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Consider the frictionless roller coaster shown:

http://i299.photobucket.com/albums/mm286/lanvin12/physics-2.jpg [Broken]

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

Here'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?

http://i299.photobucket.com/albums/mm286/lanvin12/physics-2.jpg [Broken]

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

Here'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?

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