Kinetic energy 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. G

    How to calculate the change in kinetic energy on a plane?

    Homework Statement A crate is pulled by a force (parallel to the incline) up a rough incline. The crate has an initial speed shown in the figure below. The crate is pulled a distance of 9.33 m on the incline by a 150 N force. The acceleration of gravity is 9.8 m/s 2 . What is the change in...
  2. Suraj M

    Derive the equation for kinetic energy

    question: I came across a question which said: Derive the equation for kinetic energy of a body of mass m and velocity v. What do they mean? Attempt: I actually just wrote that by work energy theorem diff. in KE = work done so Fx = KE $$ max = m \frac {v²-u²}{2x} x = ½mv² - ½mu² $$ each of...
  3. **Mariam**

    Kinetic Energy and Work problem

    Homework Statement [/B] A horizontal force of 50 N is applied to a 2.0 kg trolley, initially at rest, and it moves a distance of 4.0 m along a level, frictionless track. The force then changes to 20 N and acts for an additional distance of 2.0 m. (a) What is the final kinetic energy of the...
  4. B

    Calculating Kinetic Energy of a Gas at Different Temperatures

    Homework Statement A stationary gas has a kinetic energy of 500 J at 30 C. What is its kinetic energy at 60 C? Homework Equations KE = 3/2 RT The Attempt at a Solution I first converted T to Kelvin = 333K. I substituted all the values into find KE but my answer is around 40K, which is not...
  5. S

    How Does Dropping Rocks from Different Heights Affect Kinetic Energy Ratios?

    Homework Statement A rock is dropped from a distance RE above the surface of the Earth, and is observed to have a kinetic energy of K1, when it hits the ground. An identical rock is dropped from 2RE above the surface and has kinetic energy K2 when it hits the ground. Re is the radius of the...
  6. H

    Total Kinetic Energy: Moment of Inertia & CM Axis

    K = Ktranslational + Krotational My book says that in order for this equation to be valid the moment of inertia must be taken about an axis through the center of mass. Why is this true?
  7. irre1evantt

    Relativistic Kinetic energy, momentum, speed.

    Homework Statement An Electron (rest mass=9.11*10^-31kg) is accelerated to an energy (mass energy+kinetic energy) of 30*10^6 eV (30 MeV). What is its kinetic energy? Its momentum? Its speed? (Note: 1 eV = 1.602*10^-19 Joules; c=2.998 * 10^8 ms^-1) Homework EquationsThe Attempt at a Solution...
  8. Ravenalia

    From rotational KE to translational displacement

    Homework Statement A frictionless pulley has the shape of a uniform solid disk of mass 5.00 kg and radius 28.0 cm . A 1.40 kg stone is attached to a very light wire that is wrapped around the rim of the pulley, and the stone is released from rest. As it falls down, the wire unwinds without...
  9. D

    How to find final kinetic energy for a charged particle

    Homework Statement An alpha particle (helium nucleus, charge +2e) starts from rest and travels a distance of 2.5 cm under the influence of a uniform electric field of magnitude 12.5 kV/m. What is the final kinetic energy of the alpha particle? Homework Equations U = 1/2 QV = 1/2 C(V^2) =...
  10. S

    Confused about kinetic energy

    The equation for kinetic energy is: k = 1/2*m*v2 This confuses me because this indicates it take more and more energy to accelerate... Lets imagine a rocket in space (assume the mass of the rocket stays the same when accelerating) - the formula suggests it would take more energy (therefore...
  11. Tyrannosaurus_

    Kinetic energy & speed in a pursuit - Ek possible to find?

    Homework Statement A cat is chasing a mouse in a straight line. The cat's mass, mc, = 5.0kg. The mouse's mass, mm, is 0.035kg. Problem 1. If the kinetic energy of the cat is 100 times the kinetic energy of the mouse can the cat catch the mouse? Problem 2. If the cat and the mouse have the...
  12. Q

    Finding kinetic energy consevered after collision

    Homework Statement 2 cars of equal mass and traveling in opposite directions on a wet and slippery road collide and lock together after impact. Neither car brakes before the collision. The tangled wreck moves off in an easterly direction at 5 m/s immediately after the collision. if one car was...
  13. J

    Who Decided that Work = Force * Distance?

    In other words, why is change in kinetic energy defined this way? (In contrast to momentum being defined as Force times time?) I'm just trying to anchor my understanding of kinetic and potential energies into something intuitive? And, since Force is a vector, why isn't Work a vector quantity...
  14. 2

    Why is kinetic energy due to a planet's rotation treated as negative?

    Homework Statement I am trying to answer the following question: Among the animals that appear in the zoo of the Universe there are black holes and neutron stars. The mass of each of these is often the order of the mass of the Sun. The radius of a neutron star is about 10 km and a certain...
  15. B

    Avg. Kinetic Energy: Neon Ratio @ Diff. Temps

    Homework Statement What is the ratio of the average speed of an atom of neon to another atom of neon at twice the temperature but the same pressure? Homework Equations KE = 3/2 RT; v1/v2 = sqrt. m2/sqrt. m1 The Attempt at a Solution I first used KE = 3/2RT and substituted 1 and 2 for T and...
  16. A

    Relativity and kinetic energy, mass-energy systems

    Homework Statement An object with mass of 900 kg Is moving at a speed of 0.85c when it collides with an object at rest with mass of 1400 kgs. Find the speed and mass of the composite object. Homework Equations mc^2/gamma +mc^2/ gamma=Mc^2 The Attempt at a Solution My issue is that I am not...
  17. P

    Calculating the Initial Kinetic Energy & Momentum of a Truck

    Homework Statement A truck is initially moving at velocity v. The driver presses the brake in order to slow the truck to a stop. The brake applies a constant force F to the truck. The truck rolls a distance x before coming to a stop, and the time it takes to stop is t. 8. Which of the following...
  18. 2

    Sending a satellite to Jupiter?

    Homework Statement "In order to launch a space probe out of the solar system, it is decided to send it close to Jupiter. Why does this reduce the amount of fuel needed?" Homework EquationsThe Attempt at a Solution I can't think of anything at all. I am trying to think in terms of it gaining...
  19. E

    What is the force needed to stop an 8,000lb tractor moving at 5mph in one foot?

    I have a situation where I need to figure how much force it will take to stop an 8,000lb tractormoving at a max speed of 5mph in somewhere around a foot. It will not be an impact stop as there is nothing for it to hit but rather a heavy brake stop. It has been quite some time since I have dealt...
  20. R

    Energy transfer in Newton's cradle

    Homework Statement Three balls of masses m1, m2 and m3 are suspended in a horizontal line by light wires and are almost touching. The mass m1 is given a horizontal velocity v so that it collides head-on with the mass m2. Find an expression for the final kinetic energy of m3? What value of m2...
  21. C

    Expressing kinetic energy as sum of vector and tensor terms

    Homework Statement A system of N particles described by the vector coordinates ##\mathbf{r}_k, k = 1,2, \dots, N ## subject to 3N - f constraints can be expressed in terms of generalised coordinates ##q_i, i=1,2, \dots, f## by ##\mathbf{r}_k = \mathbf{r}_k(q_1, q_2, \dots, q_f, t)## a) Prove...
  22. G

    Answer Work & Kinetic Energy for Mass m Whirling on Table

    Homework Statement Mass m whirls on a frictionless table, held to a circular motion by a string which passes through a hole in the table. The string is slowly pulled through the hole so that the radius of the circle changes from ##l_1## to ## l_2## Show that the work done in pulling the string...
  23. AdityaDev

    Is the expression still valid for large differences in radius?

    If a ball rolls in a semicircular track starting from one end of track,( the track is kept vertical) and if radius of ball is r and radius of track is R is this expression correct? (When ball reaches lowest point) ##mg(R-r)=\frac{1}{2}I_0\omega^2 + \frac{1} {2}I\omega_1^2+\frac{1}{2}mv^2## where...
  24. AdityaDev

    Does Zero Linear Momentum Always Mean Zero Kinetic Energy?

    "if kinetic energy of system of particles is zero, then linear momentum of that system of particles is zero but the reverse is not true. That is if linear momentum of a system of particles is zero, then the kinetic energy may not be zero" This is what I got from my text. Can you provide me with...
  25. starchaser2020

    What is the K.E. of the satellite?

    A satellite has been placed in a circular, sun-synchronous orbit at an altitude of 1300.0 km. The satellite has a mass of 5,000.0 kg. What is the K.E. of the satellite? I know K=(1/2)mv^2 ... but I have no idea where to go from here. I Know I am over-thinking this. So any help would be greatly...
  26. G

    Temperature, Kinetic Energy, Boltzmann Factors, and SHO

    I am confused about the following; where am I going wrong here? 1. (1/2)kT is defined as the average kinetic energy of the molecules of a substance at temperature T, right? 2. You can derive the Boltzmann distribution/Boltzmann factors using (1/2)kT as the kinetic energy, making an argument...
  27. Ahmad Kishki

    Kinetic energy in quantum mechanics

    Given psi as function of x^2, and the potential energy as function of x, find the kinetic energy. My reasoning: KE=P^2/2m and use the momentum operator. My professor's reasoning: Calculate the hamiltonian operator and subtract the potential energy then divide by psi. Note: I talked to my...
  28. Ganesh Ujwal

    How was the formula for kinetic energy found?

    How was the formula for kinetic energy found, and who found it? My questions mostly concern the history of physics. Who found the formula for kinetic energy ##E_k =\frac{1}{2}mv^{2}## and how was this formula actually discovered? I've recently watched Leonard Susskind's lecture where he proves...
  29. B

    Does object lose kinetic energy due to emitting gravitational waves?

    I always thought when there is no force acting on an object it moves at constant speed but every object that moves generates gravitational waves what causes that object to lose energy. Does it mean that object loses kinetic energy and slows down and after some (very long) time will stop.
  30. T

    How does kinetic energy change in circular motion?

    Could someone explain to me how the kinetic energy of a body moving in a circle is like? I got tempted it stays constant as the speed is constant but that turned out to be false. I am interested in places where the body is at top, side and bottom and so on. So I'd like to also know what the KE...
  31. freddie_mclair

    Relativistic kinetic energy derivation (from Work expended)

    Hi, I'm trying to get the relativistic kinetic energy, ## T ##, from the work expended, ## W ##, (assuming that the body is at rest initially) and I'm doing it like this (in 1D): \begin{equation} W = T = \int F ds = m \int \frac{d(\gamma u)}{dt}u dt = m\int u d(\gamma u) \end{equation} Where...
  32. R

    Solving kinetic energy of reaction's products

    Homework Statement This is my first thread in this forum, please forgive me if I made any mistake on posting. Homework Equations I am having difficulty on solving the Problem 5. The Attempt at a Solution The answer I obtained is 1.5MeV, is it correct ?
  33. ZARATHUSTRA

    A question about Momentum and kinetic energy.

    this question is from the book AP Physics C A mass m1 initially moving at a speed v0 collides with and sticks to a spring attached to a second, initially stationary mass m2. the two masses continue to move to the right on a frictionless surface as the length of the spring oscillates...
  34. K

    What is KE of the system using F = ma ?

    Homework Statement Three particles of mass all = 3 kg are located at the vertices of an equilateral triangle and are spinning about their center of mass in an empty space. The sides are length d = 2 m which doesn't change with time. Homework Equations What is the PE of the system? What is the...
  35. K

    How Do You Calculate the Kinetic Energy of a Moving Body?

    Homework Statement A body, which has mass of m = 1 kg , is dropped with a horizontal speed of vo = 20 m/s . What is its kinetic energy after 4 s ? Homework Equations Ek = mv2/2 s = vot + gt2/2 The Attempt at a Solution Is it correct? P. S. There is a mistake: Ek = 3200 J
  36. M

    Kinetic Energy & Velocity: What's the Connection?

    Homework Statement Is the velocity in the kinetic energy=1/2mv2 average velocity or final velocity?
  37. D

    Kinetic energy and direction of rotation

    Hi, I would like to study these two cases: Case A 1/ I turn counterclockwise the ring at w2, this need the energy \frac{1}{2}mr^2w_2^2 with m the mass of the ring 2/ I turn the ring with arm clockwise at w1, this need the energy \frac{1}{2}md^2w_1^2 with d the length of the arm 3/ I eject...
  38. S

    Calculate elasticity of collision from kinetic energy loss?

    Homework Statement After a lot of searching I can't seem to find a way to solve this. Basically, for a bouncing ball, if I know the dropped height and rebound height in a vacuum. How do I calculate the elasticity between the ball and the floor? Homework Equations K = 1/2 mv2 The Attempt at a...
  39. grandpa2390

    The kinetic energy formula for lagrange doesnt make sense

    Homework Statement This is a real basic question I am sure. Maybe I just missed something. so in the book, t = the kinetic energy . only for a pendulum, they add kinetic energy of x dot squared, plus kinetic energy of y dot squared. Homework Equations T = 1/2 m v^2 a^2 + b^2 = c^2 The Attempt...
  40. N

    Calculate kinetic energy transferred

    Homework Statement http://i.imgur.com/hiNHMZZ.jpg - I am struggling with the right-hand page, questions b i, b ii and b iii. I am not sure how to calculate the total amount of kinetic energy transferred to the fluid when given the mass before and after the experiment? Homework Equations EK =...
  41. S

    2D Elastic collision of varying mass, velocities, and angles

    Problem statement: Two pucks of radius 0.05 meters collide as shown in attached picture. The mass of puck 1 is 0.1 kg and that of puck 2 is 0.15 kg. The initial velocities are v1i = 1 m/s and v2i= 0.6 m/s. (1) Assuming no friction between the pucks, only normal forces during collision, in...
  42. S

    Balls elastic collision off center

    Problem Statement: Moe Mentum and Ken Ettik are playing pool. Moe hits the cue ball, sending it towards the 6 ball at 2 m/s. It strikes the stationary 6 ball off-center, moving off at a 60 degree angle from the original direction after a perfectly elastic collision. Both balls have a mass of...
  43. relskhan

    Lennard Jones Potential & Kinetic Energy

    So I'm trying to model two particle interaction subject only to Lennard Jones potential. I have a specific potential I am using: My problem is forcing the two particles into the potential well. I have the particles at a separation distance of 2.5*10-8. The way I interpret this potential is...
  44. B

    Relationship between force and (kinetic) energy

    A car of mass 1kg rests on top of a large flat mass of 1,000,000 kg (10^6 kg). They are at rest (relative to the sun) in space. The car has a battery and an electric motor with 100% efficiency. We can assume that when a torque is applied to the wheels, they roll on the surface of the flat mass...
  45. J

    Maximum kinetic energy of a Pion produced via a kaon decay

    Homework Statement A possible decay mode a of a positive Kaon in the production of three Pions as shown below:. K+ → π+ + π+ + π− Whats is the maximum Kinetic energy that anyone of the pions can have? The kaon is a rest when...
  46. K

    Temperature as a measure of the kinetic energy of molecules

    Homework Statement I know that temperature is a measure of the kinetic energy of gas molecules. at a given temperature different gases have the same average kinetic energy. But in solids and liquids there is also potential energy between the close atoms/molecules. how do i know that temperature...
  47. S

    Lagrange mechanics: Pendulum attached to a massless support

    Homework Statement A simple pendulum of length ##b## and bob with mass ##m## is attached to a massless support moving vertically upward with constant acceleration ##a##. Determine (a) the equations of motion and (b) the period for small oscillations. 2. Formulas ##U = mgh## ##T = (1/2)mv^2...
  48. maxhersch

    Work and Rotational Kinetic Energy (Falling Chimney)

    Homework Statement A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 32.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.) (a) What is the...
  49. S

    Kinetic energy after falling to 100m

    Homework Statement A 250 g object is dropped from a height of 150 m. What is the kinetic energy after falling to 100m Homework Equations V2^2 = V1^2 +2ad Ek = 1/2 mv^2 The Attempt at a Solution I used the kinematics equation to find my v2 then I used this to find Ek. I got the answer 120J but...
  50. T

    Kinetic Energy and Displacement of a 2 piece system

    Homework Statement You stand at rest on one end of a 3.00m long platform (also at rest). The platform is on a smooth friction-less surface. If you walk from one end of the platform to the other at the constant rate of 2.00m/s, what is the kinetic energy of the system (you and the platform)...
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