car seat strap travel
At a given instant, someone strapped into a roller coaster car hangs upside down at the very top of the circle
(of radius 24.5 m) while executing a so-called loop-the-loop. At what speed must s/he be traveling if at that moment the force exerted on her/his body on the seat is half her/his actual weight? Assume that at the start of the ride the straps were fairly loose.
Please help ! thank you!
In order to do this properly, you first need to consider Newton’s Second Law at the top of the loop.
At the top of the loop, the seat exerts a normal force on the person; since they are on the inside of the loop, this force points to the center of the loop; gravity acts on the person with a force equal to his/her weight which also acts down.
These two forces combine to equal the centripetal force which acts toward the center of the circle, so we have:
-N-mg=-mv^2/r where N is the force the person will feel
we are told that the force exerted on the seat is half the person’s weight, this is equal to the force exerted by the seat, so we set N=mg/2 and have:
-mg/2-mg=-mv^2/r or
3mg/2=mv^2/r
solve for v:
v=sqrt[3/2 gr]
=sqrt[1.5 9.8*24.5]
=19 m/s
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As I see it: Why not tell the truth?
In my last column, I rambled on about my trip out West but promised to explain “self inflicted work shortage” and “self inflicted financial shortages.”
