Derivation of Kinetic Energy

In summary, the conversation discusses the derivation of the equation KE=(mv^2)/2 and the possibility of using dimensional analysis to understand it. The "work-energy" theorem is mentioned, which involves integrating the net force over distance to obtain a change in kinetic energy. Newton's 2nd law is used to start the derivation and the last step is left for the reader to figure out.
  • #1
francescopadormo
5
0
Hi,

I've always tken for granted that KE=(mv^2)/2, but never seen the derivation! I think it probably comes from U= - inegral of the force, but I can't see which force to use. Any help anyone? Maybe dimensional analysis was used?

Thanks!
 
Physics news on Phys.org
  • #2
I suspect you are thinking of the "work-energy" theorem, in which one integrates the net force on an object over the distance traveled to obtain the change in KE.

Start with Newton's 2nd law:
[tex]F = m \frac{dv}{dt}[/tex]

[tex]\int F dx = \int m \frac{dv}{dt} dx = m \int \frac{dx}{dt} dv = m \int v dv[/tex]

I'll leave the last step to you.
 
  • #3


Hello,

The derivation of kinetic energy can be traced back to the work-energy theorem, which states that the net work done on an object is equal to its change in kinetic energy. This can be mathematically expressed as Wnet = ΔKE.

To derive the equation KE = (mv^2)/2, we can start by considering a constant force acting on an object over a certain distance. The work done by this force can be calculated as W = Fd, where F is the force and d is the distance traveled.

Now, using the definition of acceleration (a = Δv/Δt), we can rewrite the equation for work as W = maΔt, where m is the mass of the object.

Next, we can substitute the equation for acceleration into the work equation, giving us W = m(Δv/Δt)Δt. The Δt terms cancel out, leaving us with W = mΔv.

Recall that the work done on an object is equal to its change in kinetic energy. Therefore, we can rewrite the equation as ΔKE = mΔv.

Finally, we can use the definition of average velocity (v = Δx/Δt) to rewrite the equation as ΔKE = m(vf - vi), where vf is the final velocity and vi is the initial velocity.

Since we are interested in the final kinetic energy of the object, we can set vi = 0, and the equation becomes ΔKE = mvf^2.

If we divide both sides by 2, we get the final equation of KE = (mvf^2)/2, which is the familiar equation for kinetic energy.

In summary, the derivation of kinetic energy involves using the work-energy theorem and the definition of acceleration and average velocity. No dimensional analysis is required. I hope this helps clarify the derivation process for you.
 

1. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is a type of mechanical energy that depends on the mass and velocity of the object.

2. How is kinetic energy derived?

Kinetic energy is derived from the equation KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

3. What is the relationship between kinetic energy and potential energy?

Kinetic energy and potential energy are forms of mechanical energy that can be converted into each other. Potential energy is the energy an object possesses due to its position or state, while kinetic energy is the energy an object possesses due to its motion.

4. How is kinetic energy affected by mass and velocity?

Kinetic energy is directly proportional to both mass and velocity. This means that an object with a greater mass or velocity will have a greater kinetic energy.

5. What are some real-life examples of kinetic energy?

Some common examples of kinetic energy in everyday life include a moving car, a rolling ball, a swinging pendulum, and a person running. Essentially, any object in motion has kinetic energy.

Similar threads

  • Mechanics
Replies
11
Views
929
Replies
14
Views
2K
Replies
5
Views
787
Replies
9
Views
2K
Replies
4
Views
934
Replies
4
Views
12K
  • Mechanics
Replies
3
Views
9K
Back
Top