Question

A 190-kg object and a 490-kg object are separated by 4.40 m.

(a) Find the magnitude of the net gravitational force exerted by
these objects on a 63.0-kg object placed midway between them.

(N)

(b) At what position (other than an infinitely remote one) can the 63.0-kg object be placed so as to experience a net force of zero from the other two objects?

(m from the 490 kg mass toward the 190 kg mass)

(N)

(b) At what position (other than an infinitely remote one) can the 63.0-kg object be placed so as to experience a net force of zero from the other two objects?

(m from the 490 kg mass toward the 190 kg mass)

Answer #1

Force = G * M1 * M2 /r^2

When the 63 kg particle feels the same force of attration to the 190 and 490 kg objects, the 63 kg object is in equlibrium, so net force = 0 N

G * 490 * 63 /r1^2 = G * 190 * 63/r2^2

490/r1^2 = 190/r2^2

490 * r2^2 = 190 * r1^2

r2^2/ r1^2 = 190/490 = 13/28

r2/r1 = (19/49)^0.5

r2 = r1 * (19/49)^0.5

The is ratio of distances.

The distance to the 490 object is (19/49)^0.5 * the distance to the 190 kg object

If the 190-kg object and a 490-kg object are separated by 4.40 m, r1 + r2 = 4.40

Now you have 2 equations in 2 variables, solve for r1and r2

r1 + r2 = 4.40

r2 = r1 * (19/49)^0.55

A 275-kg object and a 575-kg object are separated by 4.40 m.
(a) Find the magnitude of the net gravitational force exerted by
these objects on a 46.0-kg object placed midway between them.
N
(b) At what position (other than an infinitely remote one) can the
46.0-kg object be placed so as to experience a net force of zero
from the other two objects?
m from the 575 kg mass toward the 275 kg mass

A 295-kg object and a 595-kg object are separated by 4.30 m.
(a) Find the magnitude of the net gravitational force exerted by
these objects on a 44.0-kg object placed midway between them.
___N
(b) At what position (other than an infinitely remote one) can the
44.0-kg object be placed so as to experience a net force of zero
from the other two objects?
___m from the 595 kg mass toward the 295 kg mass

A 105-kg object and a 405-kg object are separated by 4.50 m.
(a) Find the magnitude of the net gravitational force exerted by
these objects on a 59.0-kg object placed midway between them.
(answer)N
(b) At what position (other than an infinitely remote one) can
the 59.0-kg object be placed so as to experience a net force of
zero from the other two objects? (answer)m from the 405 kg mass
toward the 105 kg mass

A 165-kg object and a 465-kg object are separated by 4.30 m.
(a) Find the magnitude of the net gravitational force exerted by
these objects on a 41.0-kg object placed midway between them.
Answer: 1.77*10^-7, Got this , Can't find B
(b)At what position (other than an infinitely remote one) can
the 41.0-kg object be placed so as to experience a net force of
zero from the other two objects?
Answer? ______

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0.500 m.
(a)
Find the net gravitational force exerted by these objects on a
69.0 kg object placed midway between them.
magnitude N
direction ---Select--- toward the 240 kg mass/ toward the 540 kg
mass /The magnitude is zero.
(b)
At what position (other than infinitely remote ones) can the
69.0 kg object be placed so as to experience a net force of
zero?
m from the...

Objects with masses of 225 kg and a 525 kg are separated by
0.410 m.
(a) Find the net gravitational force exerted by these objects on
a 57.0 kg object placed midway between them.
magnitude _____ N
direction ---Select--- (toward the 225 kg mass toward the 525 kg
mass The magnitude is zero.)
(b) At what position (other than infinitely remote ones) can the
57.0 kg object be placed so as to experience a net force of
zero?
______m from...

Objects with masses of 245 kg and
a 545 kg are separated by 0.480 m.
(a) Find the net gravitational force exerted by these objects on
a 60.0-kg object placed midway between them.
Magnitude: ___________
Direction: (Toward the 545- kg mass)
(b) At what position (other than infinitely remote ones) can the
60.0-kg object be placed so as to experience a net force of
zero?
: _____________m from the 545-kg mass

Objects with masses of 170 kg and a 470 kg are separated by
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(a)Find the net gravitational force exerted by these objects on
a 45.0 kg object placed midway between them.
magnitude?
(b) At what position (other than infinitely remote ones) can the
45.0 kg object be placed so as to experience a net force of
zero?
_____m from the 470 kg mass

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0.370 m.
(a) Find the net gravitational force exerted by these objects on
a 45.0 kg object placed midway between them.
magnitude N
(b) At what position (other than infinitely remote ones) can the
45.0 kg object be placed so as to experience a net force of
zero?
m from the 560 kg mass

Objects with masses of 145 kg and a 445 kg are separated by
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(a) Find the net gravitational force exerted by these objects on
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(b) At what position (other than infinitely remote ones) can the
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