MYTUTOR SUBJECT ANSWERS

315 views

Why is Kinetic Energy mv^2/2?

Whilst this proof is beyond the scope of A level physics, it is well within the scope of A level Maths as it relies solely on the chain rule.

First let us note that F*x = W where F is force, x is distance and W is work or energy.

However if we have a varying force, we must sum the Force in dx sized chunks, ie. W = int ( F dx) and it is from there we get our proof.

F = ma (from Newton II)

a = dv/dt

F = m*dv/dt

Putting this in our integral:

int(F*dx) = int (m * dv*dx/dt)

We also know that v = dx/dt.

Therefore int(m*dv*dx/dt) = int(m*dv*v) = int(mv dv).

Taking the integral we can see that W = mv2/2 + C where C is dependant on the initial speed we take the work done from. If initial speed is 0 then C also becomes 0 and we get the well known formula.

Vandan P. Mentoring -Oxbridge Preparation- tutor, A Level Physics tut...

2 years ago

Answered by Vandan, an A Level Physics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

48 SUBJECT SPECIALISTS

£20 /hr

Amilah C.

Degree: Physics with a year abroad (Masters) - Edinburgh University

Subjects offered: Physics, Maths+ 1 more

Physics
Maths
Chemistry

“Hi there, welcome to me page! About Me: I am currently studying Physics at the University of Edinburgh. From a young age, science has always been a passion of mine, and hopefully I can convey this in my tutorials. Previously, I found...”

£26 /hr

Vandan P.

Degree: Physical Natural Sciences (Bachelors) - Cambridge University

Subjects offered: Physics, Science+ 6 more

Physics
Science
Maths
Further Mathematics
Chemistry
.STEP.
.MAT.
-Oxbridge Preparation-

“I am a second year undergraduate at Corpus Christi College Cambridge. I am studying Natural Sciences. In my first year I did Physics, Chemistry, Computer Science and Maths and passed with first class honours....”

£26 /hr

James L.

Degree: Medical Sciences (Bachelors) - Exeter University

Subjects offered: Physics, Science+ 3 more

Physics
Science
Maths
Chemistry
Biology

“Hi, I'm James, a 2nd year Medical Science student. I'm really passionate about science, and I hope i can share some of it with you! ”

About the author

£26 /hr

Vandan P.

Degree: Physical Natural Sciences (Bachelors) - Cambridge University

Subjects offered: Physics, Science+ 6 more

Physics
Science
Maths
Further Mathematics
Chemistry
.STEP.
.MAT.
-Oxbridge Preparation-

“I am a second year undergraduate at Corpus Christi College Cambridge. I am studying Natural Sciences. In my first year I did Physics, Chemistry, Computer Science and Maths and passed with first class honours....”

You may also like...

Posts by Vandan

How to sum an arithmetic progression?

What is sin(x)/x for x =0?

Why is Kinetic Energy mv^2/2?

Other A Level Physics questions

Find the magnitude of the force on an electron that is travelling with velocity 2 x 10^4 ms^(-1) in the x direction through a uniform magnetic field of strength 2T in the y direction.

What is the Strong Nuclear Force?

Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together. What is the speed of the trucks after the collision?

A satellite is in a stationary orbit above a planet of mass 8.9 x 10^25 kg and period of rotation 1.2 x 10^5 s. Calculate the radius of the satellite's orbit from the centre of the planet.

View A Level Physics tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok