Rollercoaster engineers have chosen the moon as the site of their latest creatio

Question

Rollercoaster engineers have chosen the moon as the site of their latest creation. Aside from a weaker
gravitational force (gmoon = 1.62 m/s2), the lack of an atmosphere eliminates air resistance and the views
are spectacular. The ride will feature a maglev (frictionless) car that will carry two passengers at a time,
with an estimated mass of car plus riders of 500 kg. This car will be propelled up an initial 60o
incline using a hydraulic piston that provides a constant force of 5975 N for 6.00 s.

a. How fast is the car going when it reaches point B, 1.00 km high?

b. How much force is felt as the car goes over the top from point B to point C if the radius of the curve is 150 m?

c. Is this force positive or negative, and how many g's is it?

d. As the car passes point C, it plunges down a vertical drop, then curves around to be horizontal at
point D, which is level with the starting point of the ride. How fast is the car going as it passes point D?

e.The car continues to point E, which is at the top of a 400 m uphill climb at a 30o
angle, where the track abruptly ends and the car is launched as a projectile in a ballistic trajectory. How far away will a similar, but opposite, hill need to be constructed for the car to land on it and continue?

Explanation / Answer

a) Fnet = 5975 - m*g*sin(60)

m*a = 5975 - m*g*sin(60)

a = 5975/m - g*sin(60)

= 5975/500 - 1.62*cos(60)

= 10.56 m/s^2

distance travlled in 6 s

s = 0.5*a*t^2
= 0.5*10.56*6^2
= 190 m

Net work done as it moves from bottom to top,

Wnet = F*s - m*g*h

= 5975*190 - 500*1.62*1000

= 325265 J

Wnet = gain in kinetic enrgy

Wnet = 0.5*m*v^2

==> v = sqrt(2*Wnet/m)

= sqrt(2*325265/500)

= 36 m/s <<<<<<<<<<--------Answer

b) N = m*g -m*v^2/r

=   500*1.62 -500*36^2/150

= -3510 N

c) force is negative

a = v^2/r = 36^2/150 = 8.64 m/s^2 = 5.333*g

d) v = sqrt(2*g*h)

= sqrt(2*1.62*1000)

= 56.92 m/s

e) v^2 - u^2 = 2*a*s

v = sqrt(u^2-2*a*s)

= sqrt(56.92^2 - 2*1.62*400)

= 44 m/s

R = v^2*sin(2*40)/g

= 44^2*sin(80)/1.62

= 1181 m

f) u = 56.92 m/s

v = 0

v^2-u^2 = 2*a*s

a = -u^2/(2*s) = -56.92^2/(2*500) = -3.24 m/s^2

Fnet = m*a = 500*3.24 = 1620 N

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