Why do we use the work energy theorem in systems of energy and work problems?

[FeelTheFire]

Hey all, I was feeling confident with the idea of work when dealing with vectors and using the dot product to find the work.
However, recently we have begun to discuss work while considering the object experiencing the force as part of a system. I'm having trouble transitioning into this idea and I don't really know when to consider energies and apply the work energy theorem versus using vectors and dot products. An example that I'm having trouble with:

The first thing I'm tempted to do is draw a free body diagram and begin plugging vectors into Newton's second law.

I was able to solve the problem using a hint from my instructor but I don't understand why the method works. It was as follows:

Ki + Wg + Ws = Kf Where Ki is initial kinetic energy, Wg is the work done by the gravitational force, Ws is the work done by the spring force and Kf is the final kinetic energy. When you substitute and simplify all this down you can solve for the displacement (x) via a quadratic equation and arrive at 0.131 m.

We have not learned about the conservation of energy yet. Any insight would be much appreciated. I really want to understand this concept!

 

[PhanthomJay]

Well that is odd that you would be given a problem that uses work-energy principles when you haven't been taught it yet. Your instructor has hinted at using the Work-Energy principle that states that the net or total work done on an object is equal to its change in kinetic energy. You could also use conservation of energy that states that the sum of the initial potential and kinetic energy is equal to the sum of the final potential and kinetic energy (in the absence of any work done by non conservative forces), which I thiink is a bit simpler because of issues with plus or minus signs. It isn't very helpful to use an equation you are not familiar with and just plug in numbers without knowing when or how to properly use the equation with little understanding of the theory behind it.

 

[FeelTheFire]

Thanks for the reply PhanthomJay, I appreciate it.

Well that is odd that you would be given a problem that uses work-energy principles when you haven't been taught it yet.

Sorry I must not have been clear. I have heard the lecture and read the text on the ideas of energy and work, but I'm having a hard time understanding and applying the new concepts.

In particular, I can't distinguish which problems would be better solved using energy concepts instead of Newtonian vector concepts. I don't really understand the difference or the NEED to work with energies.

Also, until you said it, I didn't even recognize the instructors hint as the work-energy theorem. I have never seen it used with multiple sources of work before, only as W = delta K.

The next chapter in my text deals with the "conservation of energy", and I'd really like to understand conceptually the idea of energies before I move on to it. So I guess my query is more about the nature of energy concepts rather than a specific problem...

 

[PhanthomJay]

Oh, fine.. The work energy principle is derived form the conservation of energy principle which basically states that energy cannot be created or destroyed---just transferred into different forms. Often you can use Newton's laws and the kinematic equations OR energy methods to solve a problem.. In your specific problem, it would be rather difficult to solve using the Newton/kinematic approach. Rather than me explain the principle and do probably a lousy job at it, you should check the Physics tutorial in the 'Math and Science Learning Materials' section of this sub-forum.

 

[Nickie]

The work-energy theorem is a fundamental concept in physics that relates the work done on an object to its change in kinetic energy. In systems of energy and work problems, we use the work-energy theorem because it allows us to consider the total energy of a system, rather than just the forces acting on a single object.

In the example you provided, the work-energy theorem is used because the system consists of multiple objects (the spring and the object experiencing the force) and we need to consider the energy of both objects. By using the work-energy theorem, we can take into account the work done by both the gravitational force and the spring force on the object, as well as the initial and final kinetic energies of the system.

Using vectors and dot products to find the work done on an object can be useful in simpler cases, but in more complex systems, it may not give us a complete understanding of the energy changes in the system. In these cases, the work-energy theorem allows us to analyze the system as a whole and take into account all energy changes.

It is also important to note that the work-energy theorem is a general principle that applies to all types of forces, not just gravitational and spring forces. So, as you continue to learn about different types of forces and their effects on objects, the work-energy theorem will still be applicable.

In summary, we use the work-energy theorem in systems of energy and work problems because it allows us to consider the total energy of a system and take into account all the forces and energy changes involved. It is a powerful tool in understanding and solving complex problems in physics.