1)An 8.00 kg point mass and a 12.0 kg point mass are held in place 50.0 cm apart
ID: 1702957 • Letter: 1
Question
1)An 8.00 kg point mass and a 12.0 kg point mass are held in place 50.0 cm apart. A particle of mass m is released from a point between the two masses 15.0cm from the 8.00 kg mass along the line connecting the two fixed masses.a)Find the magnitude of the acceleration of the particle.
2)Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 9.00 s; the circumference of Mongo at the equator is 1.00×10^5 km; and there is no appreciable atmosphere on Mongo.
a)The starship commander, Captain Confusion, asks for the following information: what is the mass of Mongo?
b)If the Aimless Wanderer goes into a circular orbit 2.00×10^4 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?
Explanation / Answer
2 ) freefall of the mongo g = 14.0 m/s / 4.5 s
= 3.1 m/s^2
radius r = 1.00 *10^5 km / 2
= 0.15 *10^8 m
a ) mass of the plannet M = r g^2 / G
= 0.15*10^8m ( 3.1 m/s^2 )^2 / 6.67 *10^-11
= 2.29 *10^18 kg
b ) The radius of the orbit would be height +radius of planet
= 0.15 *10^8 m + 2.00 *10^4 km
= 3.5 *10^7 m
T^2 = ( 4^2 / G M ) * r^3
= 4 ^2 / 6.67*10^-11 * 2.29*10^18 kg * ( 3.5*10^7 m ) ^3
= 10.5 *10^7 s
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