Solve Box/Pulley Q with Rollercoaster Q: Acceleration & Tension

[jagerflyger]

A box of mass m2 = 3.4 kg rests on a frictionless horizontal shelf and is attached by strings to boxes of masses m1 = 2.0 kg and m3 = 2.6 kg as shown below. Both pulleys are frictionless and massless. The system is released from rest. After it is released, find the following:

(a) the acceleration of each of the boxes
a1 = m/s2
a2 = m/s2
a3 = m/s2

(b) the tension in each string
T1 = N
T2 = N


I also have a rollercoaster question that I have not been able to solve:

The radius of curvature of a loop-the-loop for a roller coaster is 10.6 m. At the top of the loop, the force that the seat exerts on a passenger of mass m is 0.35mg. Find the speed of the roller coaster at the top of the loop.


I have no idea how to solve this, our book does not give a good related example. I would highly appreciate any help.

 

[ideasrule]

A box of mass m2 = 3.4 kg rests on a frictionless horizontal shelf and is attached by strings to boxes of masses m1 = 2.0 kg and m3 = 2.6 kg as shown below. Both pulleys are frictionless and massless. The system is released from rest. After it is released, find the following:

Did you forget to attach the diagram? Try drawing a free-body diagram for each mass, then writing out Newton's second law (for each mass).

The radius of curvature of a loop-the-loop for a roller coaster is 10.6 m. At the top of the loop, the force that the seat exerts on a passenger of mass m is 0.35mg. Find the speed of the roller coaster at the top of the loop.

Assuming you know the speed at the top, can you find the force the passenger exerts on the seat (the normal force)? Once you have an equation relating force with speed, you can plug in force=0.35mg and get the speed.