A car around a loop?

Question

A small car rolls down a ramp and through a vertical loop. The mass of the car is m=50g, and the diameter of the vertical loop is d=300mm. If the car is realease from rest from a height of h, determine.

a) the minimum realease height h such that the car will travel all the way around the loop.

b) the force exerted on the track by the car when it is at point B (one quater of the way around the loop).

This is a principle of work and kinetic energy problem

T1+Ui-f=Tf

Answer 1

h=5/2 R

At the top of the loop...

Energy = Mg(2R) + 1/2 Mv^2

and the forces are in balance there, so...

Mv^2/R = Mg and v=SQRT(gR)

Energy at top of loop is thus...Mg(2R) + 1/2 M(gR) = 5/2 MgR

At the point where you release the car...Energy must equal this and so..

5/2 MgR = Mgh and tada...height = 5/2 R

A "classic" problem.

1/4 of the way around, the energy is still 5/2 MgR of which MgR is height, so

3/2 MgR is available for kinetic and so...

v=SQRT(3gR) making the centripital force = Mv^2/R

The force exerted by the track is thus 3Mg

-Fred