Circular Motion & Universal Gravitation: Gravity Between

[cocobandit13]

1. Homework Statement
Two "swarms" of krill each contain 1.200×107 identical individuals. The centers of gravity of the "swarms" are 15.0 meters apart. By what factor will the gravitational force of attraction between the two "swarms" change, if 9.231×106 new krill join each "swarm?"

Use the Law of Universal Gravitation and proportional reasoning. Also, remember that any individual factor of change is simply the new value divided by the old value. A factor is the number you must multiply your old value by to get your new value.

2. By what factor will the gravitational force of attraction between the two original "swarms" change, if 9.231×106 krill move from one swarm to the other?

Use the Law of Universal Gravitation and proportional reasoning

3.By what factor will the gravitational force of attraction between the two original "swarms" change, if 1.080×107 new krill join each "swarm", and the swarms move until they are 6.52 meters apart?

Use the Law of Universal Gravitation and proportional reasoning

4.By what factor will the gravitational force of attraction between the two original "swarms" change, if the swarms drift to 45.00 meters apart?

Use the Law of Universal Gravitation and proportional reasoning

Homework Equations

F=G(m1m2/r^2)
G=6.67x10^-11
F=ma
a=v^2/r
a=4pi^2r/T^2
r=radius
T=period or time
etc...

The Attempt at a Solution

no attempts

 

[LowlyPion]

Welcome to PF.

How would you think to start?

For instance by what percentage does the effective mass of a swarm increase?

 

[thomate1]

needed for a response

I would approach these questions by using the Law of Universal Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers of mass. In this case, the two "swarms" of krill can be treated as point masses.

1. If 9.231×106 new krill join each "swarm," the total mass of each swarm will increase by a factor of (1.200×107 + 9.231×106)/1.200×107 = 1.7693. Using the Law of Universal Gravitation, we can calculate the new force of attraction between the two swarms as follows:

F' = G[(1.7693m1)(1.7693m2)]/(15.0m)^2 = (1.7693)^2F = 3.129F

Therefore, the gravitational force of attraction between the two swarms will increase by a factor of 3.129.

2. If 9.231×106 krill move from one swarm to the other, the total mass of each swarm will remain the same. However, the distance between the centers of mass will decrease from 15.0m to (15.0m - 9.231×106/1.200×107) ≈ 14.23m. Using the Law of Universal Gravitation, we can calculate the new force of attraction between the two swarms as follows:

F' = G(m1m2)/(14.23m)^2 = F/1.0146

Therefore, the gravitational force of attraction between the two swarms will decrease by a factor of 1.0146.

3. If 1.080×107 new krill join each swarm and the swarms move until they are 6.52 meters apart, the total mass of each swarm will increase by a factor of (1.200×107 + 1.080×107)/1.200×107 = 1.9. The distance between the centers of mass will decrease from 15.0m to 6.52m. Using the Law of Universal Gravitation, we can calculate the new force of attraction between the two swarms as follows:

F' = G[(1.9m1)(1.