Just before reaching the bottom of a semi circular section of a roller coaster r

Question

Just before reaching the bottom of a semi circular section of a roller coaster ride,the automatic emergency break inadevertly goes off. assume the car has a total mass of 750kg,the radius of that section of the track is 55m, and the car entered the bottom after decending vertically from rest 25.0m on a frictionless straight incline.if the breaking force is a steady 1700N

A. cars centripetal acceleration incuding direction

B.normal force of the track on the car

C.The tangential acceleration of the car including direction

d. TOTAL acceleration of the car

Explanation / Answer

1. centrip accel = v^2/r

the v comes from the drop in PE = mgh = KE = 1/2mv^2

mgh = 1/2mv^2
v^2 = 2gh

Substituting for v^2 in the first equation: centrip accel = 2gh/r = 2 x 9.8m/s^2 x 25.0 m / 55.0 m = 8.9m/s^2

2) The normal force is the centripetal force plus the weight = mass x (centripetal accel + grav accel) =
750 kg (8.9m/s^2 + 9.8m/s^2) = 1.4x10^4N

3) a = F/m = 1700N / 750 kg = 2.27 m/s^2

4) combine the tangential accel and radial (upward accel) by vector addition

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