Mech. engineering; Homework Help; Velocity&BrakeForce

[DTskkaii]

PROBLEM
The problem models a theme park ride similar to the 'Tower of Terror' or Drop Tower (photo below)

http://www.zamperla.com/uploads/product/big/Prodotti/tower-rides/flashtower_main.jpg

The carriage mass is 1532kg and carries a maximum number of 8 riders with an average of 75kg per person. The vehicle drops from the rest position at a height of 110,000mm until the position at 35,000mm from the ground level. After this position, constant brakes are applied to slow the vehicle down. Assuming there is no friction force along the track:
1) Calculate thhe velocity at the position where the brakes start to engage
2) Calculate the deceleration during braking
3) Using the energy method, calculate the brake force and the energy required to bring the carriage to a stop (900mm above ground level)


NEXT STEP
Every time I look at this, I get new ideas about where to begin, but can never really settle, so if someone could point me in the right direction, it would be much appreciated.

1) I feel like this should just be v=ma by the distance, but that seems way too simple.
The total mass should be 2123kg, acceleration due to gravity is 9.8m/s^2, and its over a distance of 75,000mm.

 

[PhanthomJay]

For part 1, the carriage and riders are in free fall. You can use one of the kinematic equations to find the speed after it has dropped 75 m.

For part 2, you need to read part 3 first before calculating the deceleration in the same manner.

 

[DTskkaii]

Thankyou Jay!

I worked out the first part using the kinematic eqn Vf^2 = Vi^2 + 2AD
and got that Vf = 38.34m/s.

Moving to parts 2 and 3, I am a little bit stuck.
I believe that I am supposed to use this 'energy eqn':
U1-2 + T1 + Vg1 + Ve1 = T2 + Vg2 + Ve2 or U1-2 = deltaT + deltaVg + deltaVe
but honestly I don't know how to implement that with the values that I have.
I think just having a bit of a mental block, but if you could explain it a little, that would be amazing.

Cheers.

 

[PhanthomJay]

Thankyou Jay!

I worked out the first part using the kinematic eqn Vf^2 = Vi^2 + 2AD
and got that Vf = 38.34m/s.

Yepp!

Moving to parts 2 and 3, I am a little bit stuck.
I believe that I am supposed to use this 'energy eqn':
U1-2 + T1 + Vg1 + Ve1 = T2 + Vg2 + Ve2 or U1-2 = deltaT + deltaVg + deltaVe
but honestly I don't know how to implement that with the values that I have.

Well OK you started with part 3, and your energy equation looks good provided you understand the terms. T is kinetic energy, V is potential energy, and U is the work done by the braking force (usually designated as W). Calculate the initial kinetic and potential energies at the start of the braking (at 35 m), and the final potential and kinetic energies when it stops (at 0.9 m, where v =0). Then you can find the brake force using the definition of work.

I think just having a bit of a mental block, but if you could explain it a little, that would be amazing.

Cheers.

Don't forget part 2 using an approach similar to the one you used in part 1. And in part 3, the problem asks for the energy (presumably due to the work done by the brake force) required to bring the thing to a stop.

 

[DTskkaii]

Got it all done, hopefully correctly!

Thanks heaps Jay :)