Grade 12 Physics pronlem!?
Im trying to finish my physics homework, but theres one question i dont understand. Here it is: Two spheres are placed so their centers are 3.26 metres apart. The force between the two balls is 3.11x10 to the -11 N. What is the mass of each sphere if one sphere is triple the mass of the other?
Comments
use the law of universal gravitation
F = G M1 M2/r^2
F = 3.11x10^-11N
G=6.67x10^-11 Nm^2/kg^2
r= 3.26m
and you are told that M1 = 3M2, so that the product M1 x M2 can be written as 3 M^2
then you have
3.11x10^-11N = 6.67x10^-11Nm^2/kg^2(3M^2)/3.26m
and solve for M; the second sphere will have a mass of 3M
The force between the spheres is given by the Newton's famous formula for gravitation:
F = G. M1.M2/D^2
Where G = gravitational constant = 6.67x10^(-11) N.m²/s²
See:
http://en.wikipedia.org/wiki/Gravitational_constan...
D^2 is the square of the distance between their centers
Since M1 = 3xM2,
we can replace M1 in that formula by 3xM2 yielding to:
F = G (3M2).(M2)/D^2
F = 3xG[M2^(2)]/D^2
F[D^(2)]/(3xG) = (M2)^2
M2 = SQRT{F[D^(2)]/(3xG)}
SQRT stands for square root
M2 = Dx{SQRT [F/(3xG)]}
M2 = 3.26x{SQRT[3.11x10^-11/(3x6.67x10^-11)]}
M2 = 3.26x{SQRT[3.11/(3x6.67)]}
M2 = 0.15kg
So,
M1 = 3M2 = 0.75kg
Answer: one sphere has mass M2 = 0.15kg and the other has M1 = 0.75kg
M1 =
F = G*m*3m/D² or
m = Dâ[F/3G] = 1.285 kg
and
3m = 3.855 kg