You decide to visit santa claus at the north pole to put in a good word about your splendid behavior throughout the year. while there, you notice that the elf sneezy, when hanging from a rope, produces a tension of 505 n in the ropea. if sneezy hangs from a similar rope while delivering presents at the earth's equator, what will the tension in it be? (recall that the earth is rotating about an axis through its north and south poles.)

To solve this problem it is necessary to apply the concepts related to the Rotational Force described from the equilibrium and Newton's second law.

When there is equilibrium, the Force generated by the tension is equivalent to the Force of the Weight. However in rotation, the Weight must be equivalent to the Centrifugal Force and the tension, in other words:

Where

Angular velocity is equal to the Period, at this case Earth's period

Radius of the Earth

m = mass

= Force of Tension

Newton's second law

Replacing and re-arrange to find the Tension we have,

Therefore when Sneezy is on the equator he is in a circular orbit with a Force of tension of 503.26N

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day

neither accurate nor precise.