The difference in force per mass (N/kg) across a body, tidal force T, is approxi
ID: 1435629 • Letter: T
Question
The difference in force per mass (N/kg) across a body, tidal force T, is approximated by T = 4GMR/d^3, where G is the gravitational constant, M the mass of the body causing tides, R the radius of the body having tides, and d the center-to-center distance between the bodies..
Make two calculations:(a) T that the Moon exerts on you,_______
(b) T that a 1-kg melon 1 m above your head exerts on you._____
For simplicity, let R for you be 1 m (pretend you're 2 m tall). Let d to the Moon be 3.8e8 m and to the melon be 2 m. Mass M of the Moon is 7.3e22 kg. Compare which is larger, and share this information with any friends who say that the tidal forces of planets on people influence their lives.
Explanation / Answer
here,
a.
radius of moon , r = 1 m
mass of moon , M = 7.35 * 10^22 kg
distance from moon centre , d = 4.07 * 10^8 m
T that moon exerts on me , T = 4 * G * M * R/d^3
T = 4 * 6.67 * 10^-11 * 7.35 * 10^22 * 1 /( 3.8 * 10^8)^3
T = 3.57 * 10^-13 N/kg
b.
R = 1 m
d = 2 m
mass , M = 1 kg
T = 4 * G * M * R /d^3
T = 6.67 * 10^-11 * 4 * 1 * 1 /2^3
T = 3.34 * 10^11 N/kg