Please show all work please. For this problem, look up any necessary astronomica

Question

Please show all work please.

For this problem, look up any necessary astronomical values to at least 3 significant figures: a. What would be your linear (tangential) speed, due to the Earth's rotation, if you were located on the Earth's equator? Show your work. [Thought question (not for credit): How would you find the linear speed of someone located in Honolulu or Seattle WA, or Anchorage AK? What is the linear speed of someone standing at the North Pole?] b. While located on the equator, what is the magnitude and direction of your centripetal acceleration (the acceleration needed to keep you moving in a circle on the Earth as it rotates)? Convert your final answer to gees. (1 gee = 9.80 m/s^2) Show your work. c. Suppose that you have a mass of 75.00 kg. While located on the equator, what must be the magnitude and direction of the net force acting on you, in order to create your centripetal acceleration? Name the two physical forces whose vector addition creates this net force, and give the magnitude and direction of each. Show your work. [Thought question (not for credit): Suppose you were to stand on a bathroom scale on the equator. Due to the rotation of the Earth, how much less than your true weight would the scale read?]

Explanation / Answer

a)

Imagine that the equator is a giant wheel that spins once in 24 hours

Distance for one revolution = 2R

Speed = Distance / time = 2R / (24 x 3600) m/s

Speed = (2 x 3.142 x 6.4 x 10^6) / (24 x 3.6 x 10^3) = 465 m/s

b)

centripetal (inward) acceleration is a = r^2 = v^2/r

moving in a circle of radius r, with an angular velocity of , is angular velocity in radians/sec

earth radius = 6.37 x 10^6 meters

one circle is 2 radians, so the for earth is

2 / (3600*24) = 0.0000727 rad/s

a = 6.37 x 10^6 x (0.0000727 rad/s)^2= 0.0337 m/s^2

c) Not sure about that sorry......

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