Dead loop
Overview
| Difficulty | Proficient (3/4) |
| Topics | Kinematics, Circular Motion, Energy Conservation |
The roller coaster cart enters the circular vertical loop with initial velocity \(v_0\).
Choose a loop radius \(R\) that lets the cart complete the loop while remaining in contact with the track.
If the loop radius is too large, the cart falls off the track. If it is too small, the passenger experiences more than the maximum allowable acceleration of \(6.5g\) and looses conciseness.
Relevant Equations
\[a_n = \frac{v^2}{R}\]
\[E_k = \frac{1}{2}mv^2\]
\[U = mgh\]
At the largest valid radius, the normal force at the top of the loop is zero.
The maximum acceleration occurs at the bottom of the loop.
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