An approach to conservation of electrical mechanical energy

AI Thread Summary
The discussion centers on the application of conservation of energy in a scenario involving a point charge and a moving charged sphere. The user questions whether external work should be included in the energy conservation equation since an external force is applied to fire the sphere. It is clarified that the work done by the external force, akin to gravitational potential energy in a similar scenario, must be considered in the energy balance. The external agent is identified as the force exerted during the firing process, which is not a conservative force. Ultimately, the conversation emphasizes the need to account for this external work when analyzing the system's energy.
ehabmozart
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Homework Statement



A point charge q1=5μC is held fixed in space. From a horizontal distance of 6.00 cm, a small sphere with mass 4g and charge 2μC is fired toward the fixed charge with an initial speed of 40.0 m/s. Gravity can be neglected. What is the acceleration of the sphere at the instant when its speed is 25.0 m/s?

Homework Equations



Conservation of Energy and Coulomb's law

The Attempt at a Solution



I am able to solve the full question but I am wondering is it possible to use conservation of energy in this case. I mean the work has been done by an external force, so how is it possible to say
Ka+Ua = Kb+Ub ALONE... Shouldn't we add W other to the initial mechanical energy? If someone can explain with analogy to gravity, it would be great too :)
 
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ehabmozart said:
I am able to solve the full question but I am wondering is it possible to use conservation of energy in this case. I mean the work has been done by an external force, so how is it possible to say
Ka+Ua = Kb+Ub ALONE... Shouldn't we add W other to the initial mechanical energy? If someone can explain with analogy to gravity, it would be great too :)

What is the work done here (what is W)? Who/what is the external agent?
 
Sunil Simha said:
What is the work done here (what is W)? Who/what is the external agent?

The external agent is the force given by the firing.. It is not a conservative force?
 
ehabmozart said:
The external agent is the force given by the firing.. It is not a conservative force?

Say the 2μC sphere is a bullet, the gun and the bullet are at rest right? So all the work that the guy holding the gun to bring the bullet up to the point of firing has simply gone into increasing the potential energy of the bullet (while bringing it from infinity to that point). So W is simply the potential energy at that point.
 
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