A car in an amusement park ride rolls without friction around thetrack. It start

Question

A car in an amusement park ride rolls without friction around thetrack. It starts from rest at point A at a height h above thebottom of the loop. Treat car as particle a)what is the minimumh(in terms of R) such that the car moves around the loop withoutfalling off at the top? b)If h=3.5R and r=20m, compute the speed,radial acceleration, and tangential acceleration of the passengerswhen the car has gone 3/4 around the loop, which is at the end of ahorizontal diameter.

Explanation / Answer

at the bottom it will gain a speed of v m*v^2/2=mg*h v=2gh not to fall off at the top: m*v'^2/R>=mg or v'>=2gR v' is speed at the top m*v'^2/2+mg*R=m*v^2/2 or h{min}=2R (b) h=3.5 R=3.5*20=70 m at 3/4 round of the track tangential acc. is g=9.8 m/s^2 radial acc. v^2/R=gR/R=g =9.8 m/s^2 the speed m*v^2/2+mgR=2mgR =>v=gR=14 m/s

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