4) The moon travels around the earth with an orbital speed of roughly 1026 m/s.

Question

4) The moon travels around the earth with an orbital speed of roughly 1026 m/s. If the moon has an average orbital distance of 3.85 x 108 m and a mass of 7.35 x 1022 kg: a. What is the centripetal acceleration of the moon? b. What is the centripetal force the earth exerts on the moon? c. What type of force causes this centripetal force between the earth and the moon?

5) Early skeptics of the idea of a rotating Earth said that the fast spin of Earth would throw people at the equator into space. The radius of Earth is about 6,400,000 m and at the equator it spins with a velocity of 465 m/s (~1000 mph!). Show why this objection is wrong by calculating... a. The centripetal force acting on a 97 kg person at the equator. b. What is the weight (Fg) of the person?

6) A 1500 kg car rounds a corner with a radius of 25 m at 20 m/s. a. What is the car’s centripetal acceleration? b. What is the magnitude of the centripetal force acting on the car?

Explanation / Answer

4)

a)

centripetal acceleration,a = v^2/R

= 1026^2/(3.85*10^8)

= 2.73*10^-3 m/s2

b)

centripetal force = m*a

= 7.35*10^22*(2.73*10^-3)

= 2*10^20 N

c)

The gravitational force causes this centripetal force

5)

a)

centripetal force = m*v^2/r = 97*465^2/(6.4*10^6) = 3.28 N

b)

Weight , Fg = m*g = 97*9.8 = 950.6 N

As weight > centripetal force , so the persont wont be thrown out into space

6)

a)

centripetal acceleration,

a = v^2/r = 20^2/25 = 16 m/s2

b)

centripetal force,

F = m*a = 1500*16 = 24000 N

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