A new rollercoaster at a famous amusement park has just opened up. It has a large vertical drop near the end, and at some particular point, your velocity is 82.7mi/hr. At this same point, you calculate that the potential energy due to gravity is 32.9kJ. At the top of the drop, however, you knew that the potential energy due to gravity was 422.5kJ at the moment you were not moving. Find the mass of the rollercoaster cart you are riding in. (You may neglect any changes to internal energy, including friction and air resistance/drag. Assume there is no radiant energy).

Question

anonymous · Answer

???

anonymous · Answer

@iambatman

dan815 · Answer

^

anonymous · Answer

ok so what do i plug in ?

anonymous · Answer

potential energy due to gravity is 32.9kJ.

festinger · Answer

There are many ways to write conservation of energy, but I take:
$$(KE_{1}-KE_{2})+(GPE_{1}-{GPE}_{2})=0$$
where the subscripts 1 and 2 are some arbitrary point. As an example, if 1 is top and 2 is bottom it will appear as
$$(KE_{top}-KE_{bottom})+(GPE_{top}-{GPE}_{bottom})=0$$
Note this this is not the case for this question. It is just an illusration of what the subscripts mean.

Here, $$GPE=mgh$$
and 
$$KE=\frac{1}{2}mv^{2}$$

But since you are given what the GPE is you can directly put them in:
$$(KE_{top}-KE_{2})+(422.5kJ-32.9kJ)=0$$
What is the KE at the top? If you can't answer that think of what is the speed and recall the formula for KE. For KE2, you have to use the formula again but make sure to convert mi/hr into m/s before plugging in the equation. KE2 will have something you cannot plug in: mass. Leave that be and solve for the conservation of energy equation.

anonymous · Answer

would it be the 32.9 ?

anonymous · Answer

ooo but wait - At the top of the drop, however, you knew that the potential energy due to gravity was 422.5kJ at the moment you were not moving. so 0 since not moving?!

festinger · Answer

Yes, at the top KE is 0 since it is not moving (for that instance).

anonymous · Answer

so do i plug that into the KE=1/2mv^2 or the other formula

festinger · Answer

you have to use both.

festinger · Answer

currently the equation should look like:
$$(0-KE_{2})+(422.5kJ-32.9kJ)=0$$
You have to put in 1/2mv^2 into KE2 and solve for mass since you know the speed v.

dan815 · Answer

, your velocity is 82.7mi/hr, 32.9kJ.  422.5kJ  not moving

dan815 · Answer

Energy is not lost so u can just write it out

dan815 · Answer

x=422.5-32.9
1/2mv^2=x
convert.. mi/hr into m/s
87mi/h= 87*1/3600 * 1.6 m/s=v
plug and solve
m=?

anonymous · Answer

0.570160376865
did 1/2(M)(36.968)^2=389.6

anonymous · Answer

yes - 36.970208 Meters per Second?