Question

Consider two plastic spheres, 1 meter apart: one sphere has a mass of 1 kg and an electric charge of +1nC and the big sphere with a mass of 11 kg and an electric charge of +11 micro Columbs.

Answer 1

a. find the electric force and the gravitational force between the spheres.

and

b. if the big sphere is fixed in position and the little sphere is free to move, describe the resulting motion of the little sphere if it's released from rest.

Answer 2

@sweetburger @zepdrix

Answer 3

@agent0smith

Answer 4

My thoughts are for part A. that both formulas are basically the same so there wouldn't be a difference.

Answer 5

I thought gravitational forces only had impacts on large objects so, I don't get how this would be of any consequence here.

Answer 6

The formulas are not the same, since the grav. constant G is not remotely equal to the coulomb constant k

Answer 7

And... gravity depends on mass, electrostatic force on charge which are two entirely different quantities.

All you need to do is plug numbers into formulas here, it's not hard.

Answer 8

so they are not related in any way because one depends on mass while the other charge

Answer 9

Zero relation. The formulas just look very similar.

Answer 10

\[\frac{ 6.7*10^{-11} N*m^{2}/kg^{2}*(1)(11)kg^{2} }{ 1m } = 7.4*10^{-11}~N\]

\[\frac{ (9*10^{9}N~m^{2}/c^{2})*(11*10^{-6}C*1*10^{-9}C }{ 1m } = 9.9*10^{-5} C\]

Answer 11

Okay so now.. one force has to do with electric charge the other has do to with just force. Seems like the gravitational force is so small compared to the columbic force. is there any other ways I can interpret this answer?

Answer 12

What direction is the coulomb force on each charge?

Answer 13

Says +11 micro columb and +1 nano columb

Answer 14

so the way I interpreted it was this: they are both headed towards each-other? I'm a little conufsed is + the sign of the charge but does it also tell you the direction of the charge?

Answer 15

Read my question again. I didn't ask about the size of the charges.

Like charges repel. Unlike charges attract.

Answer 16

okay so because they are both + that means that they will repel each-other and go off in opposite directions right?

Answer 17

Right. Gravity pulls them inward, coulomb force pushes them outward.

Answer 18

okay so the second part of the question is this:

b. if the big sphere is fixed in position and the little sphere is free to move, describe the resulting motion of the little sphere if it's released from rest.

so like based on what we said before both spheres are + charged.



this means that the small sphere is going to go off in the opposite direction.

was wondering how would we describe the acceleration of the small sphere?

Answer 19

Use Net force = ma

Find the net force using the two forces acting on the small sphere... gravity and coulomb force both act on it

Answer 20

I'll do that and post what I get. So in the formula F = Gm1m2/r^2 is the force of gravity exerted on both objects, same with Q = kq1q2/r^2

Answer 21

Yes but you already know the forces.

Answer 22

sorry, bear with me here thanks for your patience. the reason why I thought it was different was because I thought once the small sphere is repelled from the large sphere, the force between the two objects is going to get smaller because the r the distance between them is going to get bigger.

maybe then acceleration would go down too because F =ma

so from what you said, the force of gravity and the columbic forces are acting in differnet directions.


\[-F_{g}+F_{c~\small~sphere } = F_{net~small~sphere }\]

Answer 23

Yes it will go down, but you're only interested in the initial acceleration. You could write an equation for acceleration in terms of distance, if you wanted to.

Answer 24

let me see if I can work that out

Answer 25

\[F = ma => a => \frac{ F }{ m } => \frac{ 9.9*10^{-5}~N }{ 1~kg } = 10^{-4} \frac{ m }{ s^{2} }\]

Answer 26

I was also wondering about these two formulas is that what prevents say one object from crashing into another one?

Answer 27

Looks about right.

What do you mean? Nothing prevents them... except for the fact that it can't happen here, since they're repelling away from each other.

Answer 28

ok that makes sense but what if both charges are opposite then they would clearly attract one another.

Answer 29

Yes, in which case they'd collide.

Answer 30

interesting. yeah that clarified things up. so in summary we can compare the two formulas force of gravitation and columbic force in terms of their effect on an object . but they deal with different things, charge and mass.

so gravitational force will always try to pull things closer together while columbic force the efffect depends on whether the charges are opposite or the same.

Answer 31

Exactly.

Answer 32

thank you very much!

Answer 33

You're welcome! Good job.

Answer 34

Oh @greatlife44 "describe the resulting motion of the little sphere if it's released from rest. "

You could also just say that it'd accelerate away with an increasing velocity, and the acceleration will decrease as it moves further away

Answer 35

hm so I get why it would increase as we get further away from the other sphere. but how would it initially increase?

Answer 36

Velocity increases forever, since it's always accelerating away. The acceleration just gets smaller as it gets further away.

Answer 37

Acceleration will never reach zero, which means velocity continually increases.

Answer 38

\[a = \frac{ V_{2}-V_{1} }{ t_{2}-t_{1} }\]

I figure that if acceleration is going down then so must the change in velocity.

Answer 39

sorry could you explain that again @agent0smith

Answer 40

okay so my book says that because the acceleration is pointing in the opposite direction to the big sphere the velocity is always increasing. I don' understand why though

Answer 41

@jim_thompson5910

Answer 42

As long as acceleration is positive, velocity will increase.

Acceleration getting smaller just means the velocity increases LESS, it still increases, just not as much.

Like if the acceleration is 2m/s^2, the velocity is increasing much faster than if the acceleration is 0.1m/s^2.