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## Homework Statement

Bob starts at rest from the top of a frictionless ramp. At the bottom of the ramp, he enters a frictionless circular loop. The total mass of the child and the cart he sits in his

**m**. What must the height of the ramp be in order for the cart to successfully traverse the loop.

r = radius of loop

h = height of ramp

theta = angle of the ramp (irrelevant though)

## Homework Equations

## The Attempt at a Solution

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I solved for the minimum speed at the top of the loop.

Fy = F + mg = mv^2/r

v= sqrt(rg)

I then used conservation of energy.

Initial : mgh

Final : mg2r + (m(sqrt(rg))^2)/2

mgh = mg2r + mrg/2

mgh = 5mgr/2

Cancel stuff out h = 5r/2 (WRONG)

Instead the solution calls for using kinematics not energy conservation.

v= sqrt(rg) stills hold.

vf^2 = vi^2 + 2ax

rg = 0 + 2gsin(theta)*(h/sin(theta)

rg = 2gh

r = 2h

h = r/2 (CORRECT answer)

I understand the mathematical process of the correct solution.

However, I don't understand why I can't use conservation of energy(gives me wrong answer) instead of kinematics.