Question

An amusement park designer wants his swing to have a centripetal acceleration of 24 m/s2. If the velocity of the swing is 11 m/s, how long should the chain on the swing be?

A. 6.5 m
B. 5.5 m
C. 5.0 m
D. 6.0 m

Answer 1

Answer: 5.0 meters (choice C)

This length is approximate.

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Step-by-step explanation:

The centripetal acceleration formula we use is

a = (v^2)/r

where v is the linear velocity and r is the radius. The swing moves in a circular path, so the chain acts as the radius. If we can find the radius, then we have found the chain length. The goal is to find r when a = 24 and v = 11

So we have...

a = (v^2)/r

24 = (11^2)/r

24 = 121/r

24r = 121

r = 121/24

r = 5.041667 approximately

r = 5.0 meters when rounding to the nearest tenth

The chain should be approximately 5.0 meters.

Answer 2

radius is C: 5.0 m

Step-by-step explanation:

formular for centripetal acceleration:

`a = \frac{ {V}^(2) }{r}`

a is acceleration

V is velocity

r is radius

`24 = \frac{ {11}^(2) }{r} \\ \\ r = \frac{ {11}^(2) }{24} \\ \\ r = 5.0 \: m`