thank you so much TinyTim for responding and helping.