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__First Problem:__A 200 kg object and a 700 kg object are separated by 0.700 m.

(a) Find the net gravitational force exerted by these objects on a 60.00 kg object placed midway between them.

(b) At what position (other than an infinitely remote one) can the 60.00 kg object be placed so as to experience a net force of zero?

m from the 700 kg object (on a line connecting the 200 kg and 700 kg objects)

I already solved for the first part. I got 1.63e-5 N, which was correct.

For the second part I thought you could just set the gravitational force equation, F=G(m1)(m2)/r^2 equal to zero, plug in my variables and solve for r, but I can't solve for r with that setup. Can anyone help?

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__Second Problem__A spacecraft in the shape of a long cylinder has a length of 100 m and its mass with occupants is 1840 kg. It has strayed too close to a 1.0 m radius black hole having a mass 106 times that of the Sun (Fig. P11.8). The nose of the spacecraft points toward the black hole, and the distance between the nose and the black hole is 10.0 km.

(a) Determine the total force on the spacecraft.

(b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole?

Again with this one I got the first answer, which was 2.55e17 N. For the second part I tried finding the gravitational force equation at the front end and then at the back end of the rocket and solving for the difference, but it didn't work. Also, it says the answer should be in Newtons per kilogram. What does that mean?