Question

A roller-coaster track has six semicircular "dips" with different radii of curvature. The same roller-coaster cart rides through each dip at a different speed.
For the different values given for the radius of curvature R and speed v, rank the magnitude of the force of the roller-coaster track on the cart at the bottom of each dip. Rank from largest to smallest. To rank items as equivalent, overlap them.
A) R=60m v=16 m/s
B) R=15m v= 8m/s
C) R=30m v= 4m/s
D) R=45m v= 4m/s
E) R=30m v= 16 m/s
F) R= 15m v=12 m/s

Answer 1

Answer:

E > A = B > C > D

Explanation:

On a semicircular curve, the magnitude of force is given by the formula as :

$F=\dfrac{mv^2}{r}$

Here, m is the mass of the vehicle

Case A : R = 60 m v = 16 m/s

$F_1=\dfrac{m(16)^2}{60}=4.27m\ N$

Case B : R = 15 m v = 8 m/s

$F_2=\dfrac{m(8)^2}{15}=4.27m\ N$

Case C : R = 30 m v = 4 m/s

$F_3=\dfrac{m(4)^2}{30}=0.534m\ N$

Case D : R = 45 m v = 4 m/s

$F_4=\dfrac{m(4)^2}{45}=0.356m\ N$

Case E : R = 30 m v = 16 m/s

$F_5=\dfrac{m(16)^2}{30}=8.53m\ N$

The order of the magnitude of the force of the roller-coaster track on the cart from largest to smallest is :

E > A = B > C > D