Did I do this question correctly?

[andgabbana]

Consider the frictionless roller coaster shown:
http://i299.photobucket.com/albums/mm286/lanvin12/physics-2.jpg

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 EHere's what I did...

a)
E(T) = E(K) + E(P)
= 1/2(mv^2) + mgh
=1/2(12000 x 0) + (12000 x 9.8 x 95)
=1.1x10^7 J

b)
E(T1) = E(T2)
1/2(V1^2) + gh(1) = 1/2(v2^2) + gh(2)
9.8 x 95 = 1/2(v2^2) + (9.8 x 65)
931 = 1/2(v2^2) + 637
V(2) = 24m/s

c)
1/2(V1^2) + gh(1) = 1/2(v2^2) + gh(2)
9.8 x 95 = 1/2(v2^2) + (9.8 x 25)
V(2) = 37.04m/s

F = mass ([Vf^2 - Vi^2] / [2 x delta d])
= 12000 ([0^2 - 37.04^2] / [2 x 7])
=-3.2x10^4 J

d)
W=E(K)
=1.1x10^7 J

Do you see any mistakes?

 

[LowlyPion]

Welcome to PF.

Mostly good.

c) however must have a stopping force that absorbs all the potential energy, as in d) which you figured correctly.

 

[andgabbana]

Welcome to PF.

Mostly good.

c) however must have a stopping force that absorbs all the potential energy, as in d) which you figured correctly.

Thanks.

I don't think I understand...? I just used the formula F = ma for c). Do I change my answer to a positive? And I'm not sure how to fix d)...

 

[LowlyPion]

Thanks.

I don't think I understand...? I just used the formula F = ma for c). Do I change my answer to a positive? And I'm not sure how to fix d)...

Not quite.

9.8 x 95 = 1/2(v2^2) + (9.8 x 25)

That's incorrect. That gives the KE at the top of the last hill. It's the whole 95 m of PE that needs stopping

 

[andgabbana]

Not quite.



That's incorrect. That gives the KE at the top of the last hill. It's the whole 95 m of PE that needs stopping

c)
I think I need to change my approach?
F = W/d
=(1.1x10^7 J) / 7m
=1.6x10^6 J

d)
W=E(P)
=1.1x10^7 J
...I thought the work required to stop the roller coaster is equal to the total energy of the system?

 

[LowlyPion]

c)
I think I need to change my approach?
F = W/d
=(1.1x10^7 J) / 7m
=1.6x10^6 J

d)
W=E(P)
=1.1x10^7 J
...I thought the work required to stop the roller coaster is equal to the total energy of the system?

It is.

But you could have done it the first way too by taking all the potential as kinetic energy and figuring deceleration.

But not J for force.

 

[andgabbana]

It is.

But you could have done it the first way too by taking all the potential as kinetic energy and figuring deceleration.

But not J for force.

oops... my mistake!
c)
F = W/d
=(1.1x10^7 J) / 7m
=1.6x10^6 N

 

[andgabbana]

It is.

But you could have done it the first way too by taking all the potential as kinetic energy and figuring deceleration.

But not J for force.

Just to confirm, did I finally do c) and d) correctly?

 

[LowlyPion]

Just to confirm, did I finally do c) and d) correctly?

Looks OK. Total energy from potential needs to be accounted for after all.

 

[andgabbana]

Looks OK. Total energy from potential needs to be accounted for after all.

Thank you!