Question

An amusement park designer wants his swing to have a centripetal acceleration of 21m/s2. If the velocity of the swing is 13m/s, how long should the chain in the swing be?

Answer 1

To provide a centripetal acceleration of 21m/s^2 with a swing velocity of 13m/s, the swing's chain should be approximately 8.05 meters long.

Step-by-step explanation:

The student is interested in finding out the length of the chain for a swing in an amusement park that should provide a centripetal acceleration of 21m/s2. Given that the velocity of the swing is 13m/s, the length of the chain can be calculated using the centripetal acceleration formula:

\(a_c = \frac{v^2}{r}\)

By rearranging this formula to solve for r (the radius), which in this case will be equivalent to the length of the chain, we get:

\(r = \frac{v^2}{a_c}\)

Substituting the given values:

\(r = \frac{13^2}{21}\)

\(r = \frac{169}{21}\)

\(r = 8.05 m\)

So, the length of the chain should be approximately 8.05 meters to achieve the desired centripetal acceleration.