# Potential Energy of a system

## Homework Statement

a 1000kg roller coaster car is initially at to of a rise, a point A. it then moves 135ft, at an angle of 40degrees below the horizontal, to a lower point B. choose the car at point B to be zero configuration for gravitational potential energy of the roller coaster-Earth system. find the potential energy of the system when the car is at points A and B and the change in potential energy as the car moves.

U=mgh

## The Attempt at a Solution

i tried to do 1000*9.8*135
i do not get the right answer. can someone please guide me through step by step how to solve this question. help would be appreciated thx.

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diazona
Homework Helper
Think about this: the 135 ft. that the car moves is not straight down. So it doesn't correspond to 135ft. change in height. The h in the potential energy equation is the change in height, which you need to figure out.

If you're confused, draw a picture of the roller coaster.

umm sory i could not figure out wht yu said..could you please give some some steps of equation to work with? thx

Hey Urgent,

Try using:
U = mgh
U = 1000kg * 9.8m/s^2 (or 9.81) * 41.148m (transferred from feet)

Hey Urgent,

Try using:
U = mgh
U = 1000kg * 9.8m/s^2 (or 9.81) * 41.148m (transferred from feet)
That's not correct. As an above poster said, the height travelled is not 41.148m, that is only the horizontal distance travelled. To figure out the vertical distance travelled, you will need to use some trigonometry. Convert "40 degrees below horizontal" to an angle taken from the positive x-axis. Then use the appropriate trigonometric function to solve for the height. Input this in the above formula, and you have your answer.

Hey Urgent,

Try using:
U = mgh
U = 1000kg * 9.8m/s^2 (or 9.81) * 41.148m (transferred from feet)
You must convert feet to meters as Alcape said but you cannot just plug this into the equation U = mgh since as already mentioned by Diazona, the car moves a total of 135 feet but this is not a vertical height. The car moves along an incline of 40 degrees below the horizontal so draw the diagram and use trigonometric methods to find the effective height. Remember h is the vertical height. Always draw a diagram.

hey umm i got the answer by doing this..
but i do not understand that why do we not multiply it by 1000 aswel? and when i drew the tri diagram..it came out that i should be using 41.148cos40 instead of sin..but i had to use sin to get the right answer...
i am REALLY confused here..please help guys, you got me half way cleared just a little more to go..thanks=]

diazona
Homework Helper
1. Where did 41.148 come from? (I know you know this, but I want you to say it explicitly, then you will see why you don't need to multiply it by 1000)

2. Can you post your diagram?

um i converted 135 feet in metres which gave me 41...nd oh dont worry i know why we use sin now, i drew the diagram wrong before, i made 135 feet the x axis instead of the hypotenuse but yea the only thing that is worrying me know is why did we just do 41sin40 and left the 1000 out?