Tension on Pulley HW: Block A & B Force Analysis

[HydroMarioUSA]

Homework Statement

Block B is positioned on a fixed incline. Attached to block B is a massless, ideal string that runs over a massless ideal pulley and is attached to a hanging block block A at the other end. The mass of block A is 2 kg and the mass of block B is 10 kg. The angle of the incline is 41 degrees.

Homework Equations

(none) Since it never says it's constant velocity we cannot assume Fnet = 0.

The Attempt at a Solution

I drew force diagrams for both A and B, but I don't know how their tensions are related. I'm pretty sure B accelerates towards the left at 3.72 m/s², since the x component of the force of gravity on B is 64.29, and then you subtract 19.6 from that due to tension, and put that all over 12. But you somehow have to have the tension force on B? And it's not constant velocity? I'm confused...

See screenshot.

 

[HydroMarioUSA]

In general, how would you find the tension on a string if both blocks pull on the string?

 

[gneill]

Since the string and pulley are both massless, the string will have the same tension everywhere.

Consider the Free Body Diagram of block A (you could use block B's FBD, too, but block A's is a bit simpler since the slope of the incline is not involved). You have found the acceleration of the block and there are only two forces acting, gravity and the tension.

 

[HydroMarioUSA]

Thank you! The answer is C), right? Because you just need to set up the equation (x-19.6)/2 = 3.72, and x = 27.04.

 

[gneill]

Thank you! The answer is C), right? Because you just need to set up the equation (x-19.6)/2 = 3.72, and x = 27.04.

Yup!