What is Kinetic energy: Definition and 1000 Discussions

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is










1
2


m

v

2









{\displaystyle {\begin{smallmatrix}{\frac {1}{2}}mv^{2}\end{smallmatrix}}}
. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light.
The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound.

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  1. E

    Potential and Kinetic energy equations including drag coefficient

    1. Golf ball initial potential energy uncertainty (110-5kg 0.01 m 0.01m/s2)= 110-9J4.31210-5=4.31210-14j 2. Golf ball initial potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.609 m)= 4.31210-54.31210-14j 3.Golf ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J 4...
  2. Assaltwaffle

    I Question about transfer of Energy and Momentum in Ballistics

    My apologies if the prefix is too high of complexity. I don't know where this would fall, difficulty or academically speaking. While it may be surprising to some given Hollywood's portrayal of it in movies, if a person in wearing hard bulletproof armor is struck by a projectile, the person is...
  3. C

    A rocket on a spring, related to potential/kinetic energy

    Part A) So from a force diagram we can see that the only two forces acting in our system are the spring force(positive y axis) and the weight of the rocket(negative y axis), which means the spring force is equal and opposite to the weight force. The weight is simple enough ##12* 9.8=117.6N##...
  4. D

    Can High Velocity Cause Hailstones to Melt?

    I'm pretty sure the hailstones are likely to melt/disperse because 824 m/s is a high velocity but can someone help me elaborate why it would melt?
  5. R

    I Why is momentum considered a vector and kinetic energy a scalar?

    I'm not interested in the mathematical derivation, the mathematical derivation already is based on the assumption that momentum is a vector and kinetic energy is a scalar, thus it proves nothing. Specifically, what happens if we discuss scalarized momentum? What happens if we discuss vectorized...
  6. P

    Lagrangian of a double pendulum, finding kinetic energy

    This is from Taylor's classical mechanichs, 11.4, example of finding the Lagrangian of the double pendulum Relevant figure attached below Angle between the two velocities of second mass is $$\phi_2-\phi_1$$ Potential energy $$U_1=m_1gL_1$$ $$U_2=m_2g[L_1\cos(1-\phi_1)+L_2(1-\phi_2)]$$...
  7. Dario56

    I Kinetic Energy and Potential Energy of Electrons

    Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$ Terms in...
  8. A

    Finding kinetic energy and initial velocity of a cart over time

    Here's my list of variables and things to account for: m=100kg Wnc=5000J Wfriction=-500J -Kinetic energy will be doubled (though I don't know how that plays into it exactly) -I don't think there's any PE because it's on level ground My idea of what the equation might be: Wnc +1/2mv^2initial =...
  9. rudransh verma

    B About verification on Kinetic energy and work

    1. From resnik, Halliday “Kinetic energy K is energy associated with the state of motion of an object. The faster the object moves , the greater is the kinetic energy” If I am right this means that greater the kinetic energy, greater is its speed. 2. Force transfers energy to the body due to...
  10. L

    Work and kinetic energy comprehension question

    Hello, I’ll start by saying I have the answers and the steps to the solutions, but there’s a comprehension disconnect somewhere that I’m trying to figure out. There are two parts to my question but the second one may not apply depending on the answer to the first. I wasn’t sure from the forum...
  11. L

    I The time derivative of kinetic energy

    Lets consider T(\vec{p})=\frac{\vec{p}^2}{2m}=\frac{\vec{p}\cdot \vec{p}}{2m}. Then \frac{dT}{dt}=\vec{v}\cdot \vec{F}. And if we consider T=\frac{p^2}{2m} than \frac{dT}{dt}=\frac{1}{2m}2p\frac{dp}{dt} Could I see from that somehow that this is \vec{v}\cdot \vec{F}?
  12. R

    I Kinetic Energy derivation assumption?

    The classical definition to the Kinetic Energy equation is KE=integral of F*dx where F=d(m*v)/dt. When mass is constant, KE=(1/2)m*v^2. I am working on a vibration problem at work and having to review my Lagrangian Dynamics books from 30 years ago. So my question is about all of the authors...
  13. MattGeo

    I Work Done/Energy Transferred in One Dimensional Collision

    I spend a lot of time thinking about collision problems because for me they are both extremely interesting and often very difficult to grasp when one thinks about them beyond the basics we are taught in introductory or even intermediate university courses. Suppose there is a perfectly elastic...
  14. mattlfang

    A bullet collides perfectly elastically with one end of a rod

    A bullet with mass m, velocity v perfectly elastically, vertically collide with one end of a rod on a slippery plane and the bullet stops moving after the collision. Find the mass of the stick M the bullet stops moving after an elastic collision, so all energy is transformed to the rod. There...
  15. Iwanttolearnphysics

    About KE and PE of a stone falling down a tube filled with oil

    This question does not have numbers, so I'm stumped. Here's my thinking. (I), the gain in KE is less than the loss in GPE is correct according to the key, but I think I don't understand this conceptually. Can you ask me questions to make me think about this a bit more? I can't even form...
  16. C

    B Colliding balls: Conservation of momentum and changes in kinetic energy?

    I got curious about firearm ballistics and googled something similar to "bullet momentum vs kinetic energy". IIRC, momentum P = mv (checked); and kE = (mv^2)/2 (also checked). So I essentially wondered if it's worse to get hit by a bullet with greater kE than by one with lesser kE, presuming...
  17. Iwanttolearnphysics

    About Kinetic Energy of a ball falling vertically and bouncing up

    Hello again. I don't believe there are rules about posting twice in a day. I'm not a student and I answer Physics questions as a hobby, but I've only just started learning, so please help me out. I'm answering IBDP Physics questions. Here's my thinking: KE is not a vector quantity, so it's...
  18. M

    Find Final Kinetic Energy of a particle subject to two forces

    I'm having trouble putting the rest of the equations together, I believe I need the different from (0,0,0) to (1,0,0) and then (1,0,0) to (1,1,0) right? Then solve for x direction and y direction. What would I use for Wnc tho? I'm very confused.
  19. K

    I Kinetic energy depends on ##\theta## but this argument says otherwise

    A free particle with coordinates as shown has kinetic energy ##T = \frac{1}{2}m\left(\dot r^2 + r^2\dot\theta^2 + r^2\sin^2\theta\dot\phi^2\right)## So we see ##T## depends on ##\theta##. Now suppose we rotate our coordinate system such that only one coordinate ##\theta## changes from...
  20. Tertius

    I Is Entropy the inexorable conversion of potential to kinetic energy?

    I know the math behind these, and I'm happy to use more precise language if needed, I just wanted to get some input on this sweeping generalization that entropy is the conversion of potential to kinetic energy. A brief summary of two important branches of entropy: 1) thermodynamics - the total...
  21. MattGeo

    I Reference Frame, Difference in Kinetic Energy, Fuel Consumed

    Say 2 cars are traveling side by side at 10 m/s in some flat, wide open space. Relative to each other they are stationary. Relative to someone on the ground they are both moving at 10 m/s. Now say you're in 1 of the cars and you see the other car accelerate, changing his velocity by 10 m/s in...
  22. T

    Exponential potential energy state diagram

    It is my second "energy state diagram problem" and I would want to know if I am thinking correctly. First I have done some function analysis to get a glimpse of the plot: - no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0## - y interception: ##U(0)=-U_0## - even...
  23. P

    I Question about n rotating parallel cylinders

    There are n vertical identical parallel identical cilinders rotating around their length axes with the same angular velocity. The are somehow fixed wrt to Earth and brought together (on a rail?). After the contact there is no slipping and the cilinders are coupled to their neighbor cilinders. It...
  24. S

    MHB Calculating Kinetic Energy After Collision of Balls A & B

    Ball A of mass 2kg, is moving in a straight line at 5 m/s. Ball B of mass 4kg is moving in the same straight line at 2 m/s. Ball B is traveling directly towards Ball A. The balls hit each other and after the impact each ball has reversed its direction of travel. The kinetic energy lost in the...
  25. P

    Lagrangian mechanics - rotating rod

    Hello, It might sound silly, but when I try to calculate the kinetic energy of a rotating rod to form the Langrangian (and in general), why it has both translational and rotational kinetic energy? Is it because when I consider the moment of Inertia about the centre I need to include the...
  26. greg_rack

    B How to relate relativistic kinetic energy and momentum

    Hi guys, a special relativity problem requested to choose the right graph representing relativistic momentum ##p## as a function of rel. kinetic energy ##K##, from these four: At first, I tried writing ##p## as a function of ##K##, in order to then analyze the function's graph and see if it...
  27. V

    Deriving a formula for Kinetic Energy

    I have no idea how to do this. I've tried conservation of mechanical energy and it didn't work. Ek = Kinetic Energy R = horizontal range of the ball h = height from which the ball is released
  28. Soyuz42

    Work Done by Elevator Cable in Sample Problem 7-6

    As stated, part (a) says that the work done by the gravitational force ##\vec{F_g}## is 59 kJ. If ##W_T## is the work done by the elevator cable during the 12 m fall, then using the work-kinetic energy theorem, \begin{align*} K_f -K_i &= W_g + W_T\\ \frac12m({v_f}^2 - {v_i}^2) &= 59000 + W_T\\...
  29. H

    Confirming Conservation of Kinetic Energy: An Explanation

    D is correct, the reasoning is as follows: 1/2*(M1V1)^2 + 1/2*(M2V2)^2 = 1/2 * (M1 + M2) (Vcm)^2, since V1 =V2 =Vcm KE retained = KE final = 1/2 *M(Vcm)^2 Let me know if reasoning is okay? However, why A isn't correct?
  30. Domuks

    How do I find average kinetic energy if I don't have mass of the gas?

    So always in my problems i had mass (M) but now i don't and it seems impossible to solve this problem if I don't have mass I think i am missing something. I was looking for similar problems in my book and internet and didn't find any.
  31. Mohammad Sakib

    Why the temperature of a car does not increase with velocity?

    We know temperature is a measure of average kinetic energy of molecules/particles of a system. Now if a car starts to move, its velocity increases so does its kinetic energy. Therefore all the molecules are gaining velocity too. Shouldn't this increase the temperatre as average kinetic energy of...
  32. J

    Doubt regarding functional derivative for the Thomas Fermi kinetic energy

    I have some doubts with respect on how the functional derivative for the kinetic energy in density functional theory is obtained. I have been looking at this article in wikipedia: https://en.wikipedia.org/wiki/Functional_derivative In particular, I'm interested in how to get the...
  33. AN630078

    Can heat flow into a body without increasing the mean kinetic energy?

    Yes, heat can flow into a body without increasing the mean kinetic energy of its molecules. Transferring heat energy to an object will raise its internal energy, this will not necessarily cause an increase in temperture. Specific latent heat is the energy required to change the state of one...
  34. TonyCross

    Friction/heat kinetic energy - reactive force

    Hi, Could anyone please give me a little advice. If we look at a disc brake on a vehicle, the disc brake pads apply a friction force on the disk rotor which causes the kinetic energy of the moving vehicle to be turned into heat. Does this heat reduce the reactive force experienced on the disks...
  35. AleksW

    What is the temperature change of a bullet upon impact?

    Summary:: What is the temperature change of a bullet upon impact. I have this problem to solve but I'm kinda stuck, would apricate any feedback. We fire a silver bullet with a muzzle speed of 200 ms−1 into a sack of sand. What is the temperature change of the bullet, if 40 % of its kinetic...
  36. docnet

    Expectation value of kinetic energy operator

    The expectation value of the kinetic energy operator in the ground state ##\psi_0## is given by $$<\psi_0|\frac{\hat{p^2}}{2m}|\psi_0>$$ $$=<\psi_0|\frac{1}{2m}\Big(-i\sqrt{\frac{\hbar mw}{2}}(\hat{a}-\hat{a^{\dagger}})\Big)^2|\psi_0>$$ $$=\frac{-\hbar...
  37. H

    Question about the Kinetic Energy of a baseball in flight

    A baseball is thrown and lands 120 m away. While the ball is in flight, assuming the effect of air friction is negligible, which of the following is true? a. At maximum height the ball has its greatest kinetic energy. b. The horizontal component of the baseball’s kinetic energy is constant. c...
  38. A

    Confusion about tidal locking and rotational kinetic energy

    Hello! I was reading two things: 1) tidal locking (as explained in the Wikipedia article:https://en.wikipedia.org/wiki/Tidal_locking where it is stated that, because of internal friction caused by the body of water being attracted to the moon and deforming, the kinetic energy of the system...
  39. J

    Escape Velocity Question: Why is the final kinetic energy = 0?

    So Ekf-Eki+Epf-Epi=0. I understand that the final potential energy is 0 (distance away approaches infinity), but don't get why the final kinetic energy becomes 0. If the final kinetic energy was 0, wouldn't that mean the object no longer has any velocity and would start being effected by the...
  40. T

    Average Kinetic Energy of molecules calculation

    the answer in the solution book is 29K which only comes if I use mass for only one atom. ( They did not show any working ) My attempt: 1/2 x (1.67 x 10^(-27)) x (355)^(2) = 3/2 x 1.38 x 10^(-23) x T T = 29.48820652 K The confusion arises when I tried the following question: Q. Estimate the...
  41. J

    Using Orbital Energy to Calculate Velocity

    So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m. Then I found change in potential energy, -5.597*10^11 m. Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial...
  42. rumborak

    I am confused about the meaning, and value, of kinetic energy

    This confusion has lingered in the back of my mind for years now, would be good for me to finally get a grasp on this. Say I have an object currently at rest, and I use energy X to accelerate it to speed v. According to the standard formula, it now has a kinetic energy 1/2mv^2. Now I use the...
  43. greg_rack

    Kinetic energy transformed in a collision involving coalescing particles

    This problem got me kinda confused since I cannot really understand the question... who tells me how the energy dissipated in this case? Has it all transformed into heat to cause the coalesce of the two particles, or ar the two particles now merged together still traveling with a certain amount...
  44. EchoRush

    Help with deriving the formula for kinetic energy (using calculus)

    Hello, I am learning how to use calculus to derive the formula for kinetic energy now, I understandthe majority of the steps in how to do this, however, there is one step where I get totally lost, I will post a picture of the steps and I will circle the part where I get lost. If you see the...
  45. L

    B Does an electron have kinetic energy when attached to a proton?

    does an electron have kinetic energy when attached to a proton? if not, what is it transformed into?
  46. R

    When is the rate of change of Kinetic Energy maximum here?

    Because, ##F=ma=kv##, therefore, ##a=kv/m##. Clearly, the net acceleration ##A=-(g+a)##. Also, ##A=dv/dt=-(g+ \frac {kv} m )##, so cross multiplying and integrating LHS with respect to ##v## and RHS with respect to ##t## gives me: $$ v= e^{ \frac {-tk} m } * (u + \frac {gm} k) - \frac {gm} k $$...
  47. D

    Unlocking the Mystery of Kinetic Energy

    I have a problem regarding Kinetic Energy which as we know is 1/2 m v squared. Say I have a 1kg mass moving at 10 meters/second. I have a 1 Newton rocket which I attach to the back and it burns for 1 second accelerating the mass by 1 m/sec/sec to 11 m/sec. The KE originally was 50 joules and it...
  48. Saptarshi Sarkar

    Conservation of angular momentum and rotational kinetic energy

    I first tried to get the solution by conserving the rotational kinetic energy and got ##\omega'=\frac2{\sqrt5} \omega##. But, it was not the correct answer. Next I tried by conserving the angular momentum and got ##\omega'=\frac 45 \omega##, which is the correct answer. Why is the rotational...
  49. Superposed_Cat

    I Pair production via Quantum Tunneling has negative Kinetic energy?

    If we have a photon being converted to a positron-electron pair, but we lack enough energy for this to happen (hv<2Me*c^2) but the difference is smaller than the uncertainty amount, such that tunneling may be possible, would the resultant pair have net negative energy? Would tunneling even be...
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