Energy Conservation, Work, and Kinetic Energy Rollercoaster physics. You are to
ID: 1363563 • Letter: E
Question
Energy Conservation, Work, and Kinetic Energy Rollercoaster physics. You are to design a roller coaster in which cars start from rest at a height h = 30 m, roll down into a dip, and then up another hill. For purposes of this problem, ignore friction. What is the speed of the cars at the bottom of th edip? If the passengers are to feel 8g at the bottom, what radius R of curvature is required for the bottom of the dip? The top of the second hill is an arc of the same radius of curvature R. If the passengers are to feel Og at the top of this hill, what height h' is required?Explanation / Answer
a)
potential energy at the top = kinetic energy at bottom
m*g*h = 0.5*m*v^2
g*h = 0.5*v^2
9.8*30 = 0.5*v^2
v=24.25 m/s
Answer: 24.25 m/s
b)
Normal reaction, N= m*8*g
at bottom:
upward force = N and downward force=m*g
Net force must account for centripetal force
(N-m*g) = m*v^2/R
m*8*g - m*g = m*v^2/R
8*g - g = v^2/R
7g = v^2/R
7*9.8 = (24.25)^2/R
R=8.6 m
Answer: 8.6 m
c)
Downward force acting is mg and there is no upward force
Net force must account for centripetal force
so,
mg = m*v'^2/R
g = v'^2/R
9.8 = v'^2/8.6
v' = 9.17 m/s
so,
speed at top must be 9.17 m/s
Use conservation of energy between initial point at height h and this point at h'
m*g*h = m*g*h' + 0.5*m*v'^2
g*h = g*h' + 0.5*v'^2
9.8*30 = 9.8*h'+ 0.5*(9.17)^2
h' = 25.7 m
Answer: 25.7 m
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