Question
The loop of a roller coaster has a radius of 15 m.
What is the minimum speed for the roller coaster to make the loop without falling?
What is the normal force if the speed is doubled?
Answer
If N = normal force, then at any speed as long as the roller coaster is not falling,
N + mg = mv^2/r
For minimum speed, N = 0
=> v = √(gr) = √(9.8*15) = 12.12 m/s
Normal force if speed is doubled is given by
N
= - mg + m(2v)^2/r
= - mg + 4mv^2/r
= 3mg
Hence normal force will be 3 times the weight of the roller coaster.
[Note: normal force will be different at different locations. The above calculations are for normal force on the roller coaster at its highest point of the path.]
The loop of a roller coaster has a radius of 15 m.
What is the minimum speed for the roller coaster to make the loop without falling?
What is the normal force if the speed is doubled?
Answer
If N = normal force, then at any speed as long as the roller coaster is not falling,
N + mg = mv^2/r
For minimum speed, N = 0
=> v = √(gr) = √(9.8*15) = 12.12 m/s
Normal force if speed is doubled is given by
N
= - mg + m(2v)^2/r
= - mg + 4mv^2/r
= 3mg
Hence normal force will be 3 times the weight of the roller coaster.
[Note: normal force will be different at different locations. The above calculations are for normal force on the roller coaster at its highest point of the path.]
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