A roller coaster starts from a height of 30.0 m and runs down a slope, then through a loop. If it takes a minimum speed of 15 m/s when passing the top of the loop to safely keep all the passengers in place, what is the maximum height of the loop?

A roller coaster starts from a height of 30.0 m and runs down a slope, then through a loop. If it takes a minimum speed of 15 m/s when passing the top of the loop to safely keep all the passengers in place, what is the maximum height of the loop?

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter11: Energy And Its Conservation

Section: Chapter Questions

Problem 83A

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Question

Kindly provide the solution to the following question using the GRASS method. (Unit: Energy and Momentum).

The images attached are the formulas for this unit and the question. Please make sure to show all your work using the GRASS (given, required, analysis, solution, and statement) method and using formulas from this unit (Energy and Momentum).

A roller coaster starts from a height of 30.0 m and runs down a slope, then through a
loop. If it takes a minimum speed of 15 m/s when passing the top of the loop to
safely keep all the passengers in place, what is the maximum height of the loop?

Energy
W = F d
1
Eg == k
EE
- lxx²
2
Momentum
→
Px = Px
E₁ = mgh_E₁₂ = 12 mv²
Eg
Ex
2
T=2
Py = Py
Unit 2 Energy & Momentum
m
V k
Px
px = mix
Em = Ep + Ek
1 k
2 Vm
==
Py = mvy
F
spring
E₁ = E + Ek
EFAT = Ap
= kx Eth=Fd
Fnet = 4P
At
p = p²
Ek = Ek'
Ек

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