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

Question

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 radi of curvature at the three points A, B, and C are 18.2 m, 12.0 m, and 7.00 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 these two locations? (Enter the magnitudes of the forces.) At A At B (b) At what minimum speed will the car lose contact with the track at C? m/s Additional Materials

Explanation / Answer

here,

mass , m = 510 kg

rA = 18.2 m

rB = 12 m

rC = 7 m

vA = 12.8 m/s

vB = 22.5 m/s

a)

the force by the track at A , Na = m * ( g - vA^2 /rA)

Na = 510 * ( 9.81 - 12.8^2 /18.2) N

Na = 412 N

the force by the track at B , Nb = m * ( g + vB^2 /rB)

Nb = 510 * ( 9.81 + 22.5^2 /12)

Nb = 2.65 * 10^4 N

b_)

let the minimum speed at C be vC

for the roller coaster not to loose contact

centripital accelration = gravity

vC^2 /rC = g

vC^2 /7 = 9.81

solving for vC

vC = 8.29 m/s

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