A frictonless 2,000 kg roller coaster starts from rest at ground level (point A)
ID: 1785810 • Letter: A
Question
A frictonless 2,000 kg roller coaster starts from rest at ground level (point A) and is raised up a hill to a
height of 55.0 meters (point B) where it pauses briefy. From the top of the hill, the roller coaster races
down to ground level (point C) before going through a 30.0 m diameter circular loop (point D), and then up
to a 15.0 m high plateau (point E) where the roller coaster is brought to a stop over 10.0 m (point F).
(a) How much energy does it take to move the roller coaster from point A to point B?
(b) What is the velocity of the roller coaster at point C?
(c) What is the velocity of the roller coaster at point E?
(d) What force must the brakes exert on the roller coaster to bring it to a stop in 10.0 m?
Explanation / Answer
given frictionless roller coaster of mass m = 2000 kg
height at point A, ha = 0
height of point B, hb = 55 m
speed at topmoist point = 0 m/s ( brief stop)
height of point C, hc = 0 m
height of point D, Hd = 30 M
HEIGHT OF POINT e, he = 15 m
distance from E to F = d = 10 m
a. energy taken to move coaster from A to B = PE at point B
PE = mghb = 2000*9.81*55 = 1079100 J
b. velocity of roller coaster at point C = v
then from conservation of energy
1079100 = 0.5*mv^2 = 0.5*2000*v^2
v = 32.849 m/s
c. speed at point E = u
then from conservation of eenrgy
1079100 = 0.5mu^2 + mghe = 2000(0.5*u^2 + 9.81*15)
u = 28.014282 m/s
d. let the acceleration of the braking time be a
then
2*a*d = u^2
a = u^2/2*d = 39.24 m/s/s
hence force applied = m*(a) = 78480 N