Conservation of Enery (roller coaster)

Click For Summary
SUMMARY

The discussion centers on calculating the difference in apparent weight experienced by a rider on a roller coaster at the top and bottom of a vertical loop. The conclusion is that the difference amounts to 6 times the rider's weight (6g). Key equations used include the conservation of energy (PE = KE) and centripetal acceleration (a = v^2/R). The minimum height required to complete the loop is established as 2.5R, ensuring the rider remains on track throughout the loop.

PREREQUISITES
  • Understanding of potential energy (PE) and kinetic energy (KE) principles
  • Familiarity with centripetal acceleration and its formula (a = v^2/R)
  • Basic knowledge of gravitational acceleration (g)
  • Concept of roller coaster dynamics and loop design
NEXT STEPS
  • Study the principles of conservation of energy in mechanical systems
  • Learn about centripetal force and its applications in roller coaster design
  • Explore the physics of circular motion and its effects on apparent weight
  • Investigate the minimum height requirements for safe roller coaster loops
USEFUL FOR

This discussion is beneficial for physics students, roller coaster designers, and anyone interested in the dynamics of circular motion and energy conservation in amusement park rides.

Carpe Mori
Messages
19
Reaction score
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)
centripetal 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?
 
Physics news on Phys.org
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.
 
yes problem is state correctly and do tell how maybe I am just over thinking it.
 

Similar threads

Why does the speed change at the bottom of the loop-the-loop?
  • · Replies 5 ·
Replies
5
Views
2K
Speed at the top of an elliptical roller coaster loop
  • · Replies 4 ·
Replies
4
Views
3K
Potential difference defined in non-conservative electric field
  • · Replies 12 ·
Replies
12
Views
2K
Minimum Speed for a Roller-Coaster Car to Complete a Loop without Seat Belts
  • · Replies 12 ·
Replies
12
Views
3K
A different type of roller coaster loop problem
  • · Replies 16 ·
Replies
16
Views
3K
Energy Equation for a Roller Coaster on a Full Circular Loop
  • · Replies 2 ·
Replies
2
Views
2K
Minimum safe height for a roller coaster
  • · Replies 10 ·
Replies
10
Views
6K
Roller Coaster Loop: Solve for Height and Motion
  • · Replies 21 ·
Replies
21
Views
4K
Proper use of inequality symbols in equations to do with circular motion
  • · Replies 2 ·
Replies
2
Views
1K
How Does a Roller Coaster's Loop Affect Your Apparent Weight?
  • · Replies 1 ·
Replies
1
Views
3K