# New to Physics? Get Help on Roller Coaster Speed Question

• Pizall
In summary, the question asked for the speed of a roller coaster after it climbs a 15m high hill on a horizontal track traveling at 20 m/s, with no friction. Using the conservation of energy principle, the final speed was found to be 10.28 m/s. Some confusion arose due to an incorrect algebraic equation and the fact that PE is only negative when an object goes down from the reference point.
Pizall
Hi, new at Physics so go easy.
My question is:
A roller coaster is traveling on a horizontal track at 20 m/s. What is its speed after climbing a hill 15m high? Ignore friction.

any help will be great.

Pizall said:
Hi, new at Physics so go easy.
My question is:
A roller coaster is traveling on a horizontal track at 20 m/s. What is its speed after climbing a hill 15m high? Ignore friction.

any help will be great.

Use the fact that the work done to lift a mass on a height h, equals the change of kinetic energy of that mass.

so it should be 1/2mv2 = 1/2mv1 - mgh
1/2v2 = 1/v1 - gh
v = square root of v1 - 2gh ?
Yes or No?

Pizall said:
so it should be 1/2mv2 = 1/2mv1 - mgh
1/2v2 = 1/v1 - gh
v = square root of v1 - 2gh ?
Yes or No?

No, since this is the square root of a negative number. The work done is mgh, and the change of kinetic energy is 1/2 m(v2)^2 - 1/2 m(v1)^2, where v2 is the speed at the height of 15m, and v1 the initial speed. So, this implies 2gh + (v1)^2 = (v2)^2.

so it come up to v2 = 26.34 m/s

how is going faster going up the hill then what it started out?

Pizall said:
so it come up to v2 = 26.34 m/s

how is going faster going up the hill then what it started out?

I apologize - I overlooked something. The work mgh must be negative.

Pizall said:
so it should be 1/2mv2 = 1/2mv1 - mgh
1/2v2 = 1/v1 - gh
v = square root of v1 - 2gh ?
Yes or No?

Its easier to think of this as consevation of energy-it initially has an energy of 1/2 mv^2, pure KE. Then it gains PE but for conservation to hold, it must lose KE

PE1+KE1=KE2+PE2

but PE1=0 because its at the base height of theis scenario.

KE1=KE2+PE2

1/2mv^2=1/2mv^2+mgh

the mass cacels

solve for v2

Last edited:
JSBeckton said:
Its easier to think of this as consevation of energy-it initially has an energy of 1/2 mv^2, pure KE. Then it gains PE but for conservation to hold, it must lose KE

PE1+KE1=KE2+PE2

but PE1=0 because its at the base height of theis scenario.

KE1=KE2+PE2

1/2mv^2=1/2mv^2+mgh

the mass cacels

solve for v2

Of course, it is clear what you wanted to say, but your equation 1/2mv^2=1/2mv^2+mgh implies 0 = mgh, and there is no 'v2' in it. So, be just a bit more precise when writing something.

Further on, it is not easier to think about this as conservation of energy, it's just another point of view.

Of course, it is clear what you wanted to say, but your equation 1/2mv^2=1/2mv^2+mgh implies 0 = mgh, and there is no 'v2' in it. So, be just a bit more precise when writing something.

Further on, it is not easier to think about this as conservation of energy, it's just another point of view.

I think conservation of energy

PE1+KE1=PE2+KE2

Clearly indicated that there were 2 KE's and therefore 2 velocities. And try not to tell people to be a bit more precise after you have just made a much more careless error. Mine was technical, yours was a mistake.

Furthermore, in introductory physics these concepts are developed through the conservation of energy law-always. I think that any physics teacher would agree that its necessary to understand the laws before trying to link work and PE.

I wouldn't be surprised if the particular chapter he is currently in was titled, "Conservation of Energy"

this is true it chp 4 4.7 Conservation of energy

so PE2 should be negative due to gravity

so KE1 = KE2 - PE2

Think about it this way, the initial energy must be equal to the final energy becasue energy cannot be created or destroyed, it can only change form. This is what's happening here, initially it has KE but no PE (PE is relevant to some reference point, we are choosing the initial reference point to be 0 for simplicity).

Now since it has gone up 15m from the reference 0 it has gianed PE, but where did this PE come from? It cannot be created so it must have come from a change, some of the KE transformed to PE.

Therefore the sum of energy to begin with must equal the sum of energy at the end.

the initial energy

PE+KE1, but at the beginning you have no PE to the reference because we have chosen 0 to be the reference (0-0=0)

so the initial energy becomes

KE1

and that must be equal to the final energy which is:

KE2+PE2

so mathamaically it will look like this

KE1=PE2+KE2
initial=final

solve for V in the KE2 term

Pizall said:
this is true it chp 4 4.7 Conservation of energy

so PE2 should be negative due to gravity

so KE1 = KE2 - PE2

PE is only negative when something goes down from the reference point. It lhas lost PE.

so when I plug in the number I come up with a speed greater then What you started with. Started with 20 and after the math its 26 how is this

V2=sqrt(-2mgh+MV1^2)
=sqrt(-2gh+V2^2)
=sqrt[(-2)(9.81)(15)+20^2)]
=10.28 m/s

My guess is that you are STILL using

KE1=PE2-KE2

it should be

KE1=PE+KE2

you must be subtracting the 400 (the 20^2 term)

In which case you end up with a negative number (-694), should be a hint that you have made a mistake because you cannot take the sqrt of a negative number w/o complex numbers. Your algebra MUST be solid before you can tackle physics, no matter how many calculus/physics/engineering classes you ever take, you will find the without solid algebra, you will always struggle.

Everyone makes mistakes, its recognizing them that makes the difference, often the math will tell you that you need to go back and check something like in this case.

Hope this helps

## 1. What is the formula for calculating roller coaster speed?

The formula for calculating roller coaster speed is v=√(2gh), where v is the speed, g is the acceleration due to gravity (usually 9.8 m/s²), and h is the height of the roller coaster.

## 2. How do I convert units of measurement for roller coaster speed?

To convert units of measurement for roller coaster speed, use the following conversions: 1 m/s = 3.6 km/h, 1 km/h = 0.2778 m/s, 1 ft/s = 0.3048 m/s, 1 mph = 0.44704 m/s. Make sure to use the correct units in the formula for calculating speed.

## 3. Can I use the same formula for calculating speed for all types of roller coasters?

Yes, the formula v=√(2gh) can be used for all types of roller coasters as long as the acceleration due to gravity remains constant. However, for more complex roller coasters with multiple hills and loops, the speed may vary at different points along the track.

## 4. What factors affect the speed of a roller coaster?

The speed of a roller coaster can be affected by factors such as the height of the track, the steepness of drops and inclines, the angle of curves, and the amount of friction between the track and the coaster. Other factors such as air resistance and the weight of the passengers may also play a role.

## 5. How can I use the speed formula to design a roller coaster?

To use the speed formula to design a roller coaster, you will need to determine the desired speed and the height of the track at that point. From there, you can calculate the necessary steepness of the drop or incline. You may also need to consider factors such as safety regulations, passenger comfort, and the overall layout of the roller coaster.

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