# how was E=P^2/2m derivedWatch

Announcements
#1
i have he equation E= p^2 / 2m. i figured it was somehow derived by Ek=1/2mv^2 and p=mv? but i dont understand how. can anybody explain it to me please?
0
9 years ago
#2

Once you know KE= m(v^2)/2,

and p=mv, so p^2 = (m^2)(v^2),

so m(v^2) is clearly (p^2)/m, right?

hence m(v^2)/2 = (p^2)/2m

Is that what you meant?
3
#3
aha thankyou. yea thats what i meant. i just couldnt get my head around it.
0
9 years ago
#4
(Original post by KCcrusty)
i have he equation E= p^2 / 2m. i figured it was somehow derived by Ek=1/2mv^2 and p=mv? but i dont understand how. can anybody explain it to me please?
Would you like to see the original derivation?

We tend to imagine it as a linear progression. A uniformly accelerating object is usually given by three bits of information, given as:   Combining these, we find: thus  The task from these linear sets of equations is to find a relationship between force and mass. Rearranging the final equation gives: and then multiply both sides by mass gives: Noting that Force = M times Acceleration, then converting gives: which leaves the quantity of So this is the linear kinetic energy and is the energy related to momentum. Your work done can be given as: 0
5 years ago
#5
well let me simplify how the equation was derived: you know that P=mv and Ek=1/2 m(v^2)
Therefore, make v the subject in the momentum equation you will have v=P/m substitute this in to the kinetic energy equation for value of v...you will now have Ek=1/2m(p/m)^2 if you solve that you get: Ek= 1/2m(p^2)/(m^2) you can now see that one m cancel out with the other and you are left with Ek= (p^2)/2m
1
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Bournemouth University
Wed, 31 Jul '19
• Staffordshire University
Wed, 7 Aug '19
• University of Derby
Foundation Open Event Further education
Wed, 7 Aug '19

### Poll

Join the discussion

#### Are you tempted to change your firm university choice on A-level results day?

Yes, I'll try and go to a uni higher up the league tables (156)
17.63%
Yes, there is a uni that I prefer and I'll fit in better (76)
8.59%
No I am happy with my course choice (526)
59.44%
I'm using Clearing when I have my exam results (127)
14.35%