Acceleration of particles with differing masses in a uniform electric field

[squimmy]

Homework Statement

The diagram shows two charged spheres X and Y, of masses 2m and m respectively, which are just prevented from falling under gravity by the uniform electric field between the two parallel plates.

If the plates are moved closer together
A X and Y will both remain stationary.
B X and Y will both move upwards with the same acceleration.
C X will have a greater upward acceleration than Y.
D Y will have a greater upward acceleration than X.

(I haven't posted the diagram, but it just shows 2 plates lying horizontally with 2 circles directly in the middle of the 2 plates, one circle twice the size of the other)

Homework Equations

F = eq
F = ma
E = V/D

The Attempt at a Solution

The answer is B, but I don't understand why.

Plates moved closer together, E=V/D, so electric field increases in strength.

I understand that in a gravitational field the only force is W=mg, so F=W so ma = mg, g's cancel so a is constant. But in a gravitation field surely F=eq so eq=ma so a = eq/m. In other words, suerely mass would have an effect on the upwards acceleration? So the upwards acceleration of both would not be equal?

 

[kuruman]

Hi squimmy and welcome to PF. It seems you are a bit confused. When the spheres are suspended (prevented from falling), this means that their acceleration is zero. This also means that the net force on each is zero. Can you write an equation saying that the net force (sum of all the forces) is zero?

 

[squimmy]

Confused indeed!

Not entirely sure what you mean...

The spheres are suspended so the downward force, gravitational, equals the upwards force, electrical. So eq=mg? Thus F = 0, so ma = 0, so a must be zero.

But why, when the electrical field is made stronger, do they accelerate equally regardless of mass?

 

[kuruman]

One sphere has twice the mass of the other. What does this say about its charge relative to the charge on the other sphere?

 

[squimmy]

I was under the impression that the question implied the charges were equal?

 

[kuruman]

The problem doesn't say that they are. In fact if they were, they would have unequal downward gravitational forces acting on them but equal upward electrical forces. This means that, for given E field value, one or the other can be suspended but not both.

 

[squimmy]

Oh. In that case I suppose it would be logical for one mass to have twice the charge of the other. Therefore using a=eq/m, q and m are both twice as large so the acceleration should be equal for both, leading to B. Is that correct?

Thanks a lot! :)

 

[kuruman]

That is correct. Two particles that have the same q/m ratio will have the same acceleration.