EK 1001 Physics #163

[MedPR]

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Stuck, again. Merry Christmas to me.

This is a law of universal gravitation problem based on F=G(m1*m2)/r^2

r=10m. m1 and m2 each have a mass of 10^9kg, and a radius of 1.67m. If they start from rest, the accelerations of the masses will:

A: remain at 0
B: remain constant but not at zero
C: Increase
D: decrease

Explanation C is correct. From F=GmM/r^2 we see that the force on each mass grows greater as r decreases. From F=ma we see that as F grows larger, a grows larger.

That's great, I know that as radius increases, force decreases, thus increasing acceleration, but based on the question, how do you know that the radius between them will increase?

 

[grapepopsicle]

The objects are starting at rest 10 m away from each other. They are attracted to each other so the distance between them decreases, increasing the gravitational force, and hence the acceleration.

 

[MedPR]

The objects are starting at rest 10 m away from each other. They are attracted to each other so the distance between them decreases, increasing the gravitational force, and hence the acceleration.

I got that after looking at the answer, but how do you know that 10m isn't the distance between them? How do you know that their attraction will bring them closer together than 10m?

 

[grapepopsicle]

They are initially at rest 10m apart. According to the passage information, they are infinitely far from any other mass so they will only experience a force due to each other. They are definitely going to accelerate toward each other because of this gravitational force between them, so they will accelerate toward each other until they collide. The distance between them decreases, increasing the force and the acceleration.

 

[MedPR]

They are initially at rest 10m apart. According to the passage information, they are infinitely far from any other mass so they will only experience a force due to each other. They are definitely going to accelerate toward each other because of this gravitational force between them, so they will accelerate toward each other until they collide. The distance between them decreases, increasing the force and the acceleration.

I guess I'm missing a major concept then. I thought that objects would eventually repel each other when they reach a certain distance to each other...

 

[grapepopsicle]

Gravitational forces are always attracting, so (in the absence of any other forces) these two masses will accelerate toward each other until they collide. The only force on each is the grav. force given by the equation in your first post, and it increases as they get closer together.

 

[MedPR]

Gravitational forces are always attracting, so (in the absence of any other forces) these two masses will accelerate toward each other until they collide. The only force on each is the grav. force given by the equation in your first post, and it increases as they get closer together.

Ok, thanks! I guess I was thinking that the forces each exerted on the other was enough to repel them but also enough to keep them at a consistent radius -- like a satellite orbiting the earth.

 

[ljc]

Satellites orbiting earth are not held in place by any repelling force - they are always experiencing gravity, and so are always accelerating towards Earth, they just keep "missing." Think if you could fire a cannon ball along the earth's surface fast enough that the earth curved at exactly the same rate as the ball fell.

Gravity is always an attracting force - there is no counter repelling force.

 

[MedPR]

Satellites orbiting earth are not held in place by any repelling force - they are always experiencing gravity, and so are always accelerating towards Earth, they just keep "missing." Think if you could fire a cannon ball along the earth's surface fast enough that the earth curved at exactly the same rate as the ball fell.

Gravity is always an attracting force - there is no counter repelling force.

Thank you.