Question

A point particle of mass m1 = 2.00 kg is at the origin and a second point particle of mass m2 = 6.00 kg is on the x axis at x = 8.0 m. Find the gravitational field at the following locations.a. x = 2.0m b. x = 12.0 m c. Find the point on the x axis for which g = 0.

Answer 1

Ok, the gravitational field in the x-axis can be written as:

g(x) = G*∑mₙ/(xₙ - x)

where the field points in the positive x-axis

where mₙ is the mass of the n-th particle, and xₙ is the position of the n-th particle, then, in our case we have:

g(x) = G*(- 2kg/x + 6kg(8m -x))

then; g(2) = G*( -2kg/2m + 6kg/(8m- 2m)) = G*( -1kg/m + 1kg/m) = 0

g(12) = G*( -(2/12)kg/m +6/(8 - 12)kg/m) = G* (-2/12 kg/m - 6/4kg/m) = -G*(20/12)kg/m

and we already find that the point where g(x) = 0 is 2

this is the x such:

G*(- 2kg/x + 6kg(8m -x)) = 0

then, the thing inside the parentheses must be zero, now we have:

2kg/x = 6kg(8m -x)

then:

x/2kg = (8/6) m/kg - x/(6kg)

x (1/(2kg) + 1/(6kg)) = (8/6)m/kg

x*(4/(6kg)) = (8/6)m/kg

x = (8/6)*(6/4)m = 2m