Kinetic energy - what is the exact definition

[logearav]

Kinetic energy -- what is the exact definition

Homework Statement

some books define kinetic energy as work done for bringing a moving body to rest and some books say " kinetic energy of a moving body at a given velocity v is equal to the work done in making the body move from rest and attain this velocity. so which one is correct? members please help. thanks in advance. the definition for potential energy is work done in moving the body from one place to other. i am confused.

Homework Equations

The Attempt at a Solution

 

[flyingpig]

It's the energy you have when you are in motion.

So if yuo speed was 0, then you aren't moving and you have no kinetic energy.

 

[wbandersonjr]

Homework Statement

some books define kinetic energy as work done for bringing a moving body to rest and some books say " kinetic energy of a moving body at a given velocity v is equal to the work done in making the body move from rest and attain this velocity. so which one is correct? members please help. thanks in advance. the definition for potential energy is work done in moving the body from one place to other. i am confused.
QUOTE]

Work is equal to a change in kinetic energy. So, in accelerating an object from one velocity to a higher velocity, the work done by some force to move the object will be positive. Conversely, if the object is accelerated from a higher velocity to a lower one, then the work done by some force on the object would be negative. Both statements seem correct, however, they don't account for the value of work being opposite for the two cases.

As far as potential energy, what you wrote is correct too. It is important to recognize that when "moving" and object from one place to the other, the initial and final velocities are zero. So, the initial and final kinetic energies are zero.

 

[Quinzio]

Homework Statement

some books define kinetic energy as work done for bringing a moving body to rest and some books say " kinetic energy of a moving body at a given velocity v is equal to the work done in making the body move from rest and attain this velocity. so which one is correct? members please help. thanks in advance. the definition for potential energy is work done in moving the body from one place to other. i am confused.

Homework Equations

The Attempt at a Solution

The two definitions are basically the same.
One say:
- bring a body from rest to v
The other:
- bring a body from v to rest

The energy played here is the same, in the first case you have to supply energy to the body, in the second energy will be given by the body to the system.

 

[Redbelly98]

Technically, it takes a negative amount of work to bring a moving body to rest, whereas kinetic energy is always a positive quantity.

If we understand that we mean the absolute value of the work done, then the two definitions are the same. If we are not taking the absolute value, then the correct definition is the work done to bring an object initially at rest up to some speed v.

 

[Andrew Mason]

Just to follow up on what others have said, the concepts of work and energy are slightly different. Work is the application of a force through a distance: $W = \int dW = \int \vec{F}\cdot d\vec{s}$. It can be positive or negative depending on the direction of the force relative to the direction of the path over which it is applied.

Energy is the ability to do work. It can be positive or negative. Kinetic energy, however, is a measure of the ability of a body to do work in a particular frame of reference i.e. the frame of reference with respect to which its speed is measured. So it is always positive:

$$W = \int \vec{F}\cdot d\vec{s} = \int m\frac{d\vec{v}}{dt}\cdot d\vec{s} = \int m\frac{d\vec{s}}{dt}\cdot d\vec{v} = = \int m\vec{v}\cdot d\vec{v} = +\frac{1}{2}mv^2$$

AM

 

[logearav]

Thanks a lot to all the members who responded with excellent replies