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. A131313

    Why is the Kinetic Energy 0 at an infinite distance away from a point?

    Hello! I'm trying to understand the concept of escape velocity, and I know you equate the initial mechanical energy to the final mechanical energy, where the final mechanical energy is at a distance of infinity. I know that the gravitational potential energy approaches 0 as the distance r gets...
  2. N

    How would we increase the rotation rate of very large structures in deep space?

    Imagine a 400-meter-long pipe with a 1600-meter diameter, floating in inter-planetary space. It is spinning at 0.5 gravity along its major axis and there are no secondary-axes spins. We need to increase rotation to 0.85 g. Its density is a uniform 2.3 kg/m³ and it weighs 49,120,056 kg. Thanks to...
  3. Curtiss Oakley

    Problem Concerning Rotational Kinetic Energy

    For parts A and B I used energy to find the vcom and omega, but that won’t work for C. I have an answer by combining the three formulas that use acceleration above. My answer for alpha=-5g/3r. The next two are easily solvable if you find C, but I still feel like I’m missing something. Any help...
  4. HammerAndChisel

    Could the kinetic energy of space junk be recycled?

    First time poster here, and I need some experts to weigh in on a debate that I'm having on the Skeptics Guide to the Universe forum, here (https://sguforums.com/index.php/topic,51110.0/topicseen.html ). In my opinion, a few of the other posters are being pessimistic. Given recent advances in...
  5. EEristavi

    Relation between Potential Field, Force, Kinetic Energy and Abs.Energy

    I understand that the work done is Change of Energy. W = ∫xixf F dx = ΔEThe force is gradient of potential energy F = -∇U (For conservative forces of course) from here, we can say that change of potential energy is W: ΔU = -W but also ΔU = -W = ΔE I'm little bit lost here.. Can you help me...
  6. ChrisXenon

    Temperature and molecular Kinetic Energy

    We are told that temperature measures the average kinetic energy of the molecules or atoms in a substance, but this cannot be true. If I take a jar of water and put the jar in my car and drive it aorund, it won't get hotter, though it's kinetic energy must surely be higher. Clearly, I've got...
  7. M

    Force on a pin from a pendulum and a string

    1. Determine the velocity of the ball when it is 30degrees from the horizontal: U1 = mgh = mg(0.8m) U2 = mgh = mg(0.4+0.4cos(30)) = mg(.74641) ΔU = U2 - U1 = mg(.74641 - .8) = mg(-0.051433) T1 =0 T2 = 0.5mv^2 ΔT = T2 - T1 = 0.5mv^2 ΔU = ΔT mg(-0.051433) = 0.5mv^2 ====> v = 1.025394 2. Use...
  8. nineteen

    Why is Kinetic Energy a scalar quantity?

    Why is Kinetic energy a scalar quantity? I read in an article, it said, when the velocity is squared, it is not a vector quantity anymore. Can someone fill in the gaps for me? I can't quite get what that article said. And I would be pleased if you provide some other examples other than kinetic...
  9. D

    How to find the energy of an object that was at rest?

    Homework Statement In two rockets, one of which moves and the other is at rest, the motors are connected for a short time. During their operation they throw the same mass of gas (small in comparison with the mass of the rocket) at the same speed with respect to the rockets. The kinetic energy...
  10. M

    How far does the block slide? (work, spring, incline)

    Homework Statement The system is released from rest with no slack in the cable and with the spring stretched 225 mm. Determine the distance s traveled by the 3.2-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 2.5 kg. Assume no mechanical interference and no friction...
  11. velvetmist

    Real life elastic collision and variation of kinetic energy

    How small should ##\Delta T## be in a collision to be considered elastic? In elastic collisions ##\Delta T =0##, but as far as I know, just atomic collisions are considered perfectly elastic. Then, which criterias are used to considere a collision between two objects elastic?
  12. DeathByKugelBlitz

    Kinetic energy and velocity of electron after compton scatte

    Homework Statement A photon with an initial wavelength of 0.1120 nm collides with a free electron that is initially at rest. After the collision the wavelength is 0.1140 nm . a) What is the kinetic energy of the electron after the collision? b) What is its speed? c) If the electron is...
  13. Curtiss Oakley

    Problem involving energy/motion

    Homework Statement A ball of mass m=0.300 kg is connected by a strong massless rod of length L = 0.800 m to a pivot and held in place with the rod vertical. A wind exerts constant force F to the right on the ball as shown below. The ball is released from rest. The wind makes it swing up to...
  14. matai

    Using Integrals to Calculate the Rotational Energy of Earth

    So I found the linear velocity by using the circumference of the Earth which I found to be 2pi(637800= 40014155.89meters. Then the time of one full rotation was 1436.97 minutes, which I then converted to 86164.2 seconds. giving me the linear velocity to be 465.0905584 meters/second. I know that...
  15. Arman777

    Is This a Valid Derivation of Kinetic Energy from Work?

    I am trying to derive the kinetic energy from the work and can I derive it like this ? $$W=\int Fdr$$ $$W=\int \frac {dp} {dt}dr=\int (dp) \frac {dr} {dt}=\int (mdv)v=1/2m[v_f^2-v_i^2]$$
  16. Sherlock01

    Need help with finding thermal and Kinetic energy

    Homework Statement A block starts at rest. A hand pushes the block with 6.1 N to the right across a rough surface, with 1.5 N of friction. if the block moves 1.6 m horizontally determine the following (a) work done by hand (b) work done by friction (c) the amount of thermal energy created (d)...
  17. J

    Initial and Final Kinetic Energy

    Homework Statement How do Initial and Final Kinetic Energy depend on each other? Homework EquationsThe Attempt at a Solution Do they remain equal? For example for the same mass m, can we write KE1 = KE2 1/2 m v1^2 = 1/2 m v2^2
  18. S

    Kinetic energy and momentum of two satellites colliding

    Homework Statement Two satellites in space collide inelastically. What happens to the kinetic energy and momentum? a. both are conserved b. KE conserved but momentum reduced c. KE reduced but momentum conserved d. both are reduced e. KE reduced but momentum increased Homework Equations elastic...
  19. B

    Calculate rest mass given relative speed and kinetic energy?

    The answer is 3.079*10^-26 kg I tried doing E=mc^2 20*10^9*1.602*10^-19=m*(3*10^8)^2 m=3.56*10^-26 kg However when I do E=γmc^2 I get the correct answer. Is the question wrong, because isn't it 20 GeV of kinetic energy, not total energy?
  20. DLeuPel

    Temperature and the kinetic energy of everything

    Earth rotates, it also orbits the Sun, the Sun orbits the galaxies and these have they’re own velocities as well. We know that the kinetic energy is measured by its velocity, and also that kinetic energy is related with temperature. By this I mean that the movement of particles are a measure of...
  21. F

    Is Mechanical Energy Conserved for Non-Conservative Forces?

    Hello, A generic force ##F##, which may be conservative or not, performs mechanical work which is always equal to $$W=\Delta KE=KE_{final}-KE{initial}$$ i.e. produce a change in the object's kinetic energy ##KE##. Work is essentially a way to inject or subtract kinetic energy from a system. If...
  22. M

    How is momentum conserved if you lose kinetic energy?

    The energy component of KE is the velocity. Momentum is mass x velocity so, in a collision containing in-elasticity, if KE is lost to heat then that heat energy must have been supplied by the velocity of the object. And since velocity has been lost to supply the heat then the overall momentum...
  23. Benjamin Fogiel

    A rocket burns out at an altitude h above the Earth's surface

    Homework Statement A rocket burns out at an altitude h above the Earth's surface. Its speed v0 at burnout exceeds the escape speed vesc appropriate to the burnout altitude. Show that the speed v of the rocket very far from the Earth is given by v=(v02-v2esc)1/2 Homework Equations KEf-KEi=Ui-Uf...
  24. P

    Kinetic Energy & Momentum of a Ball released from Spring

    Homework Statement "A spring with a spring constant "k" is compressed 10 cm from equilibrium. A ball of mass 100 g is at rest next to it. The spring then decompresses quickly back to its equilibrium position causing the ball to shoot forward. If the spring constant is 500 N/m, what is the...
  25. T

    Kinetic energy & Conservation of energy

    Homework Statement You are driving with your car (of total mass: 1.2tonnes) with a speed of v=50km/h, until you see an obstacle. a) What is the kinetic energy of the car? b) When you start to brake, there is still 15m until the obstacle. What must be the size of the friction coefficient (µ)...
  26. N

    How to break up kinetic energy for circular motion?

    Homework Statement Homework Equations L = T-V For constant frequency tangential velocity is (radius)*(w) The Attempt at a Solution I need to find r(t) using the Langrangian L = T-V I just was not sure whether I am on the right track for calculating the total kinetic energy for the above...
  27. S

    Calculating Rotational Kinetic Energy of a Baton

    Homework Statement A drum major twirls a 94-cm-long, 500 g baton about its center of mass at 150 rpm. What is the baton's rotational kinetic energy? Homework Equations KE_rot = 0.5 I w^2 The Attempt at a Solution w = (150rpm*2pi)/60 = 15.708rad/s I = (1/12)*0.5kg * 0.94m = 0.039167kg*m^2...
  28. J

    Rank the four objects from fastest to slowest

    Homework Statement Rank the four objects (1kg solid sphere, 1kg hollow sphere, 2kg solid sphere and 1kg hoop) from fastest down the ramp to slowest. (Please see the attached screenshot for more details.) Homework Equations KE_rot = 1/2Iw^2 (where omega = w) The Attempt at a Solution Since we...
  29. Abimbola1987

    Joule's first law - kinetic energy of electrical current

    Dear Sirs, If I take this explanation as being true "The heat is generated on the microscale when the conduction electrons transfer energy to the conductor's atoms by way of collisions." So a "current" must have a quantum of kinetic energy going into the conductor (resistive element) and a...
  30. J

    Moving Down a Ramp: Answers & Explanations

    Homework Statement Please look at the problem attached as a screenshot. Homework Equations Assuming frictionless, Ei = Ef, which means objects that are the same will end up in the same heights (so we can group A&C, B&D, and E&F). For A&C and E&F, mgh = KE_rot + KE_trans For B&D, it is mgh...
  31. J

    Solid sphere rolling along a track

    Homework Statement Please see the attached file. Homework Equations Ei = Ef The Attempt at a Solution I don't have an answer key provided, but I'd really like to verify that I'm right (or if I'm wrong, why). I think ti'd be (c) because assuming that due to inertia, B will continue going...
  32. J

    Do A and C have same or different KE at the end?

    Homework Statement Please look at the attached screenshot. Homework Equations Assuming the ramp is frictionless, Ei = Ef and thus mgh = KE ( = 1/2mv^2, which isn't really necessary here) The Attempt at a Solution I'm okay with all other examples except for A and C. From the answer template...
  33. J

    What velocity does a train need to go up and down the hill

    Homework Statement There is a train of length d and speed v. It is heading towards a hill with height h and length of each side l. What velocity requirement must be met so that the train can go up and down the hill? Homework Equations Ek=m⋅v2/2 Ep=m⋅g⋅h The Attempt at a Solution I'm basically...
  34. S

    Kinetic energy problem -- What am I doing wrong?

    <Moderator's note: Moved from a technical forum and thus no template.> kinetic energy problem I just want to know what is wrong with how I am solving this problem A block slides to the right on frictionless surface at speed of 20m/s and encounters a 20N force to left when it is at the 1cm...
  35. DracoMalfoy

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    Homework Statement What is the kinetic energy of a particle in 2mol of nitrogen gas at atmospheric pressure that is within a volume of 100m^3?a. 1.27X10^-17J b. 3X10^5J c. 6.8X10^-16J d. 2.97X10^7 e. 9.9X10^-14J Homework Equations PV=nRT n=Numberof particles/Na Na=6.02x10^23 R=8.13 J/Mol The...
  36. K

    Kinetic energy of Himalayan plate

    In this video (2:30 to 4:00) you can see the Indian continental plate zipping across the Indian Ocean and smashing into Eurasia, raising the Himalayas. Estimate its kinetic energy.
  37. J

    Speed or turning point using energy

    Homework Statement Please look at the attached screenshot. This problem is really confusing for me and I can't seem to make much sense out of it. Homework Equations Ei = Ef The Attempt at a Solution As you can see, I did get (a). (The other checkmarks, I guessed — there were only two...
  38. A

    Work Required to Move a Piano Onto a Truck

    Homework Statement Movers must push a piano onto a truck, the bed of which is a height 1.35 m above the ground. To do this they will use a frictionless ramp. If the piano has a mass of 1806.0 kg and the movers push it up the slope at a constant velocity, how much work do they need to do on it...
  39. S

    Kinetic Energy for particles (alpha decay)

    Homework Statement Many heavy nuclei undergo spontaneous "alpha decay," in which the original nucleus emits an alpha particle (a helium nucleus containing two protons and two neutrons), leaving behind a "daughter" nucleus that has two fewer protons and two fewer neutrons than the original...
  40. DracoMalfoy

    Rotational Kinetic energy of bar, and new kinetic energy

    Homework Statement A bar of length 2.5m and mass 5kg, whose rotation point is at its center, rotates at 5 rad/s. What is the rotational kinetic energy of the bar?If a point mass of mass 1.5kg is added to each end of the bar, assuming the angluar velocity is the same, what is the new kinetic...
  41. Ricardo

    B Questions about the relativistic kinetic energy expressions

    <Moderator's note: Moved from New Member Introduction.> I am asking assistance in addressing several questions I have with the relativistic kinetic energy expressions given as {I am sorry for the format of the notations. It was inadvertently distorted.} KE=mc2 [1/sqrt(1-(v2/c2)) -1]...
  42. M

    Elastic collision with particles, find the kinetic energy

    Homework Statement A proton strikes a stationary alpha particle (4He nucleus) head-on. Assuming the collision is completely elastic, what fraction of the proton’s kinetic energy is transferred to the alpha particle? Homework Equations Pi = Pf Ki = Kf The Attempt at a Solution Tried finding...
  43. CRuff

    Calculating kinetic energy turned into Pressure (Pascals) during an impact

    Hello, A silly question I'm sure, if a projectile moving at 13.59 m/s with a KE = 527.47 J hits an area of 3 cm^2, what is the force transfer to that area and the resultant pressure applied expressed in Pascals? Do I divide the KE by a volume instead of area to Pa?
  44. sush

    I Why E=mc^2 is different from E=1/2 mv^2?

    Why kinetic energy is ½ m v2? Why it is different from Einstein’s equation for Energy E= m c2?
  45. jamiebean

    The formulae for kinetic energy and Joules

    The formula for kinetic energy is 0.5x kg x v^2, where v= velocity The formula for joules is kg x v^2 I don't understand why does the difference exist and what is the difference between joules and kinetic energy isnt joule the unit for energy?? Thank you guys for helping me.
  46. D

    Kinetic energy loss in disintegrated matter

    What happens to the kinetic energy when an object is disintegrated? Does it survive? For example, if I throw a baseball at the sun at 100 mph, I will get X amounts of heat energy released and X amount of light as it burned up before contact. If I threw another baseball 100,000 mph into the sun...
  47. K

    Calculating the Maximum Kinetic Energy of pions

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  48. F

    Distance traveled with linearly increasing kinetic energy

    Homework Statement An object of mass 50 kg gains 20,000,000 joules every second. Devise formulae to find the distance covered at any given point in time, and the time necessary to cover a certain distance. Homework EquationsThe Attempt at a Solution E = 20,000,000 * t V = (E * 2/50)1/2 That's...
  49. W

    B Relativistic Kinetic Energy: Does Mass Change?

    Hello, According to Special Relativity, the mass of an object must increase as its speed approaches the speed of light. m=m0γ In the formula that allows us to calculate the kinetic energy of a body, KE=0.5mv2, should we take into consideration such increase in mass? Weam Abou Hamdan Wednesday...
  50. Krushnaraj Pandya

    Kinetic energy of a photoelectron

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