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

Ranking the magnitude of the forces from largest to smallest is;

N₆ > N₅ > N₁ = N₂ > N₃ > N₄

Thus;

Force of gravity; F_g = Mg

Normal force = N

Centripetal Force; F_c = Mv²/r

Thus;

N = Mg + Mv²/r

A) r = 60 m and v = 16 m/s

Thus; N = 9.8M + (16²/60)M

N₁ = 14.07M

B) r = 15 m and v = 8 m/s

Thus; N = 9.8M + (8²/15)M

N₂ = 14.07M

C) r = 30 m and v = 4 m/s

Thus; N = 9.8M + (4²/30)M

N₃ = 10.33M

D) r = 45 m and v = 4 m/s

Thus; N = 9.8M + (4²/45)M

N₄ = 10.16M

E) r = 30 m and v = 16 m/s

Thus; N = 9.8M + (16²/30)M

N₅ = 18.33M

F) r = 15 m and v = 12 m/s

Thus; N = 9.8M + (12²/15)M

N₆ = 19.4M

We want to rank the magnitude of the forces from largest to lowest. Thus;

N₆ > N₅ > N₁ = N₂ > N₃ > N₄

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it about 600 mph from what i calculated

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)