Calculating Tension and Acceleration in a Two-Pulley System

[savelieffd]

Hope someone can help me with this one. I have two blocks with m1 and m2 connected to two pulleys. I need to figure out T1, T2, a1, and a2 using only the values of g, m1, and m2. But I've been unable to come up with an equation that will work with it. I have a picture attached.

I tried using the following expression: ((m2*g)-(m1)*g)/(m1+m2) to find a1, but that didnt work and I am stumped. does anyone have any ideas? any help would be great!


http://img292.imageshack.us/img292/374/p438ym8.gif

 

[Doc Al]

Instead of trying to force fit some derived formula, use Newton's 2nd law. Analyze the forces acting on each mass and set up equations of motion for each. Hint: How does the acceleration of m1 compare to m2? How does the tension T1 compare to T2?

 

[savelieffd]

well i know that a1 = 2 *a2, and i know that T2 = 2 *T1. But i don't know how i can put these together to work with Newtons 2nd law.

 

[Doc Al]

well i know that a1 = 2 *a2, and i know that T2 = 2 *T1.

Good.

But i don't know how i can put these together to work with Newtons 2nd law.

What forces act on each mass? Set the net force equal to ma! (Careful with signs.)

You'll get a separate equation for each mass. Combine to solve for your unknowns.

 

[savelieffd]

Would m1 accelerate at 2*g? BEcause of the pulley?

 

[Doc Al]

Don't guess or try to do it in your head. Write the equations and then solve them.

 

[savelieffd]

Because of the frictionless surface, would the net force be just the tension? If so, would a1 = ((m1*m2*(Sin(theta)+1)*g)/(m1+m2))/m1) and Sin(theta) equals 1 becuase theta is equal to 90?

 

[Doc Al]

Because of the frictionless surface, would the net force be just the tension?

Net force on what? Which tension?

(Write the equations.)

 

[savelieffd]

Aha, revelation. Looks like i figured it out!

T1 = (m1*m2)/(2m1 + .5m2)*g

then

T2 = (m1*m2)/(m1 + .25m2)*g

yes?

and using the equations of tension,

a1 = t1/m1 = (m2*g)/(2m1 +.5m2)

and so a2 = half of a1 which is = (m2*g)/(4m1+m2)

and in the end we get a correct answer for all of them! Brilliant!

Thanks so much!