How Do You Calculate the Kinetic Energy of a Roller Coaster?

In summary, the problem asks for the kinetic energy of a roller coaster at a given point on its track. The coaster has a mass of 4.0 x 10^4 kg and starts at a height of 54m. It then goes down to a height of 15m before going up again to a height of 47m. The initial kinetic energy at the top of the ride is not given, but can be calculated using the given potential energy. From there, the conservation of energy equation can be used to solve for the kinetic energy at the other points.
  • #1
anna sung
46
0

Homework Statement




the rollar coaster is at a height of 15m and going up hill of 47m. its mass is 4.0 x 10^4kg.
find the kinemetic energy of it.


Homework Equations


Ek + Eg = Ek2 + Eg2
PE= mgh
KE= 1/2mv^2


The Attempt at a Solution


i find the potential energy of it which is
PE= 15(9.80)(4.0 X 10^4)
= 5.9 X 10^6 J
PE2= 47(9.80)(4.0 X 10^4)
= 1.8 x 10^7 J

and i said KE + PE = KE2 +PE2
0J + 5.9 X 10^6J = KE2 + 1.8 X 10^7J

the answer is 2.4 x 10^6 J
please tell me what i am doing wrong i am so confused.
 
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  • #2
Anna ----you have not described the problem completely. There is missing information. For example, why did you choose the iinitial kinetic energy at elevation 15 to be 0??
 
  • #3
uh. i don't know that's the only information that the text is given us. it gave us the mass,
and the roller coaster starts from 15m going up a hill of 47m.
and asked to calculate the kinetic energy.
 
  • #4
Was there a sketch? Was the initial height of the coaster given when it started its first drop from the top when at rest? Is the problem asking for KE at 47 m or KE at 15 m? Is the missing info the data from the other problem you asked about, where the coaster height at rest is 54 m??
 
  • #5
oh yes yes. sorry it starts at 54m. and go down to 15m then up again 47m.
yes. there is a sketch. i wanted to asked for only one part of it. cause if i know how to do
point c to b . then i could do the rest.
 
  • #6
Well, that problem is asking for the kinetic and potential energy of the coaster at a given point. Once you know the kinetic and potential energy at one point, and the PE at another point, you can use the conservation of energy equation to solve for the KE at that other point. The KE at elevation 15 can't be zero, that means it would have no speed at that point. Instead, start at point A (the top of the coaster ride) where you know the PE and you should know the KE at that point A where the coaster is at rest. Then continue from there.
 

1. What is the physics behind roller coaster rides?

The main physics principles involved in roller coaster rides are gravity, acceleration, and conservation of energy. Roller coasters use potential energy (stored energy) at the top of the initial hill to propel the train down the track. As the train goes down, the potential energy is converted into kinetic energy (motion energy). Throughout the ride, acceleration and changes in direction are caused by the forces of gravity and the design of the track, which create thrilling drops, twists, and turns.

2. How are roller coasters designed to ensure safety?

Roller coasters are designed with safety as the top priority. Engineers use computer simulations and mathematical calculations to test and refine the design of the track and train. Roller coasters also undergo rigorous testing and inspections before they are open to the public. Safety features such as seat restraints, emergency brakes, and sensors are also implemented to ensure a safe and enjoyable ride.

3. What makes some roller coasters faster than others?

The speed of a roller coaster is determined by the initial height of the first hill, the angle of descent, and the design of the track. The higher the first hill and the steeper the drop, the faster the train will go. Additionally, some roller coasters have magnetic motors or launch systems that give the train an extra boost of speed.

4. How do roller coasters stay on the track and maintain their speed?

Roller coasters use a combination of wheels and friction to stay on the track and maintain their speed. The train is attached to the track with wheels on the top and bottom of each car. These wheels keep the train from derailing and also allow it to navigate through twists and turns. The wheels also create friction, which helps to slow down the train as it travels through the track.

5. Are there any environmental impacts of roller coasters?

Roller coasters use electricity to power their motors and lights, which can have an environmental impact. However, many amusement parks are working towards using more sustainable energy sources such as solar power. Additionally, some parks have implemented recycling programs and other eco-friendly initiatives to reduce their environmental impact. Overall, the environmental impact of roller coasters is relatively small compared to other industries.

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