Two carts and two masses on one ramp.

[Xarath]

Two "carts" and two masses on one ramp.

Homework Statement

[URL]http://web.ics.purdue.edu/~tkissel/hell.jpg[/URL]

Assume that both of the masses on the ramp are carts with equal masses. Assume no friction in this problem. There is no acceleration. Calculate the unknown mass (on the right side of the problem). The angles are 19 degrees and 32 degrees.

This problem was copied down quickly on the fly, so if I'm missing some crucial information, please let me know.

Homework Equations

Fp=mgsinΘ
F=ma

The Attempt at a Solution

Fw1 + Fp1 = Ft2 + Fp2

(2.5)(9.8) + (9.8)(m)(sin19) = (9.8)(m)(sin32) + (9.8)(m2)

Stuck after this :(

 

[tiny-tim]

Welcome to PF!

Hi Xarath! Welcome to PF!

Assume that both of the masses on the ramp are carts with equal masses. Assume no friction in this problem. There is no acceleration. Calculate the unknown mass (on the right side of the problem). The angles are 19 degrees and 32 degrees.

Call the mass of each cart m, and the unknown hanging mass M.

What are the tensions in each section of rope, starting from bottom left?

 

[Xarath]

I'm not quite sure how the sections of rope are divided. Excuse my ignorance, its been over a year since the last time I did a physics problem like this and I seem to have forgotten this.

 

[tiny-tim]

If a pulley is frictionless, then the tensions on either side of that pulley are the same.

For each block (not accelerating), the difference in the tensions on either side has to balance the "slope" component of the gravitational force.