objects with masses of 285 kg and a 585 kg are separated by 0.420 m.

(a) Find the net gravitational force exerted by these objects on a 62.0 kg object placed midway between them.

To find the net gravitational force exerted by the two objects on a 62.0 kg object placed midway between them, we can use Newton's law of universal gravitation.

Newton's law of universal gravitation states that the force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The formula for the gravitational force between two objects is:

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

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67 × 10^-11 N*m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects

In this case, the two objects have masses of 285 kg and 585 kg, respectively. The distance between them is given as 0.420 m. The mass of the 62.0 kg object placed midway between them will have no effect on the net gravitational force between the two larger objects.

To calculate the net gravitational force exerted by the two objects on the 62.0 kg object, we need to add the individual forces exerted by each object on the 62.0 kg object.

Let's calculate the gravitational force exerted by each object on the 62.0 kg object:

First object:
F1 = (G * m1 * m3) / r1^2

Second object:
F2 = (G * m2 * m3) / r2^2

Where:
F1 is the gravitational force exerted by the first object on the 62.0 kg object
F2 is the gravitational force exerted by the second object on the 62.0 kg object
m3 is the mass of the 62.0 kg object
r1 is the distance between the first object and the 62.0 kg object (0.420 m divided by 2)
r2 is the distance between the second object and the 62.0 kg object (0.420 m divided by 2)

Now, let's calculate the forces:

F1 = (6.67 × 10^-11 N*m^2/kg^2 * 285 kg * 62.0 kg) / (0.420 m / 2)^2

F2 = (6.67 × 10^-11 N*m^2/kg^2 * 585 kg * 62.0 kg) / (0.420 m / 2)^2

Finally, to find the net gravitational force, we simply add the forces:

Net gravitational force = F1 + F2

Now you can calculate the net gravitational force exerted by these objects on the 62.0 kg object placed midway between them.