Kinetic Definition and 1000 Threads

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. pete94857

    I How to calculate the kinetic energy of an object propelled by a magnet?

    How to calculate the kinetic energy of an object propelled by a magnetic field. For example I have 2 magnets face to face in opposition. Each magnet is a N42 Neodymium cube dimensions 10, 10, 10 mm they are in free space with no interference. The maximum pull strength is 4.7 kg. If I were to...
  2. S

    B General relativity and frame of reference

    All three questions concern general relativity. 1. Does the curvature of spacetime depend on the frame of reference? 2. Does kinetic energy exist? 3. If it exists, does it contribute to the curvature of spacetime?
  3. I_Try_Math

    Determine energy required to stop rolling mass

    Is it possible to solve this without knowing the radius of the cylinder? My initial thoughts were that the energy required to stop it would be the sum of its rotational and translation kinetic energy, but I'm not sure it can be calculated without knowing the radius.
  4. murshiddreamengineer

    I How can we prove the kinetic energy equation

    Proof of kinetic energy work done equals a change in kinetic energy in a mechanical system. δW = F.ds W = ∫F.ds W = m∫a.ds W = m∫(dv/dt).ds W = m∫v.dv here if v and dv are in the same direction the change in kinetic energy will be the usual equation. what happens if both are in different...
  5. A

    A Braking System with Spikes for Cars

    Attached to the post is a file with an attempt at a solution. The braking system is said to be a center-pull clamping system, which when activated by a brake lever (which equates to 355kN of force applied), triggers a tension force in the cables then clamps together two brake pads with spikes...
  6. J

    A cylinder rotating on a plane with friction and then moving across a frictionless plane to a collision

    I think the angular velocity keep increasing on the plane with friction and the translational velocity keep decreasing due to friction while the total kinetic energy is conserved. When it moves to the frictionless plane, all energy converts to translational kinetic energy and it stop rolling...
  7. kal8578

    I Change of coordinates in a potential energy field

    Hello, I am having some confusions in what should be basic pointwise Newtonian mechanics, and would like to get some help with that. It is all about changing coordinates in potential energies. Let us start by considering a point particule in a 2d world with an axis x (left-right) and an axis z...
  8. J

    Problem with KE and work equation (perfect rocket in space example)

    Can someone help me by taking a look at the attachment and figuring out where I am making a bad assumption? It's driving me nuts.
  9. Heisenberg7

    Tension Force Problem (applying Work-Kinetic Energy Theorem)

    We know that net work done is equal to the change in kinetic energy, so we write: $$\Delta K = W$$ The tension is acting at angle ##\theta## due to the x axis, so we will only be taking its x component ##T_x = T \cos{\theta}##. Since we can look at this as one dimensional motion (##T_y## does no...
  10. R

    I Deriving e=mc^2, how is it possible?

    I was recently very surprised when I had a looked up relativistic kinetic energy. All sources gave the kinetic energy as the difference between total energy and rest energy, in some or other variant of the formula ##E_k=(\gamma−1)mc^2##. I didn't really understand at first. It seemed overly...
  11. Heisenberg7

    Closest distance of approach between 2 charged particles

    A few hours ago, I tried solving this problem and I'm still not quite sure if I've made a mistake somewhere or perhaps the guy in the video is wrong? Anyway, here's my solution: In the problem we're given that the total kinetic energy of of these 2 charges at this instant(look at the picture)...
  12. A

    Conservation of Momentum Problem - Mechanical and Kinetic Energies

    I'm confused on this problem, as I feel they state two completely contradictory things in the explanation of how to solve it. The first statement that I feel contradicts the second is this: "We can see that the bullet’s speed v must determine the rise height h. However, we cannot use the...
  13. L

    Internal energy of a gas and kinetic energy, "typical velocity"

    Source: Shankar Yale OCW physics I have three questions here: 1. K_avg is 3/2kT, sure. But isn't this the kinetic energy of one particle only? So why isn't the answer multiplied by avogadro's number (because one mole). 2. When doing the "typical velocity" derivation, I noticed that they used...
  14. T

    B The relationship between mc^2 and mc^2 x 1/2

    Kinetic energy = 1/2 m V^2 I was thinking about this and thought another formula… E = mc^2 These look very similar except for the multiplication by 1/2. Let’s say you take a kilogram ball of uranium and accelerate it to the speed of light. I know, I know. You can’t. But let’s say you did...
  15. M

    Classic Incline problem with cylinder

    FOr this, Use alternate coordinate system With ##ȳ##-axis parallel to incline and ##x̄##-axis parallel to the x-axis. Kinetic energy using this alternate coordinate system is ##T = \frac{1}{2}M\dot x_p^2 + \frac{1}{2}mR^2\dot \phi^2 + \frac{1}{2}m(\dot x̄^2 + \dot ȳ^2 + 2\dot x̄ \dot ȳ...
  16. dannolul

    The value of the spring constant k that I calculate seems too high

    I expanded ET1=ET2 to get (Total energy at top) 1/2mv^2+mgh = 1/2kx^2 (Total energy at bottom) Rearanged i got k = (mv^2+2mgh)/x^2 so [(73)(20)^2+2(73)(9.8)(52)]/0.465^2 =479137.945N/m
  17. R

    Rolling Sphere On Incline

    I did some algebra and got the final equation mgh=1/2MR^2omega^2+1/2(2/5MR^2)omega^2, then plugged in the numbers and got an omega value of 111.09. Using 1.7 as h instead of cos(17)*1.7=1.63 I got 114.09. Both answers were wrong. Am I missing something, or did I just screw up the math?
  18. hello478

    Change in the kinetic energy of a car driving up a hill

    part i) i did 1/2 * 1700 * v^2 i dont know what v is... so how do i solve it? part ii) i calculated it correctly by 440*25 please explain in detail why i used 440? and part d) i did 1.7*10^4 = 48000/t my t= 2.82 s but correct answer is 3.5s
  19. seonjunyoo

    B I have a question regarding temperature and the kinetic energy of molecules

    Does the high temperature increase the kinetic energy of molecules or atoms, or does the high kinetic energy of atoms or molecules increase the temperature ? I'm so curious about this. Which concept is more accurate between the two
  20. N

    Equations of motion of an electron emitted from a surface

    Homework Statement: Real world application of freshman physics Relevant Equations: TBD This is not a homework question, this is relevant to my work. It seems simple enough (introductory) but I keep running into problems. An electron is emitted from an surface (material is irrelevant, could...
  21. daisy7777

    Frames of Reference: Using tie-downs to hold a load on a flatbed truck

    I calculated the net force. I got 6500. I determined this is bigger than the force of static friction so the force of friction acting on the object must be kinetic. From there I got kinda lost. I know for the component to not slip Fnetx = 0 and Fnety = 0. But I'm not sure what to do from there...
  22. C

    I I'm calculating more energy out than I put in

    Hello everyone, I'm currently working on a physics problem involving the rotation of a 5 kilogram ##M=5## solid sphere subjected to a force of 5 newtons ##F=5##, and I've encountered an inconsistency in my calculations. I'm seeking guidance or insights into where I might have gone wrong. My...
  23. J

    Find out kinetic Energy using Rutherford Formula

    Hello everyone, I am working on this problem and I think I almost solved it, but then I noticed, that I do not know what values I have for dn, n and dθ. Can anyone help me with this?
  24. M

    Why kinetic energy of system of particles is not equal to p^2/2m

    It is good for the people who wants to know physics and it's beauty
  25. D

    I Spacecraft With Solar Mass Energy Equivalent Kinetic Energy

    Suppose in a different star system, a space shuttle sized spacecraft acquired a solar mass energy equivalent amount of kinetic energy, then passed through our solar system. While it was passing through the solar system would the craft’s gravitational effects be more similar to the space shuttle...
  26. physicsmaster123

    Work done by gravity on a car rolling down a hill

    I tried E =Fxcos0 but only ended up with 243kJ
  27. Govind

    Gibbs free energy of activation and activation energy

    Let's consider a reaction A (reactant) -> B(product) and activated complex is denoted by C. This graph ( potential energy vs reaction coordinate ) tells us that reactant need some amount of activation energy (Ea) to convert in product, which has low potential energy which is shown here in...
  28. M

    Work energy KE theorem for a book being lifted up in a gravitional field

    For this, From the work kinetic energy theorem, if we assume that the book and the earth is the system, and that the finial and inital speed of the system is zero, then is the work KE theorem there is no net work done on the system. However, clearly there is work done on the system is shown by...
  29. 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...
  30. 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...
  31. 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...
  32. 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...
  33. rogdal

    Deriving the kinetic energy flux in an effusion process

    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...
  34. KataruZ98

    Kinetic energy transfer from shockwave to secondary body

    I would guess that by multiplying the pressure exerted by the shockwave on the body, and then the resulting force - here ~69 Newtons - per the distance the shockwave passed through when traversing body A, I could get the work done but I’m not sure if it’s that easy and whether or not I should...
  35. Muu9

    Kinetic Energy / Potential Energy / Total Energy question

    W_ext is the external work done on B and C, which is 12 J Delta K_tot is the internal work, which is the work done by A on B plus the work done by A on C Delta K_tot = 5 Solving for \Delta U, we find that the change in potential energy is 7 J This answer says otherwise...
  36. J

    Expectation of Kinetic Energy for Deuteron

    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}...
  37. V

    B Conflicting definition of degree of freedom in Kinetic Theory of Gases

    I am seeing conflicting definitions of degree of freedom in my textbook. If I look at the definition given as per screenshot below then it is the number of independent terms/variables/coordinates used to define the energy of a molecule. But, if I look at the statement of Equipartition of energy...
  38. 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...
  39. A

    Net work and kinetic energy (pushing a wagon to accelerate it)

    I'm a little confused because my teacher used Bill's 500J of work for the kinetic energy equation and I don't understand why. I used the net work, so 300J, to find the speed and I'm not sure why that's wrong. Wouldn't friction make the wagon move slower than if there was no friction? So why...
  40. 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...
  41. haha0p1

    Kinetic energy of an alpha particle

    Kindly help me solve this question. The only thing so far that I know in this question is that energy is conserved and the momentum of Alpha particle will equal momentum of Thorium.
  42. 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...
  43. Argonaut

    Find the Coefficient of Kinetic Friction

    Young & Freedman 13th ed, Exercise 7.81 Starting with the crate, here is its free-body diagram: In accordance with Newton's First Law: $$ \Sigma F_y = 0 = n+(-w_c \cos{\alpha}) $$ Thus ## n = w_c \cos{\alpha} ##. And according to Newton's Second Law: $$ \Sigma F_x = m_c a_x = w_c...
  44. phos19

    Falling stick problem (no friction): What is the kinetic energy?

    Since there is no friction : $$ m \ddot{x} = 0 $$ (no x motion).For the kinetic energy , I've tried: $$ K = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m v^2_cm = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m \dot{z}^2$$ . Giving me a weird expression , shouldn't the kinetic energy just be half the the moment...
  45. Differentiate it

    Why is the Kinetic Energy of a Spring (1/6)mv²?

    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?
  46. codebpr

    A The kinetic term of the Hamiltonian is not positive definite

    I am trying to reproduce the results from this paper. On page 10 of the paper, they have an equation: $$ \frac{S}{T}=\int dt\sum _{n=0,1} (\dot{c_n}{}^2-c_n^2 \omega _n^2)+11.3 c_0^3+21.5 c_0 c_1^2+10.7 c_0 \dot{c_0}{}^2+3.32 c_0 \dot{c_1}{}^2+6.64 \dot{c_0} c_1 \dot{c_1} \tag{B12} $$ where they...
  47. K

    How do I find the coefficients of static friction and kinetic friction?

    I have found that μstatic= 5.6 (found on graph) / 18.20 = 0.3077 I don't know how to find Force of friction from the graph to calculate μKinetic
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