A 450.0 kg roller coaster is traveling in a circle with radius 15.0m. Its speed at point A is 28.0m/s and its speed at point B is 14.0 m/s. At point A the cart is already moving with circular motion. a) Draw free bodydiagramsfor the cartatpointsAand B(two separate free body diagrams). b) Calculate the acceleration of the cartat pointsAandB(magnitude and direction). c) Calculate the magnitude of the normal force exerted by the trackson the cartat point A. d) Calculate the magnitude of the normal force exerted by the tracks on the cart at point B.

a) In the attached we can see the free body diagrams for the two positions, position A in the lower part of the circle and position B in the upper part of the circle

b) Let's start at point A

Let's use that the acceleration is centripetal

a = v² / r

let's calculate

a = 28² / 15.0

a = 52.26 m / s²

as they relate it is centripetal it is directed towards the center of the circle, therefore for this point it is directed vertically upwards

Point B

a ’= 142/15

a ’= 13.06 m / s²

in this case the acceleration is vertical downwards

c) The values of the normal force

point A

let's use Newton's second law

∑ F = m a

N- W = m a

N = mg + ma

N = m (g + a)

N = 450.0 (9.8 + 52.25)

N = 2.79 10⁴ N

d) Point B

-N -W = m (-a)

N = ma -m g

N = m (a-g)

N = 450.0 (14.0 - 9.8)

N = 1.89 10³ N