- #1

rsala

- 40

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## Homework Statement

problem should be solved somewhat with energy conservation.

A car in an amusement park ride rolls without friction around the track shown in the figure . It starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle.

What is the minimum value of h (in terms of R) such that the car moves around the loop without falling off at the top (point B)?

## Homework Equations

conservation of energy

centripetal force [tex] \frac{v^{2}}{R}[/tex]

## The Attempt at a Solution

Energy at point A

U = [tex] mgh_{max} [/tex]

K = 0

Energy at point B

U = [tex]mgh_{b}[/tex]

K = [tex] \frac{1}{2} * mv^{2} [/tex]

set them equal

[tex] mgh_{max} = mgh_{b} + \frac{1}{2} * mv^{2} [/tex]

all masses cancel out

[tex] gh_{max} = gh_{b} + \frac{1}{2} * v^{2} [/tex]

move all terms with gravity to the right side, and factor g

[tex] gh_{max} - gh_{b} = \frac{1}{2} * v^{2} [/tex]

[tex] g(h_{max} - h_{b}) = \frac{1}{2} * v^{2} [/tex]

with [tex] \frac{v^{2}}{R} = g [/tex] remove all g from equation. because i need V^2/r to be equal to g or the coaster won't make it past b,,, is my thinking wrong?

[tex] \frac{v^{2}}{R}(h_{max} - h_{b}) = \frac{1}{2} * v^{2} [/tex]

solve for H-max

[tex] H_{max} = H_{b} + \frac{R}{4} [/tex]

height at b is 2R of course.

[tex] H_{max} = 2R + \frac{R}{4} [/tex]

simplify

[tex] H_{max} = \frac{9R}{4} [/tex]

Wrong answer, mastering physics says, off by a multiplicative factor, of course that's mastering physics for , your wrong start all over.

any ideas?