# What is the need for the concepts of Work and Energy (KE)?

Gold Member
What is the need to introduce the concept of work and energy when the motion can be completely understood by the concept of force and acceleration and momentum and velocity and displacement, etc?
Why do we need to understand the same thing once again in terms of Work and energy?
Also the kinetic energy produces velocity not that the velocity produces kinetic energy. So why we define Kinetic energy in terms of velocity and not define velocity in terms of Kinetic energy?

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You have 10ml of gasoline to power a winch, with which you need to lift a car of mass 1000kg. Assuming (unrealistically) that the winch is 100% efficient, do you have enough fuel to lift the vehicle to a height of 3m? (Note: burning gasoline releases about 33.6MJ/l.)

Where would you begin answering that question with forces?

• • Mentor
Why do we need to understand the same thing once again in terms of Work and energy?
Ibix has a good point, but even if you have a purely mechanical problem or fifty, you might notice some useful equalities repeatedly over time that you feel like giving a name to. That's a lot of what the early development of physics was.
(R.I.P. vis-viva)
Also the kinetic energy produces velocity not that the velocity produces kinetic energy. So why we define Kinetic energy in terms of velocity and not define velocity in terms of Kinetic energy?
Neither premise is true, and the correct premises would render the question moot.

What did work-energy ever do to you to deserve this abuse?

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• BvU, sysprog, Lnewqban and 1 other person
Homework Helper
Gold Member
Why do we need to understand the same thing once again in terms of Work and energy?
Both are very practical concepts.
https://en.m.wikipedia.org/wiki/Watt

Energy manifests itself in several other forms besides mechanical.
The chemical energy of a fuel can become thermal energy, and then mechanical energy, and so on.

• sysprog
ergospherical
To solve a mechanical system with ##n## degrees of freedom means to solve a system of ##n## second order differential equations in the coordinates ##q_i##. But most of the time it's not at all easy to solve the system explicitly for the time-dependence ##q_i = q_i(t)## of each coordinate. What's more likely is that you aim to solve the system implicitly for equations of the form ##\pi_i(q_1, \dots, q_n, \dot{q}_1, \dots, \dot{q}_n, t) = \kappa_i##, where the ##\kappa_i## are so-called integrals of motion. If you have ##2n## such equations then you have completely solved the problem.

For conservative systems, energy is conserved and is one integral of motion. (For systems acted upon by no net force, momentum is another such integral of motion, et cetera.). The benefit of being able to identify these special conserved quantities (energy, momentum, angular momentum, etc.) is that you can immediately write down equations involving the coordinates and their derivatives, and arrive at the required ##2n## such implicit equations more rapidly.

• sysprog and hutchphd
2022 Award
@ergospherical's post is a more mathematical and general version of what I was getting at in #2. To solve the question I posed without using energy, you'd need some method to describe how gasoline combustion turns the motor, and you'd need to write down equations describing the accelerations for the motor and winch components under the influence of the weight and the motor. These are the differential equations he's talking about. Even writing them down is a tall order - solving them is even worse.

But we don't have to care because there are conserved quantities we can use. A 1000kg car 3m up has an extra 30kJ of gravitational potential energy. Energy is conserved, so you just have to ask if the fuel contains at least that much energy. And that's why energy is useful.

• sysprog and ergospherical
Gold Member
If you can solve a problem without using the work-energy concept, it is perfectly fine. You don't need to. But it can be nice to have other options. For example, you can solve static problems with the virtual work method, even though no work is done since nothing move:

Why use that method? Sometimes it can be easier or some people might find it easier to visualize the problem this way. It is just another tool at your disposition.

Gold Member
What is the need to introduce the concept of work and energy when the motion can be completely understood by the concept of force and acceleration and momentum and velocity and displacement, etc?
You need the concepts of work and energy to develop thermodynamics; which includes thermal phenomena. Without that theory we'd be in the horse and buggy era.

• Ibix, Lnewqban and russ_watters
Gold Member
@ergospherical's post is a more mathematical and general version of what I was getting at in #2. To solve the question I posed without using energy, you'd need some method to describe how gasoline combustion turns the motor, and you'd need to write down equations describing the accelerations for the motor and winch components under the influence of the weight and the motor. These are the differential equations he's talking about. Even writing them down is a tall order - solving them is even worse.

But we don't have to care because there are conserved quantities we can use. A 1000kg car 3m up has an extra 30kJ of gravitational potential energy. Energy is conserved, so you just have to ask if the fuel contains at least that much energy. And that's why energy is useful.
So we associate velocity and mass to the energy ##K_f-K_i=W## and this helps to calculate the required energy to bring the body to a certain speed that we can provide to the system via fuel.
you'd need some method to describe how gasoline combustion turns the motor, and you'd need to write down equations describing the accelerations for the motor and winch components under the influence of the weight and the motor. These are the differential equations he's talking about. Even writing them down is a tall order - solving them is even worse.
Can you show a glimpse of the eqns?