Conservation of Enery (roller coaster)

In summary, the conversation is about a question regarding a roller coaster with a circular vertical loop. The question asks for the difference in apparent weight between the top and bottom of the loop, which is stated to be 6 times the person's weight. The conversation includes equations and an attempted solution, but the person is unsure of how to proceed and asks for help. Another person questions if the problem is stated correctly and suggests that it is easy to show the sum of apparent weights at the top and bottom is 6 times the person's weight.
  • #1
Carpe Mori
19
0
ok i this question has been asked but whoever asked it did not show work therefore did not have it answered so here we go my attempt!

Homework Statement



Show that on a roller coaster with a circular vertical loop the difference in your apparent weight at the top of the loop and the bottom of the loop is 6 g's that is 6 times your weight. ignore friction.

h = height of start of roller coaster
R = loop's radius


Homework Equations



PE = KE
a = v^2/R


The Attempt at a Solution



at the top of loop: mgh = mg2R + .5mv^2
solved for velocity v^2 = 2g(h-2R)
centripital acceleration is a = v^2/R ---> a = 2g(h-2R)/R

also i knew from another problem that minimum h had to be 2.5R to be able to go through the whole loop and stay on track so...

a = g? haha yeah i am lost i have no idea what to do. I am trying to teach this course to myself and i am really struggling without a teacher. Please help?
 
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  • #2
Are you sure you have the problem stated correctly? It's pretty easy to show the sum of the apparent weights at the top and bottom is 6mg.
 
  • #3
yes problem is state correctly and do tell how maybe I am just over thinking it.
 

Related to Conservation of Enery (roller coaster)

1. What is conservation of energy and how does it apply to roller coasters?

Conservation of energy is a fundamental physical law that states that energy cannot be created or destroyed, only transferred or transformed. In the context of roller coasters, this means that the total amount of energy at any point on the track must remain constant, with energy being converted between potential and kinetic forms.

2. How does the conservation of energy principle affect the design of roller coasters?

The conservation of energy principle plays a crucial role in the design of roller coasters. Engineers must carefully consider factors such as the height and shape of the track, the weight and speed of the train, and the forces acting on the riders to ensure that the total energy remains constant and the ride is both thrilling and safe.

3. Can you explain the transfer of energy on a roller coaster?

As a roller coaster car moves along the track, energy is constantly being transferred between potential and kinetic forms. At the peak of a hill, the car has the most potential energy, which is then converted to kinetic energy as it accelerates down the hill. At the bottom of a hill, the car has the most kinetic energy, which is then converted back to potential energy as it climbs the next hill.

4. How does friction affect the conservation of energy in roller coasters?

Friction is the force that opposes motion and it can have a significant impact on the conservation of energy in roller coasters. Friction causes the train to lose some of its energy as heat, which means that the total energy at the end of the ride will be slightly less than at the beginning. Engineers must account for this energy loss when designing the ride to ensure that it remains safe and enjoyable.

5. Does the conservation of energy principle apply to all types of roller coasters?

Yes, the conservation of energy principle applies to all types of roller coasters, including traditional steel coasters, wooden coasters, and even virtual reality coasters. It is a fundamental law of physics that is essential to understanding the mechanics of roller coasters and ensuring their safety and functionality.

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