Two blocks connected with a small string pulled up a ramp by string

[TjGrinnell]

Homework Statement

I have two blocks, one with a mass of 20.0 kg and one with a mass of 30.0 kg. I need to move them up a ramp that is inclined at (14)° above horizontal. I put them onto the bottom of the ramp and tie the two block together with a short piece of string that runs parallel to the ramp. I tie a longer piece of string to the 20.0-kg block and use it to pull both blocks up the ramp. The longer string is inclined at 40.0° from horizontal. I pull the longer string, and the blocks move up the ramp with an acceleration of 1.00 m/s^2. Assume the coefficient of kinetic friction between each block and the ramp is 0.150.

Determine the magnitudes of the net force on the 30.0-kg block, the friction force on the 30.0-kg block, and the tension in the short string.

Determine the magnitudes of the net force on the 20.0-kg block, the friction force on the 20.0-kg block, and the tension in the longer string.

I pull on the string while the blocks move 2.40 m. What is the speed of the 30-kg block at the end of that time?

Relevant Equations

Very confused on what to do with the two strings and how to calculate the magnitude of Net forces because of this.

 

[haruspex]

Looks good so far, except that your FBD for the 30kg block has it moving horizontally. Both blocks are going up the ramp.

 

[TjGrinnell]

Looks good so far, except that your FBD for the 30kg block has it moving horizontally. Both blocks are going up the ramp.

I did forget to angle gravity as I did in the 20kg diagram, but even after fixing this I am not sure what formula to use in order to calculate the forces of the tension for either string.
If you could even just give a hint that would be very helpful.

 

[haruspex]

I did forget to angle gravity as I did in the 20kg diagram, but even after fixing this I am not sure what formula to use in order to calculate the forces of the tension for either string.
If you could even just give a hint that would be very helpful.

Your equations for the 20kg block were fine. Correct your 30kg equations to take account of the slope and post them.
Avoid plugging in any numbers for the masses and forces at this stage. Just create variables for the two masses.

When you have all the equations you can proceed to eliminating unknowns and solve them.