The mass of a roller coaster car, including the riders, is 490 kg. The path of a

Question

The mass of a roller coaster car, including the riders, is 490 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 17.6 m, 10.4 m, and 7.20 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.

Part a)What is the force exerted by the track at these two locations? (Enter the magnitudes of the forces.)

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

At A ______ N At B ______ N
The mass of a roller coaster car, including the riders, is 490 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 17.6 m, 10.4 m, and 7.20 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. Part a)What is the force exerted by the track at these two locations? (Enter the magnitudes of the forces.) At A ______ N Part b) At what minimum speed will the car lose contact with the track at C?

Explanation / Answer

a) at A, N = m*g - m*v^2/r = 490*9.8 - 490*12.8^2/17.6 = 240.55 N

at B, N = m*g + m*v^2/r = 490*9.8 + 490*22.5^2/10.4 = 28654.16 N

b) at point C

N = m*g - m*v^2/r = 0

==> v = sqrt(g*r)

= sqrt(9.8*7.2)

= 8.4 m/s

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