A roller coster is passing through the very bottom of a semicircular section of

Question

A roller coster is passing through the very bottom of a semicircular section of track.

a) Which of the two forces must be larger? Explain in 1-2 sentences without equations or math, using what you know about circular motion and N2L.

b) The magnitude of the normal force acting on the coaster is 21 kN=2.1x10^4, and the coaster's mass is 840 kg. Staring from N2L and the FBD, calculate the coaster's acceleration at the bottom of the track.

c) Given that the radius of this section of track is 35m, calculate the coaster's speed at this instant.

Explanation / Answer

a)

at this moment, the roller is in circular motion hence the net acceleration will be upward(towards the center of the circlular motion).

There are only two forces in vertical direction and hence the force due to normal F_N is larger than the force due to gravity F_G.

b)

In the free body diagram of the roller there are only two forces :

Force due to normal : vertically upward,

Force due to gravity: vertically downwards.

Net force = Fn-Fg = 21000-840*9.81 = 12759.6 N = 12.76 kN

acceleration = Force/mass = 12759.6/840 = 15.19 m/s

c)

acceleration = v^2/r

v = sqrt(r*a) = sqrt(15.19*35) = 23.06 m/s.

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