Question

1) The Earth is 1.49 x 10^11 m from the Sun. If the Earth requires 365.25 days to go once around the Sun, what is the centripetal force on the Earth?

2) A satellite is located 2.75 x 10^5 m above the surface of the Earth. What is the period of the satellite’s orbit?

3) A 4.0 kg ball is swung at a constant speed in a vertical circle of radius 2.5 m. If the ball completes one revolution in 3.0 s, what is the tension in the rope at the top of the circle?

Answer 1

1)

$F=m\omega^2 r=\frac{4\pi^2mr}{T^2}=35.3\cdot 10^{21}~N,$

2)

$T=\frac{2\pi (R+h)^\frac 32}{\sqrt g R}=1.5^h,$

3)

$T=m(\omega^2 r-g)=m(\frac{4\pi^2 r}{t^2}-g)=4.7~N.$