College Physics problem. Please show all work. The mass of a roller coaster car,

Question

College Physics problem. Please show all work.

The mass of a roller coaster car, including the riders, is 518 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 18.4 m, 10.2 m, and 8.40 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

Explanation / Answer

here,

rA = 18.4 m , rB = 10.2 m , rC = 8.4 m

vA = 12.8 m/s , vB= 22.5 m/s

a)

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

Na = 518 ( 9.8 - 12.8^2 /18.4)

Na = 463.9 N

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

Nb = 518 ( 9.8 + 22.5^2 /10.2)

Nb = 30786 N = 3.08 * 10^4 N

b)

let the minimum speed will the car loose contact with the track at C ne v

m * vC^2 /rC = m * g

vC^2 /8.4 = 9.81

vC = 9.1 m/s

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