Solve Energy Change Homework: Why Alternative Fails

In summary, this alternative approach to solving the homework problem fails because the particle experiences a net force pointing to the right, which requires the application of a left-wards force to keep it moving down the center of the arrangement.
  • #1
friendbobbiny
49
2

Homework Statement


(see picture)

I understand one approach to this homework problem. I don't understand why an alternative approach fails.

Homework Equations


V = E*d

The Attempt at a Solution


The correct answer is (d), zero.

An acceptable approach:
1) Realize that V is the same at both corners
2) Thus, delta V = 0
3) delta U = q*V
4) If potential energy doesn't change, then no work has been done (or been "lost") from the system.

An alternative:

1) The particle experiences a rightwards force in the direction of the 2+ charge
2) To offset the right-wards pulling force and maintain a straight path, a new force, Fn, needs to be applied leftwards.
3) The force (Fn) is applied over a distance (Not the vertical distance between both charges. Instead: The horizontal distance that would otherwise exist were Fn not exerted)
4) This implies that energy has been exerted.
 

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  • #2
Sketch the force vector for different points along the trajectory from R to S. Work is done by the component of the force along the line of travel. Is there a symmetry involved?
 
  • #3
friendbobbiny said:
3) The force (Fn) is applied over a distance (Not the vertical distance between both charges. Instead: The horizontal distance that would otherwise exist were Fn not exerted)
Assume first the charge travels along the st. line R-S.
Why would Fn be applied over a distance? Fn is applied just enough to keep the charge along R-S, which is perpendicular to Fn always.
What is the vector formula for work?
Finally, answer this: what if the charge moves along some path other than the st. line R-S. Now Fn would not be perpendicular to the path along much or most of the way, and the charge would move in the direction of Fn back & forth as the charge travels from R to S. So W would vary along this path. Why is it still true that net W=0, going from R to S?
 
  • #4
rude man said:
Why would Fn be applied over a distance?

Doesn't the charge experience a net force pointing to the right?
If it experiences a net force to the right, don't we have to exert a left-wards force to keep it moving down the center of the arrangement?

The distance acted upon by the left-wards force isn't apparent, precisely because the force is inhibitive. It keeps the particle from moving the distance that we want to associate with energy.
This logic obviously isn't sound. Why isn't it?
 
  • #5
Force without displacement does no work. If the charge moves along a straight line perpendicular to the force that happens to be keeping it there, it does no work. This is akin to the way the floor provides a normal force to prevent an object from falling to the basement while you move it across the room. The floor does no work preventing the object from falling.

What you need to be concerned about is the component of the net force that is directed along the line of motion of the charge. That part of the force will be doing work (positive or negative). Draw the sketch as I suggested.
 
  • #6
Ah this makes sense, especially with the example of the normal force exerted by the floor.

Yes, there's a symmetry. I'll draw a picture soon so that future pf users have it for their reference.
 

What is energy change and why is it important?

Energy change refers to the transformation of energy from one form to another. It is important because it is necessary for sustaining life and powering various processes and technologies. Without energy change, our daily lives would be vastly different and many industries would not be able to function.

What are alternative energy sources, and why do they fail?

Alternative energy sources are renewable energy sources that are considered more environmentally friendly than traditional fossil fuels. However, they often fail due to their high initial costs, limitations in efficiency, and lack of infrastructure for widespread implementation. Additionally, some alternative energy sources, such as biofuels, have been found to have negative impacts on food production and land use.

How can we solve energy change and reduce our reliance on traditional fossil fuels?

One solution is to invest in research and development of alternative energy technologies, such as solar, wind, and geothermal power. Another approach is to implement energy conservation and efficiency measures, such as using energy-efficient appliances and buildings. Additionally, policies and incentives can be put in place to encourage the adoption of renewable energy sources.

What are the potential benefits of transitioning to alternative energy sources?

Transitioning to alternative energy sources can bring a variety of benefits, including reducing greenhouse gas emissions and mitigating the effects of climate change, diversifying energy sources and increasing energy security, and creating new job opportunities in the renewable energy industry.

What are the challenges and obstacles to implementing alternative energy sources?

Some of the challenges and obstacles include the high costs of initial investment, the need for new infrastructure and technologies, resistance from traditional energy companies, and potential negative impacts on certain industries and communities. Additionally, political and social barriers can also hinder the transition to alternative energy sources in some regions.

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