The mass of a roller coaster car, including the riders, is 510 kg. The path of a

Question

The mass of a roller coaster car, including the riders, is 510 kg. The path of a portion of the ride is shown in the diagram below. The radii of curvature at the three points A, B, and C are 18.8 m, 10.6 m, and 8.20 m, respectively. The car, which travels from right to left, has a speed of 12.8 m/s and 22.5 m/s at A and B, respectively.

(a) What is the force exerted by the track at the two locations, A and B? (Enter the magnitudes of the forces, in N.)

(b) At what minimum speed will the car lose contact with the track at C?

Explanation / Answer

here,

mass , m = 510 kg

a)

the force exerted by track at A , Fa = m * g - m * va^2 /Ra

Fa = 510 * ( 9.81 - 12.8^2 /18.8)

Fa = 558.5 N

the force exerted by track at B , Fb = m * g + m * vb^2 /Rb

Fb = 510 * ( 9.81 + 22.5^2 /10.6)

Fb = 29360.4 N

b)

let the minimum speed will the car lose contact with the track at C be v

m * g = m * v^2 /rc

9.81 = v^2 /8.2

v = 8.97 m/s

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