Riding a Loop-the-loop. A car in an amusement park ride rolls without friction around the track shown in the f

Question

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

If the car starts at height = 63.0 and the radius is = 21.0 , compute the speed of the passengers when the car is at point , which is at the end of a horizontal diameter.
Take the free fall acceleration to be = 9.80 .

If the car starts at height = 63.0 and the radius is = 21.0 , compute the radial acceleration of the passengers when the car is at point , which is at the end of a horizontal diameter.
Take the free fall acceleration to be = 9.80 .

If the car starts at height = 63.0 and the radius is = 21.0 , compute the tangential acceleration of the passengers when the car is at point , which is at the end of a horizontal diameter.
Take the free fall acceleration to be = 9.80 .

Answer 1

At the top of the loop the centripital acceleration a must me equal or larger then the acceleration due to gravity g.

a= v^2/R so
g<=a=a= v^2/R
v>=sqrt(gR)

Pe(top) - Pe(top of the loop)=Ke
mgh - 2mgR=0.5mV^2
V=sqrt( 2g(h-2R))
Note that if 2(h-2R)
What is horizontal diameter?