From the bottom of the first hill, the roller coaster goes up a second hill. Let

Question

From the bottom of the first hill, the roller coaster goes up a second hill. Let's say that the peak of the second hill is 48.0 m higher than the bottom of the first hill, and that the shape of the second hill is that of a vertical circular arc with radius of 30.0 m.

(d) If resistive forces acting on the coaster cause a loss of 5% of the coaster's mechanical energy as it moves from the bottom of the first hill to the top of the second hill, and if your mass happens to be 50.0 kg, what is the magnitude of the normal force acting on you at the top of the second hill? Note that the normal force you're used to feeling is 490 N. (N)

Explanation / Answer

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using conservation of energy,

.95mgh = .5*mv^2

so, v= sqrt(1.9gh)
so, v= 29.9 m/s

so the normal force and mgsin has to produce the centripetal force,

so, mg*sin+N= mv^2/ r

so, N= mv^2/r - mgsin

so, N= 1196 N

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