Question

A roller coaster car travels through a loop in 3.1 s with a centripetal acceleration of 26 m/s^2. What is the radius of the roller coaster loop?

A. 6.3 m
B. 20 m
C. 25 m

Answer 1

r = 6.32 meters

Step-by-step explanation:

Given that,

The centripetal acceleration acting on the roller coaster,
`a_c=26\ m/s^2`

Time taken by the car, t = 3.1 s

The centripetal acceleration act on an object when it moves in circular path. Its formula is given by :

`a_c=(v^2)/(r)`

v is the velocity of car,
`v=(2\pi r)/(t)`

`a_c=(((2\pi r)/(t))^2)/(r)`

On rearranging above equation,

`r=(a_ct^2)/(4\pi ^2)`

`r=(a_ct^2)/(4\pi ^2)`

`r=(26* (3.1)^2)/(4\pi ^2)`

r = 6.32 meters

So, the radius of the roller coaster loop is 6.3 meters. Hence, this is the required solution.

Answer 2

The radius of the roller coaster loop is 6.3 m.

Step-by-step explanation:

It is given that,

Time taken by roller coaster, t = 3.1 s

Centripetal acceleration,
`a_c=26\ m/s^2`

Velocity in a circular path is given by :

`v=(2\pi r)/(t)`

Centripetal acceleration,
`a_c=(v^2)/(r)`

So, acceleration,
`a_c=(4\pi^2r)/(t^2)`

`r=(a_ct^2)/(4\pi^2)`

`r=(26* 3.1^2)/(4\pi^2)`

r =6.3 m

So, the correct option is (A) " r = 6.3 m". Hence, this is the required solution