A small block of mass m = 1.3 kg slides, without friction, along the loop-the-loop track shown. The block starts from the point P a distance h = 54.0 m above the bottom of the loop of radius R = 19.0 m. What is the kinetic energy of the mass at the point A on the loop?

Question

A small block of mass m = 1.3 kg slides, without friction, along the loop-the-loop track shown. The block starts from the point P a distance h = 54.0 m above the bottom of the loop of radius R = 19.0 m. What is the kinetic energy of the mass at the point A on the loop? 
What is the downward acceleration of the mass at the point A of the loop?
What is the minimum height h for which the block will reach point A on the loop without leaving the track?

Elena · Accepted Answer

1. PE(B)=KE+PE(A) mgh= KE+mg2R KE= mgh- mg2R= =mg(h-2R) 2. mgh= mv²/2+mg2R v²= 2g(h-2R) a= v²/R= 2g(h-2R)/R 3. mgh= mv²/2+mg2R h= v²/2g +2R