Given data
mass of the ball = 3 kg ;
loop radius (r) = 5m,
Determine the height to stay the ball on an incline track (h) = ?
We know that from loop the loop concept,
h = (5r/2)
Where, r = radius of the loop,
Derivation of equation for h;
From Newtons II law F = m .a or F = m. g
Net force acting at the top of the loop,
Fr = F + m.a
since two forces acting down at the top
m. V²/r = m. g
where
m. V²/r = net force
since a = g(ball rolls due to gravitational force)
V²/r = g
V = √(g.r) ----------------- (i)
The kinetic energy is acting at the top of the loop which is equal to potential energy (from energy conservation)
m.g (2r) + 1/2 m.g.r = m.g.h
2r + 1/2 .r = h
Further simplification of above equation
h = 5r/2
----------- end of equation derivation
So, to determine the height of incline, such that ball should stay attached to the track is given by
h = 5r/2
= (5 × 5)/2
= 12.5 m
The ball to stay attached to the track, the height of incline should be 12.5 m.
