3 questions about Gravity equation
1. Three particles each with a mass of 1 kg are at the vertices of an equilateral triangle whose sides are 1 m long. How large is the gravitational force experienced by each point particle (in G)?
Solution
The magnitude of the gravitational force experienced by one of the particles.
F12 = G (m1)(m2) / r2 = G (1)(1) / 12 = G/1 = G
F13 = G (m1)(m3) / r2 = G (1)(1) / 12 = G/1 = G
Resultant gravitational force at point 1:
F1 = √12+12 = √1+1 = √2 Newton
2. The figure below depicts three objects m1 = 6 kg; m2 = 3 kg and m3 = 4 kg lie on a straight line. Determine the magnitude and direction of the resultant gravitational force experienced by m2! (state in G)
Known:
m1 = 6 kg
m2 = 3 kg
m3 = 4 kg
gravitational constant = G
r21 = 4 m
r23 = 2 m
Wanted: F resultant gravity experienced by m2
Solution:
The gravitational force between m2 and m3:
F = G (3)(4) / 22 = G 12 / 4 = 3G
The gravitational force between m2 and m1:
F = G (3)(6) / 42 = G 18 / 16 = 1,125G
3. Object A with a mass of 1 kg and object B with a mass of 2 kg are separated by a distance of 2 m from one another. Point P is 2 m from object A and 2 m from object B. How strong is the gravitational field at point P?
Known:
mA = 1 kg
mB = 2 kg
rPA = 2 m
rPB = 2 m
Gravity constant = G
Wanted: E gravity at point P
Solution:
EPA = G (mA) / r2 = G (1) / 22 = G/4 = 0,25G
EPB = G (mB) / r2 = G (2) / 22 = 2G/4 = 0,5G
Resultant gravitational field strength at point P:
E = √0,25G2+0,5G2 = √0,0625G2+0,25G2 = √0,3125G2 = 0,56G N/kg