Work, energy, impulse, momentum

[observer1]

In most "introduction to dynamics" textbooks, why do we teach work and energy?

Consider a textbook like Hibbeler's Dynamics:

Chapter 1: kinematics of particles
Chapter 2: kinetics of particles
Chapter 3: Work Energy
Chapter 4, Impuse and Momentum
AND THEN IT REPEATS FOR BODIES

Now, I understand it is important to discuss work/energy.
I mean, yes, I think it is wise to introduce these concepts and that means using precise definitions.

But these topics have no impact on a mechanical engineering student, in the context of dynamics. They are only useful for non-dissipative systems and a quick check on solutions.

In reality, these topics are critical in understanding Hamilton's approach and the Principle of Virtual work and variational methods

But why do we give them such prominence in an introductory class in rigid body dynamics of particles and bodies?

One argument might be that it is worth introducing these concepts from a mechanical perspective. But why do we bother to solve more than just a few exemplary problems? Why do we raise it to the level of an entire chapter?

The topics just seem to clutter the learning for most students, of the general idea of kinematics and kinetics.

(I can sort of justify teaching impulse and momentum, sure; but I cannot seem to justify teaching work/energy other than as a short introduction to the concept before moving back to solving problems.)

 

[Andrew Mason]

How would you analyse elastic collisions without using energy?

AM

 

[FQVBSina_Jesse]

I personally preferred energy methods to relate speed, height, and other forms of energy devices such as springs, frictional surfaces, etc.

It is simply another way to solve kinematic problems that many people (including myself) find easier and more intuitive to use than regular kinematic equations.

 

[mrm11]

it is all about understanding geometry of various curves.
the distribution of the points which formulate the path of the particles, and the rate at which particles reach the points.
basically this correlates to the Newton laws of mechanics which are the basic for all mechanical systems.
the contents mentioned herein are justified.

 

[Nidum]

I never really understood the purpose of the question .

All the topics mentioned are included in ordinary undergraduate engineering courses and all have some useful purpose .

Perhaps @observer1 would like to explain why there is really has any problem with this ?

 

[observer1]

I never really understood the purpose of the question .

All the topics mentioned are included in ordinary undergraduate engineering courses and all have some useful purpose .

Perhaps @observer1 would like to explain why there is really has any problem with this ?

OK... I am not sure I will be clear because I am still thinking about it.

Take a look at most undergraduate textbooks:
Kinematics
Kinetics
Work Energy

Now, together, Kinematics and Kinetics provides the equations of motion. OK
Work and Energy (as it is DEMONSTRATED in the undergraduate class) is just a way to find the solutoins faster (by, perhaps, pre-integrating).
In cases where the forces are conservative, you even get potential energy.

But is this ever really useful?

Would it not be more useful to spend time on 3D kinetics?

Yes, as some have said, we use work and energy in collisions, etc. But we can just as well do that with the coefficient of restituion. (Sure work and energy explains the boundaries of the ceofficient: e=0 for stick together; e =1 for elastic collisons)

However, that is NOT how work and energy are really used.

They are really useful in the Principle of Virtual work as an extnesion of Hamilton's Principle and the Lagrangian.

We we ever really care about problems where a roller coaster loops around (given its height, what is the velocity when the loop is over?)

You may still disagree with me, but does that make my concern clearer?

 

[Stephen Tashi]

Would it not be more useful to spend time on 3D kinetics?

However, that is NOT how work and energy are really used.

They are really useful in the Principle of Virtual work as an extnesion of Hamilton's Principle and the Lagrangian.

You may still disagree with me, but does that make my concern clearer?

My guess is that you care more about one particular type of application of mechanics than other types, but don't yet understand what that type of application you perfer - and why 3D kinetics would be important for it.

I also don't understand exactly how you envision the content of "3D kinetics". Does it include the precession of gyroscopes? Solving problems involving rotations - roll, pitch, yaw? Problems of controlling robot arms? Classical analysis of planetary motions?

 

[observer1]

My guess is that you care more about one particular type of application of mechanics than other types, but don't yet understand what that type of application you perfer - and why 3D kinetics would be important for it.

I also don't understand exactly how you envision the content of "3D kinetics". Does it include the precession of gyroscopes? Solving problems involving rotations - roll, pitch, yaw? Problems of controlling robot arms? Classical analysis of planetary motions?

Yes... All that you say. I would have loved to spend more time with the latter. I did not really use or understand work/energy until I studied Hamilton's Principle and Principle of Virtual work. All I really understood back then were simple roller coaster problems. I think my time would have been better spend mastering 3D dynamics.