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)
The Attempt at a Solution
I solved for the minimum speed at the top of the loop.
Fy = F + mg = mv^2/r
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.