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

Watch
Announcements
This discussion is closed.
#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
11 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
11 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
7 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
1 year ago
#6
By p=mv,v=p/mThen sub. V=p/m into E=1/2mv^2,E=1/2m(p/m)^2E=p^2/2m
1
X
new posts Back
to top
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.

### Poll

Join the discussion

#### Poll: What factors affect your mental health most right now? Post-lockdown edition

5.83%
Uncertainty around my education (84)
11.4%
Uncertainty around my future career prospects (79)
10.72%
Lack of purpose or motivation (94)
12.75%
Lack of support system (eg. teachers, counsellors, delays in care) (39)
5.29%
Impact lockdown had on physical health (41)
5.56%
Social worries (incl. loneliness/making friends) (79)
10.72%
Financial worries (50)
6.78%
Concern about myself or my loves ones getting/having been ill (32)
4.34%
Exposure to negative news/social media (45)
6.11%
Difficulty accessing real life entertainment (24)
3.26%
Lack of confidence in making big life decisions (70)
9.5%
Worry about missed opportunities during the pandemic (57)
7.73%