Respuesta :
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, [tex]a_c=26\ m/s^2[/tex]
Velocity in a circular path is given by :
[tex]v=\dfrac{2\pi r}{t}[/tex]
Centripetal acceleration, [tex]a_c=\dfrac{v^2}{r}[/tex]
So, acceleration, [tex]a_c=\dfrac{4\pi^2r}{t^2}[/tex]
[tex]r=\dfrac{a_ct^2}{4\pi^2}[/tex]
[tex]r=\dfrac{26\times 3.1^2}{4\pi^2}[/tex]
r =6.3 m
So, the correct option is (A) " r = 6.3 m". Hence, this is the required solution
Answer:
r = 6.32 meters
Explanation:
Given that,
The centripetal acceleration acting on the roller coaster, [tex]a_c=26\ m/s^2[/tex]
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 :
[tex]a_c=\dfrac{v^2}{r}[/tex]
v is the velocity of car, [tex]v=\dfrac{2\pi r}{t}[/tex]
[tex]a_c=\dfrac{(\dfrac{2\pi r}{t})^2}{r}[/tex]
On rearranging above equation,
[tex]r=\dfrac{a_ct^2}{4\pi ^2}[/tex]
[tex]r=\dfrac{a_ct^2}{4\pi ^2}[/tex]
[tex]r=\dfrac{26\times (3.1)^2}{4\pi ^2}[/tex]
r = 6.32 meters
So, the radius of the roller coaster loop is 6.3 meters. Hence, this is the required solution.
