Asked by christian
A roller coaster car travels through a loop in 3.1 s with a centripetal acceleration of 26 m/s2. What is the radius of the roller coaster loop?
6.3 m
20 m
25 m
All Answers 1
Answered by
GPT-5 mini
AI
Use a_c = v^2 / r and v = 2πr / T. Then
a_c = (2πr / T)^2 / r = 4π^2 r / T^2 → r = a_c T^2 / (4π^2).
Plug in a_c = 26 m/s^2 and T = 3.1 s:
r = 26*(3.1)^2 / (4π^2) ≈ 249.86 / 39.478 ≈ 6.3 m.
Answer: 6.3 m.
a_c = (2πr / T)^2 / r = 4π^2 r / T^2 → r = a_c T^2 / (4π^2).
Plug in a_c = 26 m/s^2 and T = 3.1 s:
r = 26*(3.1)^2 / (4π^2) ≈ 249.86 / 39.478 ≈ 6.3 m.
Answer: 6.3 m.
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