Question

Consider a system consisting of three masses on the x axis. Mass m1 = 1.50 kg
is at x1 = 1.50 m ;
mass m2 = 2.00 kg
is at x2 = 2.30 m ;
and mass m3 = 3.20 kg
is at x3 = 2.70 m .

What is the total gravitational potential energy of this system?

Answer 1

Given :-

m1 = 1.5 kg

m2 = 2 kg

m3 = 3.20 kg

x1 = 1.5 m

x2 = 2.3 m

x3 = 2.7 m

1)

Gravitational potential between m1 and m2

U1 = -Gm1m1 / (x2 - x1)

U1 = -G*1.5*2 / (2.3 - 1.5)

U1 = -3.75G

2)

Gravitational potential between m2 and m3

U2 = -Gm2m3 / (x3 - x2)

U2 = -G*2*3.2 / (2.7 - 2.3)

U2 = -16G

3)

Gravitational potential between m3 and m1

U3 = -Gm3m1 / (x3 - x1)

U3 = -G*3.2*1.5 / (2.7 - 1.5)

U3 = -4G

U = U1 + U2 + U3

U = -6G - 16G - 4G

U = -26G

U = -26 x 6.67 x 10^-11

U = 1.734 x 10^-9 J