Question

1. The moon orbits the earth at a distance of 3.85 times 10^8 m. Assume that this distance is between the centers of the earth and the moon and that the mass of the earth is 5.98 x 10^24 kg. Find the period for the moon's motion around the earth. Express the answer in days. 2. A 0.0296 kg ball is shot from the plunger of a pinball machine. Because of a centripetal force of 0.0485 N, the ball follows a circular arc whose radius is 0.309 m. What is the speed of the ball? 3. A curve of radius 113 m is banked at an angle of 16.8". At what speed can it be negotiated under icy conditions where friction is negligible? 4. Two satellites, A and B, are in different circular orbits about the earth. The orbital speed of satellite A is 6.29 times that of satellite B Find the ratio of the period of satellite A to that of satellite B.

Answer 1

Distance between earth and moon r = 3.85 x10 ⁸ m

Mass of earth M = 5.98x10 ²⁴ kg

Required period T = 2$\pi$$\sqrt{}$[r ³/GM]

Where G = Gravitational constant = 6.67x10 ^-11 Nm ²/kg ²

Substitute values you get,

T = 2(3.1415) $\sqrt{}$[(3.85 x10 ⁸) ³ /(6.67x10 ^-11)(5.98x10 ²⁴)]

= 6.283 $\sqrt{}$[1.43x10 ¹¹]

= 6.283 (378.248x10 ³)

= 2.376x10 ⁶ s

= [(2.376x10 ⁶) /3600 ] hr Since 1 hr = 3600 s

= 660.168 hrs

= (660.168/24) days Since 1 day = 24 hrs

= 27.5 days