Projectile Motion- SPH4U Grade 12 Physics

[AkadouYoroi]

Homework Statement

A pulley device is used to hurl projectiles from a ramp (uk=0.26) as illustrated in the diagram. The 5.0-kg mass is accelerated from rest at the bottom of the 4.0 m long ramp by a falling 20.0-kg mass suspended over a frictionless pulley. Just as the 5.0-kg mass reaches the top of the ramp, it detaches from the rope (neglect the mass of the rope) and becomes projected from the ramp.
*there should be an attached image at the bottom*

a) Determine the acceleration of the 5.0-kg mass along the ramp. (Answer: 6.4 m/s2 up the ramp)

b) Determine the tension in the rope during the acceleration of the 5.0-kg mass along the ramp. (Answer: 68 N along the ramp)

c) Determine the speed of projection of the 5.0-kg mass from the top of the ramp. (Answer: 7.2 m/s)

d) Determine the horizontal range of the 5.0-kg mass from the base of the ramp. (Answer: 9.5m)

The Attempt at a Solution

a) I know that to find acceleration, i need to find the total net force of the system and divide by the two masses. I found the Fgx for the 5.0 kg object using (5.0)(9.0)cos30, the Fg for 20.0 kg object (20.0)(9.8), and the Ff of the system, using uFn. I don't get the quite answer. I am not sure if I missed any calculations, or my components are not correct.

b) I believe this might have been a component I've missed in part A, but I do not really know how to start off the tension calculation. I believe it involves using the frictional force to calculate the tension, but I am not sure.

c) I tried solving using the Vfy=V1y+ayt equation, and finding the value of t using y=1/2ay(t)2. (Sorry about not doing subscripts). I end up with an answer that's about 3.0s. But I think its because I might be confusing myself, because I've never done a projectile motion that involved mass in it.

d) Determine the horizontal range of the 5.0-kg mass from the base of the ramp.
Im not sure where to start, since it involves masses. I am not too sure if the object accelerated from rest in the question indicates something I should be doing.

Thank you so much.
The answers are posted with the questions, but I had a tough time getting to the answer, or not knowing how to start it.

 

[Doc Al]

a) I know that to find acceleration, i need to find the total net force of the system and divide by the two masses. I found the Fgx for the 5.0 kg object using (5.0)(9.0)cos30, the Fg for 20.0 kg object (20.0)(9.8), and the Ff of the system, using uFn. I don't get the quite answer. I am not sure if I missed any calculations, or my components are not correct.

The best way to attack this problem is by analyzing each mass separately. What forces act on the 5 kg mass? On the 20 kg mass? Apply Newton's 2nd law to each, which will give you two equations. That will allow you to solve for the two unknowns: tension and acceleration.