Question

Consider a rollercoaster that begins from rest at a height (h) of 200 meters. At one point in the track, the coaster goes around a loop. At the top of the loop, the coaster is moving with a speed of 40 m/s. Calculate the radius of the loop. coaster A. 18.45 m B. 118.45 m C. 98.98 m D. 59.23 m

Answer 1

D. 59.23 m

Step-by-step explanation:

Given that:

initial height
`h_i` of the roller coaster = 200m

speed (v) = 40 m/s

use conservation of energy between starting height and top of loop

`m*g*h_i = (1)/(2)mv^2 + m*g*h_f`

where

`h_f` i.e the final height = 2R

R = radius of the loop

Then

`m*g*h_i = (1)/(2)mv^2 + m*g*2 R`

Divide both sides with m; we have :

`g*h_i = (1)/(2)v^2 + g*2 R`

`9.81*200 = (1)/(2)*40^2 + 9.81*2 R`

1962 = 800 + (9.81 )(2R)

1962 -800 = (9.81 )(2R)

1162 = 19.62 R

`R = (1162)/(19.62)`

R = 59.23 m