Derivation of Kinetic Energy


by RoryP
Tags: derivation, energy, kinetic
RoryP
RoryP is offline
#1
Jun23-09, 09:28 AM
P: 76
Hi all,
I was doing an A-level Mechanics paper the other day and one of the quesitons was to show that, starting with Hookes law T=(lambda)(x)/(l), show that the energy stored in an elastic rope is (lambda)(e2)/(2l).
This was ok, I just said that energy stored would be equal to the sum of the work done stretching the rope a small distance δx and as δ tended to zero it would be dx. Which could be re-written as integral with limits e and 0 dx.
Which leads to the equation for elastic potential energy.
After doing this i realised that kinetic energy is in a similar form, i.e power of 2 and has a multiplying factor of 1/2 which leads me to my question, is 1/2mv2 the result of an integral? Has it also got something to do with work done? but with respect to v?
Any help would be greatly appreciated!
Phys.Org News Partner Science news on Phys.org
Better thermal-imaging lens from waste sulfur
Hackathon team's GoogolPlex gives Siri extra powers
Bright points in Sun's atmosphere mark patterns deep in its interior
rl.bhat
rl.bhat is offline
#2
Jun23-09, 09:47 AM
HW Helper
P: 4,442
dW = f*dx = m*a*dx = m*dv/dt*dx = m*v*dv ( since dx/dt = v)
Take the integration between 0 to v.
RoryP
RoryP is offline
#3
Jun23-09, 09:55 AM
P: 76
ok brilliant thanks! what is dW? respect to work done?

rl.bhat
rl.bhat is offline
#4
Jun23-09, 10:09 AM
HW Helper
P: 4,442

Derivation of Kinetic Energy


Yes.


Register to reply

Related Discussions
Understanding derivation of kinetic energy from impulse? Classical Physics 3
Ratio kinetic energy of alpha particle / kinetic energy of proton Introductory Physics Homework 2
[SOLVED] Mechanical Energy vs Potential Energy & Kinetic Energy Introductory Physics Homework 3
Derivation for Kinetic Theory of Gases Introductory Physics Homework 6
Derivation of Kinetic Energy Classical Physics 1