Physics roller coaster question

[meso]

Homework Statement

Consider the frictionless roller coaster shown below.( the picture Is attached below)

If a 12 000 kg car starts at rest from Point A, calculate
a) the total energy of the system

b) the speed of the car at point B


c) the force that must be applied to bring it to a stop at point E


d) the work done to bring it to a stop at point E

Relevant Equations

Eg=mgh
Ek=1/2mv^2
W=Fcos0 x d
Etotal= Ek1 + Eg1
W= delta Ek ( Ek2 – Ek1)

I am stuck at C and D. I tried to solve D by applying W= delta E
W= Etotal
F x d= 11172000
F= 11172000/7
But I am not sure if it is right

 

[haruspex]

I am stuck at C and D. I tried to solve D by applying W= delta E
W= Etotal
F x d= 11172000
F= 11172000/7
But I am not sure if it is right

Looks right.

 

[Lnewqban]

The problem is not specific about the deceleration distance, but assuming the whole last 7 meters are used for stopping the 12 000 Kg car, then one needs to solve d) first in order to be able to solve c) in the way you have shown.
That is a huge stopping force.

 

[meso]

The problem is not specific about the deceleration distance, but assuming the whole last 7 meters are used for stopping the 12 000 Kg car, then one needs to solve d) first in order to be able to solve c) in the way you have shown.
That is a huge stopping force.

I found the force required to stop the roller coaster to be 1596 000 N, but I am not sure neither confident about my solution.

 

[Lnewqban]

I found the force required to stop the roller coaster to be 1596 000 N, but I am not sure neither confident about my solution.

Your solution is correct.
It is only that the problem is not very complying with real life.
With no resisting friction or aerodynamic drag, the speed at ground level would be 155 km/h (43.17 m/s in free-fall).
The corresponding deceleration during those 7 meters would be ##-133~m/s^2##, which equals 13.6 G, which would be too much for comfort.

 

[meso]

Thanks. Also, that makes sense but I am doing physics grade 12, so they disregard some factors for the sake of this course.