Acceleration of a Sphere with a Charge

In summary, the conversation discussed the use of Coulomb's Law and F=ma to calculate the acceleration of two charged spheres on a horizontal, frictionless insulating surface. The correct answer was found, and it was clarified that the initial acceleration would only differ in sign if one of the spheres is negative. However, the situation becomes more complex when considering the changing force and acceleration as the objects attract or repel each other. In these cases, it is often more useful to think in terms of energy.
  • #1
The Matador
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Homework Statement


Two Charged spheres are positioned on a horizontal, frictionless insulating surface, as shown below.

I attached the image at the bottom of the post.

Homework Equations


Coulombs Law and F=ma

The Attempt at a Solution


I plugged in ((8.99 x 10^9)(5.0 x 10^-7)(5.0 x 10^-7))/(1.25)^2

Once I got the answer I used F=ma to find the acceleration which is 9.59 x 10^-2 m/s

I believe this is the correct answer. I was wondering if one of the spheres is negative would I go about answering the question in the same way. Or would I have to factor in other things.
 

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  • #2
It sounds like the initial acceleration would only differ in sign, same force, same mass. But there's much more to it, as you may suspect. If you release 2 oppositely charged objects, they will attract toward each other with decreasing distance and increasing force. The acceleration would increase until they collide. For 2 like charged objects, they will repel away from each other with increasing distance and decreasing force. The acceleration will decrease as the force approaches zero, and a final velocity is reached when the objects are at infinity. Because these situations deal with varying force/acceleration, its usually better to think in terms of energy.
 
  • #3


Yes, you are correct in your approach to solving this problem. The acceleration of a sphere with a charge can be calculated using Coulomb's Law and Newton's Second Law (F=ma). In this case, since the surface is frictionless and the spheres are positioned on a horizontal surface, the net force acting on the sphere will be the force of attraction between the two charged spheres.

If one of the spheres has a negative charge, you would simply need to include the sign of the charge in your calculations. Coulomb's Law takes into account the signs of the charges, so if one of the charges is negative, the force will be attractive (towards the positive charge) instead of repulsive (away from the positive charge). This means that the net force acting on the sphere will be different, and therefore the acceleration will also be different.

In summary, if one of the spheres has a negative charge, you would use the same equations and approach to solve for the acceleration, but the resulting value will be different due to the change in the net force acting on the sphere.
 

1. What is the equation for calculating the acceleration of a sphere with a charge?

The equation for calculating the acceleration of a sphere with a charge is a = F/m, where a is the acceleration, F is the force exerted on the sphere, and m is the mass of the sphere.

2. How does the charge on the sphere affect its acceleration?

The charge on the sphere affects its acceleration through the force exerted on it. Objects with opposite charges will attract each other, resulting in an acceleration towards each other. Objects with like charges will repel each other, resulting in an acceleration away from each other.

3. Can the acceleration of a sphere with a charge change over time?

Yes, the acceleration of a sphere with a charge can change over time. This can happen if the force exerted on the sphere changes, such as if the distance between the charged objects changes or if the magnitude of the charge changes.

4. How does the mass of the sphere affect its acceleration?

The mass of the sphere affects its acceleration through the equation a = F/m. The larger the mass of the sphere, the smaller the acceleration will be for a given force. In other words, a heavier sphere will require a greater force to achieve the same acceleration as a lighter sphere.

5. What role does the direction of the force play in the acceleration of a sphere with a charge?

The direction of the force plays a crucial role in the acceleration of a sphere with a charge. The acceleration will always be in the same direction as the net force acting on the sphere. If the force is in the same direction as the initial velocity of the sphere, the acceleration will increase the speed of the sphere. If the force is in the opposite direction, the acceleration will decrease the speed of the sphere.

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