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

Answer:

The radius of the roller coaster loop is 6.3 m.

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 :

$v=\dfrac{2\pi r}{t}$  

Centripetal acceleration, $a_c=\dfrac{v^2}{r}$

So, acceleration, $a_c=\dfrac{4\pi^2r}{t^2}$

$r=\dfrac{a_ct^2}{4\pi^2}$

$r=\dfrac{26\times 3.1^2}{4\pi^2}$

r =6.3 m

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

Answer 2

Answer:

r = 6.32 meters

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 :

$a_c=\dfrac{v^2}{r}$

v is the velocity of car, $v=\dfrac{2\pi r}{t}$

$a_c=\dfrac{(\dfrac{2\pi r}{t})^2}{r}$

On rearranging above equation,

$r=\dfrac{a_ct^2}{4\pi ^2}$

$r=\dfrac{a_ct^2}{4\pi ^2}$

$r=\dfrac{26\times (3.1)^2}{4\pi ^2}$

r = 6.32 meters

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