The universal gravitational con- stant is 6.672 × 10−11 N m2/kg2.

Objects with masses of 152 kg and 269 kg are separated by 0.45 m. A 53.5 kg mass is placed midway between them.
Find the magnitude of the net gravitational force exerted by the larger masses on the
53.5 kg mass. Answer in units of N.

Leaving the distance between the 152 kg and the 269 kg masses fixed, at what distance from the 269 kg mass (other than infinitely remote ones) does the 53.5 kg mass experience a net force of zero? Answer in units of m.

m1 = 152 kg, m2 = 269 kg, m3 = 53.5 kg. d =0.45 m, r =d/2 =0.225 m,

G = 6.672•10^−11 N m2/kg2.

m1 …….….<-------m3--------------> …..m2
F13 F23

F13 = G•m1•m3/r^2,
F23 = G•m2•m3/r^2,
F = F23 – F13,

m1 …….….<-------m3-------> …..m2
F13 F23
F13 = F23,
G•m1•m3/(d-x)^2= G•m2•m3/x^2,
m1/(d-x)^2 =m2/x^2,
Solve for “x”

To find the magnitude of the net gravitational force exerted by the larger masses on the 53.5 kg mass, we can use Newton's law of universal gravitation:

F = G * (m1 * m2) / r^2

Where:
F is the gravitational force
G is the gravitational constant (6.672 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the two objects

Let's calculate the force:

1. Calculate the force between the 152 kg mass and the 53.5 kg mass:
F1 = G * (m1 * m3) / d1^2

Where:
m3 is the mass of the 53.5 kg object
d1 is the distance between the 152 kg and 53.5 kg objects

F1 = (6.672 × 10^-11 N m^2/kg^2) * (152 kg * 53.5 kg) / (0.45 m)^2

Calculate F1.

2. Calculate the force between the 269 kg mass and the 53.5 kg mass:
F2 = G * (m2 * m3) / d2^2

Where:
d2 is the distance between the 269 kg and 53.5 kg objects

Since the 53.5 kg mass is placed midway between the larger masses, the distance between the 53.5 kg mass and the 269 kg mass is the same as the distance between the 53.5 kg mass and the 152 kg mass. So, d2 = 0.45 m.

F2 = (6.672 × 10^-11 N m^2/kg^2) * (269 kg * 53.5 kg) / (0.45 m)^2

Calculate F2.

3. Calculate the net gravitational force:
Net Force = F1 + F2

Calculate the sum of F1 and F2.

Now, let's proceed to find the distance from the 269 kg mass where the 53.5 kg mass experiences a net force of zero.

To find the distance, we'll equate the magnitudes of the gravitational forces exerted by the 152 kg and 269 kg masses on the 53.5 kg mass.

1. Set F1 = F2
2. Solve the equation for d2, which is the distance from the 269 kg mass.

This will give you the distance from the 269 kg mass (other than infinitely remote ones) where the 53.5 kg mass experiences a net force of zero.