A car around a loop?
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
thanks I also need to build this and prove it some how any ideas?
I’m thinking on using a platic clear tube and spheres, is there any possible physical way to measure the force at point B?
thanks again
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
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