A car in an amusement park ride rolls without function around a track. The car s

Question

A car in an amusement park ride rolls without function around a track. The car starts from rests at point A at height h above the bottom of the loop. Treat the car as a particle. What it the minimum value of h (in terms of R) such that the car moves around the loop without falling offal the top (point B)? If h = 3.J R and R - U m. compute the speed when the car is at point C. which it at the end of a horizontal diameter Find the magnitude of the centrepetal acceleration when the car it at point C What it the direction of the centrepetal acceleration when the car it at point C.

Explanation / Answer

A.)Car needs to have a minimum velocity (5gR)^1/2 at bottom of the loop to move around the loop.

So, equating potentital energy at A to kinetic energy at bottom most point,

mgh= 1/2 m ((5gR)^1/2)^2

h=5R/2

B.) Let the speed be V at C.

Conserving energy.,

mgh=1/2 mv^2 + mgR

gh=v^2/2+gR

3.5 gR=v^2/2+gR

2.5 gR=v^2/2

v=(5gR)^1/2 =( 5*9.8*14)^1/2=26.19 m/s

C. Centrepetal acceleration = v^2/R= (29.19)^2/14=49m/s^2

D. Horizontal and towards the center of the loop

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