Answer the following Gravitation related problems: A) Four identical masses of 8
ID: 1624459 • Letter: A
Question
Answer the following Gravitation related problems:
A) Four identical masses of 800 kg each are placed at the corners of a square whose side length is 10.0 cm. What is the net gravitational force (magnitude and direction) on one of the masses, due to the other three?
B) An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and finds that it takes the rock 0.480 s to fall 1.90m. If the radius of the planet is 8.60 x 107 m, what is the mass of the planet?
Explanation / Answer
(A) due to adjacent mass,
g1 = G M / a^2 = (6.67 x 10^-11)(800) / 0.10^2
g1 = 5.336 x 10^-6 m/s^2
due to opposite corner mass,
g2 = G M / (a^2 + a^2) = 2.668x 10^-6
magnitude = sqrt(2) [ g1 + g2cos45]
= 10.2 x 10^-6 m/s^2 .....Ans
direction -> towards the opposite corner.
(B) d = u t + g t^2 /2
1.90 = 0 + g (0.480^2)/2
g =16.49 m/s^2
g = G M / R^2
16.49 = (6.67 x 10^-11)(M) / (8.60 x 10^7)^2
M = 1.83 x 10^27 kg