Two massless bags contain identical bricks, each brick having a mass m. initially, each bag contains four bricks, and the bags mutually exert a gravitational attraction f1 on each other. you now take two bricks from one bag and add them to the other bag, causing the bags to attract each other with a force f2. what is the closest expression for f2 in terms of f1?

Explanation:

According to Newton's law of universal gravitation:

Where:

is the module of the force exerted between both bodies

is the universal gravitation constant.

and are the masses of both bodies.

is the distance between both bodies

In this case we have two situations:

1) Two bags with masses and mutually exerting a gravitational attraction on each other:

  (1)

  (2)

  (3)

2) Two bags with masses and mutually exerting a gravitational attraction on each other (assuming the distance between both bags is the same as situation 1):

  (4)

  (5)

  (6)

Now, if we isolate from (3):

  (7)

Substituting  found in (7) in (6):

  (8)

  (9)

Simplifying, we finally get the expression for  in terms of :

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