What is Kinetic energy: Definition and 999 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





{\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. P

    Challenging problem about an impact with a smooth frictionless surface

    The system of two material points of identical mass connected by a rigid rod of negligible mass and length ##L## is an example of a conservation of energy problem. The initial energy of the system is the sum of the kinetic energy of the two points and the potential energy of the rod, which is...
  2. pineapplebanana

    Elastic Collision troubles...

    So i started off breaking up the problem into two sequences, right before the collision and after the collision has happened. I need to find the first ball's speed immediately before the collision which is no problem. PEi = KEf > mghi = (1/2)mvf (vf being the velocity right before the collision...
  3. Lotto

    B Does a hot coffee have bigger mass than a cold coffee?

    As far as I know, something like relativistic mass is just a concept, just a trick, there is nothing like the relativistic mass. When I move faster, I have higher kinetic energy, but my mass is still the same as if I was at rest. Kinetic and potential energies do not increase object's mass. A...
  4. Venturi365

    Masses in an Atwood machine

    I've tried to solve this exercise but I haven't used one of the properties of the system (the displacement of the masses) so I don't know if I'm wrong about my procedure. First of all, we (obviously) know that $$ P=P $$ And since we can express the power of a force in two different ways, we...
  5. S

    Calculations for accelerating particles in a Cyclotron

    For this question part d, KE=mv^2/2=q^2B^2r^2/2m (I rearranged B=mv/qr for v and subbed into mv^2/2). q^2b^2r^2/2m=2F_cyc^2r^2m(pi)^2 But when I subbed the values in I got 16.45MeV but the answer says 165keV instead. I'm not sure what went wrong? What's a good explanation for part e also?
  6. ValeForce46

    B Kinetic energy of quarks in a baryon

    If we say that a proton has a kinetic energy of ##50## GeV, can we say that each of the three quarks that compose it have roughly a mean energy of ##\approx\frac{50}{3}=17## GeV? If not, what can we say about the energy of each individual quark inside a baryon with a known energy?
  7. giodude

    MIT OCW 8.01 PS11.3: Elastic Collision Between Ball and Pivoted Rod

    Given that we're working with an elastic collision we want to populate the following system: ##k_{i} = k_{f}## ##p_{i} = p_{f}## Solve for kinetic energy just before and after the collision: ##k_{i} = \frac{1}{2}mv_{i}^{2}## ##k_{f} = \frac{1}{2}mv_{f}^{2} + \frac{1}{2}I_{P}^{sys}...
  8. mazia

    Questions Regarding a Cat Going Up a Ramp

    EDIT: I've finally found the solution, so here's what I did. First, calculate Work using the equation: (F-mgsin(theta))*displacement, where F=the force being applied by the push, theta is the angle of the ramp, and displacement is the length of the ramp. Now that you have the value for work...
  9. billard

    I Deriving formula for kinetic energy

    Hello! I am new to the differential version of classical physics, and I am trying to work how to derive kinetic energy from some pre-assumed equations: Assume that we know: ##\ddot{z} = 0## and ##m\ddot{\textbf{r}} \cdot \dot{\textbf{r}} = 0## This results in $$\frac{1}{2}m\dot{r}^2 = W =...
  10. A

    Work done during a collision -- Change in Kinetic Energy & change in Momentum

    Hello guys, I need help on this problem, "You throw a ball with a mass of 0.4kg against a brick wall. It hits the wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20m/s. (a) Find the Impulse of the net force on the ball during its collision with the wall...
  11. G

    Help me solve this integral for the equation of motion

    We have ##U(x) = U(a) + \frac{1}{2}U''(a)(x-a)^2## (by taylor series) It's known that ##U'(a) = 0## and point ##a## is a turning point, hence at that point, Kinetic energy is 0, and ##E = U(a)##, hence: We have ##U(x) = E + \frac{1}{2}U''(a)(x-a)^2## I need to get equation of motion and I...
  12. Slimy0233

    B What is m in Kinetic Energy? Relativistic mass or Rest mass?

    note: m = relativistic mass ##m_o## = rest mass v = velocity of the object Question 1: If a particle is moving at relativistic speeds what would it's kinetic energy be? I think it's ##K.E. = \frac{1}{2} m_o v^2## and my friend thinks it's ##K.E. = \frac{1}{2} \frac{m_o...
  13. zachary570

    Conservation of Energy with Gravitational Potential Energy

    I was working on this problem but after getting to the answer I questioned the methods that I used for previous problems that I had solved. I understand that the total energy of the system remains constant and that we use the conservation of momentum to relate the two velocities. This gives two...
  14. E

    Signs of work done and delta K.E.

    I'm asking about this with particular reference to the signs of the answers. Here is the question: The answers in the back of the book are: (a) ##1.2 \times 10^4 \text{ N}## (b) ##39 \text{ m}## (c) ##4.7 \times 10^5 \text{ J}## (d) ##4.7 \times 10^5 \text{ J}## Here's a rough sketch of...
  15. xkcda

    Combined Rotation and Translation of a Rectangular Plate

    I tried to solve it using the work-energy theorem.The work done to make it stand on its one vertex should be equal to the change in its kinetic energy. I am confused what will be the value of radius here? I have seen formula of kinetic energy for rolling of circular objects.Can anyone please...
  16. S

    Runner Impulse Question: Estimate Power of Runner Leaving Blocks

    i tried to calculate the the kinetic energy by using the impulse law and got that the speed is 150Ns/65kg then I calculated the Energy and later the power. My answer is was 433Watts. How would you solve this question?
  17. TonyCross

    Kinetic-Potential energy of moving Ice

    Hi, Am i correct in thinking that if we take a block of ice, moving at a constant velocity, it's then exposed to a heat source which melts the ice and turns it into water vapour, that we have simply removed any Kinetic energy, by Sublimation or converting it into heat. My question is does the...
  18. uSee2

    Kinetic Energy of a Cylinder Rolling Without Slipping

    Given that there is a cylinder rolling without slipping down an incline, the method I was taught to represent the KE of the cylinder was: ##KE_{total} = KE_{translational} + KE_{rotational}## ##KE_{total} = \frac {1} {2} mv_{cm}^2 + \frac1 2 I \omega^2## Where "cm" is the center of mass, and...
  19. L

    I Question about a Rotating system with mass moving inwards

    Dear People, I have a question. I have a rotating tube like a line that has two end and one of them is the center of rotation (like a watch arrow just tube), and inside the tube a mass that is moving towards the center of rotation. So the masses moving along the line aka along the length of the...
  20. KataruZ98

    Kinetic energy transfer from a rotating body in an inelastic collision

    The cylinder in question would have a moment of inertia of ~1.67kg*m² and rotational KE of 2.058J. At the point of impact also, assuming the body hits the sphere at a 90deg angle after traversing 90deg of displacement, it should(?) exert a force of 1.31N - enough to give an acceleration of...
  21. T

    Average Kinetic Energy of Electron in the Conduction Band

    Hello, I've seen in a few books on solid state physics that one can deduce an expression for average K.E.: $$<\:K.E.>\:=E_c+3/2\:k_B\:T$$ from the following: $$<\:K.E.>\:=\:\frac{\int \:\left(E-E_c\right)g\left(E\right)f\left(E\right)dE}{\int \:g\left(E\right)f\left(E\right)dE}$$ I can't...
  22. sinus

    I The kinetic energy of proton-electron for a black body

    I'm watching a video about " What is a black body?". That video said when the light interacts with the surface of a body, the electron and proton start oscillating. The electrons gain more transferred energy from the light that became its kinetic energy, rather than the proton because its mass...
  23. rogdal

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    I could not find any derivations in the litterature, except for the expected value of the energy flux expression itself: $$\overline{\Phi_{effusion,\epsilon}} = \overline{\dot{N_{ef}}}\overline{\epsilon_{ef}}=\frac{3Nl}{2A}\sqrt{\frac{(k_BT)^3}{2\pi m}}$$ I've started off by calculating the...
  24. KataruZ98

    Kinetic energy transfer from shockwave to secondary body

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  25. Muu9

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  26. J

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    Dear Forum, I am solving for the expectation value of the kinetic energy for the deuteron (Krane problem 4.3). I must be missing something since this has become far more complicated than I remember. The problem is as follows: ## <T> = \frac{\hbar^{2}}{2m} \int_{0}^{\infty}...
  27. vinicius_linhares

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  28. A

    Finding the final speed of a space probe using work and kinetic energy

    First I found work: W=(3.85x10^5)(2.45x10^8) W= 9.43x10^13 Then used that for difference of kinetic energy: 9.43x10^13 = (1/2) (4.55x10^4)v2^2 - (1/2)(4.55x10^4)(1.22x10^4)^2 9.43x10^13 = (22750)v2^2 - 3.386x10^12 9.43x10^13 + 3.386x10^12 = (22750)v2^2 9.77x10^13 = 22750v2^2 9.77x10^13/22750...
  29. A

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  30. S

    Rotating Rod in Plane: Kinetic Energy & Moment of Inertia

    hello guys, I wanted to ask whether I can just consider/think about this as being rotation around a fixed axis in a plane representing it as if it was 'just' a rod. This is mainly so that for the kinetic energy in the second position is where if we think about it in just a plane. Is this...
  31. haha0p1

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  32. S

    I Hubble flow kinetic energy into other types of energy?

    Spacetime expands at an accelerated rate and the particles with movement associated to this expansion are coupled to the Hubble flow. In many papers that I've read, objects coupled to the Hubble flow are treated as if they have some velocity and kinetic energy associated with it. However, can...
  33. phos19

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  34. Differentiate it

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    I tried just using the formula for kinetic energy but that was apparently the wrong answer. The answer key says it's (1/6)mv². I don't understand how they got that answer. Could someone explain?
  35. earh1liw13w35sw5e

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    If you want to find out the kinetic energy (the unit is GJ as in other cannons) of the gunpowder cannon that appears in Monster Hunter, what do you need and how can you calculate it?
  36. alichoudhry57

    I Torque and Rotational Kinetic Energy Relationship

    I am wondering if it is possible to calculate either the Kinetic Energy or Rotational Kinetic Energy of an object if we have the Power (kW), Torque (Nm), and Speed (RPM) of the object.
  37. S

    Distance travelled by a car considering only air friction?

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  38. A

    Modal mass and kinetic energy in FEM modal analysis

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  39. Ahmed1029

    I Time dependence of kinetic energy in Lagrangian formulation

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  40. Rikudo

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  41. SkyeAlen

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  42. E

    Potential and Kinetic energy equations including drag coefficient

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  43. Assaltwaffle

    I Question about transfer of Energy and Momentum in Ballistics

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  44. C

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  45. D

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  46. R

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

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  47. P

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  48. Dario56

    I Kinetic Energy and Potential Energy of Electrons

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  49. A

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  50. rudransh verma

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