Energy & Momentum Homework: Frictionless Roller Coaster from A-E

[Mary1910]

Homework Statement

Consider a frictionless roller coaster.
Point A=95m
Point B=65m
Point C=65m
Point D= 25m
Point E= Is 7m from the end of the course where the height is 0

If a 1200kg 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

The attempt at a solution

a)
The total energy in a system is the sum of all its kinetic energy and potential energy
Et=total energy

Et=½mv^2 + mgh

=½(1200kg)(0)^2 + (1200kg)(9.8m/s)(95)
=0 + 1117200
=1.1 x 10^6 J

b)
m=1200kg
d=(95m-65m)=30m
g=9.8m/s

vf^2=vi^2 + 2aΔd

=0+2(9.8m/s)(30m)
=√588
=24 m/s

Ok, now question c) and d) is where I get stuck.

I think I need to use this equation W=FcosΘΔd for part d)...but I'm not sure.

Any help for question c) and d) would be greatly appreciated. Thank you :)

 

[Dr. Courtney]

Forget momentum. You got lucky on B. You should really use conservation of energy rather than a kinematic equation.

C and D, you need to use the work-energy theorem.

 

[Mary1910]

Ok so is that W = KEf - KEi? Where KE = ½mv^2.

So Would it be W=½mv^2f - ½mv^2i

W=½(1200kg)(0)^2 - ½(1200kg)(43m/s)^2

=0 - 1109400
= -1109400 J
= -1.1 x 10^6 J

Is this closer for d)?

 

[Dr. Courtney]

That's the right idea.

 

[Mary1910]

Thanks,
Im still not sure on how to solve for force though. This is pretty new to me.

for part d) since -1.1 x 10^6 J of work was done to bring the car to a stop at point E, would 1.1 x 10^6 J of force have to be applied to bring the car to a stop for part c)?

 

[Dr. Courtney]

No, Energy is measured in Joules (or Newton Meters). Force is measured in Newtons.

You have used the Work-Energy theorem to compute the work.

Now remember how to relate work, distance, and force to compute the force.

 

[Dr. Courtney]

No, Energy is measured in Joules (or Newton Meters). Force is measured in Newtons.

You have used the Work-Energy theorem to compute the work.

Now remember how to relate work, distance, and force to compute the force.

 

[Mary1910]

Ok,

W=F•Δd
∴F=(W) / Δd

F= (1109400 J) / (7m)

=158485.71 N
=1.6 x 10^5 N

better?