# Kinetic energy Definition and 264 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. ### Work, Gravitational Potential and Kinetic Energy, Spacecraft

Hi guys. I'm new to this forum so I'm not sure if I'm posting this in the right place or correctly, but I was totally stumped on a Physics 12 question as I was studying for my exam. The question is: An explorer spacecraft is descending towards Mars using a rocket engine for braking. The...
2. ### Stuck on projectile motion problem using gravitational force

Homework Statement A projectile is fired vertically from the Earth's surface with an initial speed of 11.4 km/s. Neglecting air drag, how far (in meters) above the surface of the Earth will it go? Homework Equations (1/2)mv^2 -GmM/R The Attempt at a Solution KEi+PEi = KEf+PEf (1/2)mv^2 -...
3. ### Relate rotational kinetic energy to potential energy

Homework Statement This problem is from the 2015 AP Physics C Mechanics free response, question 3 part b. https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf Homework Equations K = 1/2Iω2 U = mgh The Attempt at a Solution The potential energy of the bar when...
4. ### A Electron's kinetic energy

Hello to All ! I have a question that Whenever an electron from bulk material trapped by a quantum well that electron's 3rd dimensional kinetic energy component vanishes, But where that goes, is it added to the other 2 dimensional kinetic energy components..?
5. ### Collisions -- conceptual questions

Homework Statement Let two particles of equal mass m collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary. A: If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2? B: Now assume that the mass of...
6. ### What fraction of its energy does accelerating proton shed?

Homework Statement If a proton with a kinetic energy of 6 MeV is traveling in a particle accelerator in a circular orbit of radius 0.75m, what fraction of its energy does it radiate per second? m = 1.67 * 10^-27 epsilon_0 = 8.854 * 10^-12 c = 3 * 10^8 Homework Equations dE/dt = (q^2 a^2) /...
7. ### Need help finding energy for escape velocity

Homework Statement The gravitational potential energy of a certain rocket at the surface of the Earth is -1.9x10^12 J. The gravitational potential energy of the same rocket 300km above the Earth's surface is -1.8x10^12 J. Assume the mass of the rocket is constant for this problem. A) How much...
8. ### Question About Potential Energy

I have two simple examples of potential energy and kinetic energy. First example: Imagine a book on the ground and I want to lift it.At first I apply a force just a little more than the gravitational force of the Earth so that it has some velocity. After the book gets that velocity, I keep my...
9. ### Explosion and conservation of momentum problem

Note: Please only give hints please! No answers because I want the satisfaction of solving it. 1. Homework Statement A mass M at height h above flat round and falling vertically with velocity v breaks up explosively into 2 parts. The kinetic energy given to the system in the explosion is E...
10. ### HW Help: Mass and Kinetic Energy

Question: Calculate the kinetic energy required to accelerate a single proton from rest position to 0.9999c. The mass of the proton is 1.67*10^-27 kg. Equations Used: Ek=(mc^2/√ 1-(v^2/c^2))-mc^2 Attempt at the problem: Ek=(1.67*10^-27kg)(3*10^8m/s)^2/√...
11. ### Kinetic energy and momentum

Homework Statement Homework Equations K.E = p^2/m The Attempt at a Solution [/B]
12. ### Conservation of Energy, Down an Incline with a Spring

Homework Statement A 4.0 kg block starts at rest and slides a distance d down a frictionless 35.0 incline, where it runs into a spring. The block slides an additional 16.0 cm before it is brought to rest momentarily by compressing the spring, whose spring constant is 429...
13. ### Analysis of collisions from data

Good afternoon! I would like to preface by saying, yes, this is for a project. I am only posting here to see if my method of solving is correct before I finish the project incorrectly. Homework Statement I chose two balls, mass A: .553 kg and mass B: .410 kg I recorded their collision and...
14. ### 1/2 m v^2 in a circle?

Homework Statement in circular motion (e.g. a pendulum) is the kinetic energy still 1/2 m v ^2 or is it a different equation? Homework Equations 1/2 m v ^2 The Attempt at a Solution
15. ### Work done on brakes vs kinetic energy lost by vehicle

When doing work on the brakes of a car or bicycle, how much of that energy is actually removed from the total kinetic energy of the vehicle? What is the most efficient braking system?
16. ### Should I consider Linear Kinetic Energy in this Equation

Sorry If the thread name confuse you. I want to know if I want to find the Torque from deriving Kinetic Energy and the system has Object the Rotate and the rotating cause linear motion(v). Let's say it a Rolling Disc on the non-slope plane which has angular velocity ω and that ω cause it to move...
17. ### Mechanical Energy Problem/non-conservative forces

Homework Statement A body of mass "m" is let go from on top of a surface A, where it slides down to B(without friction). From that point on, it displaces itself on an horizontal surface 5 meters away from B, where it stops at C. Being "m" a mass in kg "h" in meters and g = 10 m/s^2 The value...
18. ### Efficiency question

Homework Statement A motor lifts a block of mass 0.050kg at a constant velocity of 0.40m s-1. The current in the motor ia 85mA and the potential difference across it is 3.0V. Calculate the efficiency of the motor Homework Equations Ek = 1/2 x mv2 Electrical power = VIt The Attempt at a...
19. ### Ball doing a loop

Homework Statement A ball with radius ##r## is inside a hollow cylinder with radius ##r+R##. In the first part of the assignment, one has to calculate the minimum kinetic energy the ball has to have at the bottom in order to complete a full loop in the cylinder. It turns out to be...
20. ### Electron in orbit of around a single proton

Today I was doing some reading and I came across this topic. If we have a stationary hydrogen atom with a single electron in orbit around the nucleus and want to calculate the kinetic energy of the electron we would take the following approach. 1) Using Newton's second law: F = ma ⇒ FE = mac...
21. ### I Energy transfer during uphill vs downhill running

Hello Physics Gurus, Please critique the following logic... When a runner hikes/runs to the top of a mountain, the chemical potential energy inside the muscles transferred into the potential energy of the runner's body mass at the higher elevation (Pe = mass*gravity*height = mgh). Energy is...
22. ### Impulse and kinetic energy?

Homework Statement Two identical spheres A and B are kept on a smooth surface. They are given the same impulse I. The lines of action of impulses pass through the center of A and away from the center of B. Then: (A) linear kinetic energy of B will be less than that of A. (B) B will have...
23. ### How much kinetic energy do I need to impart?

Homework Statement I'm actually making up my own problem here to try to resolve some confusion I'm running into on understanding kinetic energy and reference frames... Let's launch a potato of mass m (just call it 1) horizontally with a potato gun on a fast vehicle moving 50 m/s, while I'm...
24. ### A spring with a force constant

Homework Statement Homework Equations These are the equations he provided. The Attempt at a Solution I actually have no idea how to do them. So any help would be much appreciated.
25. ### Car Crash Work and Energy Problem

Homework Statement A red van came through and crashed into a green van. The driver of the red van claims that he was driving at a speed of 11 meters/second at the moment of the crash. You want to find out if his claim is true. a. the mass of the red van is 1000 kg b. the mass of the green van...
26. ### Kinetic energy change with initial velocity

It is my understanding that to calculate the change of kinetic energy of an object that speeds up from vi to vf you use this formula: Change of kinetic energy = 1/2 * m * (vf2 - vi2) When the initial velocity is 0 m/s I have no problems, but let's say an object that weighs 2 kg speeds up from...
27. ### Angular momentum: rotating ice skaters

Homework Statement Two ice skaters of mass ##m = 50\,\mathrm{kg}## each are moving towards each other frictionless on parallel paths with a distance of ##3\,\mathrm{m}##. They both have a velocity of ##v_o=10\,\frac{\mathrm m}{\mathrm s}##. Skater 1 is holding a massless rod of length...
28. ### Loss of kinetic energy due to heat

Homework Statement I have a bloc sitting on a horizontal table, and we shoot a ball through it. The speed right before entering the block is v and the speed when it exits the block is v/2. I need to prove that the fraction of the initial energy that is lost due to heat is 3/4 - γ/4, where γ is...
29. ### Momentum not conserved?

I remember throwing clay balls at walls in my childhood and observing them stick to the wall. In a more scientific perspective, considering the ball and wall as a system, I can say that the total momentum before collision is greater than 0. But then, after the collision, the kinetic energy of...
30. ### Efficient way to convert kinetic energy to heat

I am trying to find the most efficient way to convert kinetic energy to heat. The first thing I know is friction, however friction cause wearing for long term use. The second is convert to electric energy(dynamo) and then convert to heat using electric coil, however I think that has low...
31. ### KE of alpha particle using integer values of nuclear masses

Homework Statement (a) Cobalt has only one stable isotope, 59Co. What form of radioactive decay would you expect the isotope 60Co to undergo? Give a reason for your answer. (b) The radioactive nuclei 21084Po emit alpha particles of a single energy, the product nuclei being 20682Pb. (b) (i)...
32. ### I Speed and kinetic energy in different inertial frames.

From Chris' perspective Bob is traveling with 1.5*108 m/s in direction a. Angelica is also traveling with 2.4*108 m/s in direction a. From Bob's perspective Chris is traveling with 1.5*108 m/s in direction b (The opposite of x). Angelica is traveling with 1.5*108 m/s in direction a. They all...
33. ### V required so ions passing through the region don't devitate

Homework Statement Hydrogen ions moving at various speeds are directed at a region of combined electric and magnetic fields as shown in the diagram below. The electric field is between two parallel plates 10 mm apart with a potential difference V across them, while the magnetic field of flux...
34. ### Rest, Mass, and Kinetic Energy

Homework Statement I really don't have a homework question just a thought. Is rest energy "maximum energy" for a particle? As to say a particle at rest has a given energy, so when it is in motion it transfers some mass energy to kinetic energy, where both the mass and kinetic energy together...
35. ### Finding Horsepower given Pressure, Diameter, and Distance

Homework Statement When gas is burned in a cylinder of an engine it creates a high pressure that pushes a piston. If the pressure is 100psi and it moves a 3 inch in diameter piston a distance of 5cm every .1 seconds. How much horsepower does this action produce? Homework Equations Pressure =...
36. ### Center of momentum frame question:

Homework Statement An 8.0-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 16 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume...
37. ### Finding the Value of Gravity Given Height and Velocity

Homework Statement If a ball is dropped from a height (H) its velocity will increase until it hits the ground (assuming that aerodynamic drag due to the air is negligible). During its fall, its initial potential energy is converted into kinetic energy. If the ball is dropped from a height of...
38. ### Potential difference of helium nucleus question

Homework Statement What potential difference is needed to give a helium nucleus (Q = 3.2 × 10-19 C) 50 keV of kinetic energy? Homework Equations V=U/Q 3.2 × 10-19 C = 2e The Attempt at a Solution I was quite sure I had the right answer but it keeps saying I'm wrong? V = (50*10^3 eV) / 2e =...
39. ### Velocity & Kinetic Energy

Hey guys, this question has boggled my mind not because I don't know how to approach it but apparently the method I'm using is incorrect! Question A cannonball with a mass of 150 kg is fired from a cannon. The cannonball leaves the cannon with 447.9 kJ of kinetic energy. The cannon makes an...
40. ### Water wheels and mathematical equation

Hello everyone, currently working on a physics project. I was very curios about waterwheels and actually have an overshot waterwheel setup. I was testing how the efficiency of a waterwheel would be effected by the drop height of water onto the waterwheel. Do any of you have any idea how I can...
41. ### Inelastic Collision

In an inelastic collision is the change in kinetic energy equal to the difference of final and initial momentum if one of the objects is initially at rest? For example: m1v = (m1+m2)Vf -----> 0 = (m1+m2)Vf - m1v1 1/2(m1+m2)Vf^2 - 1/2m1v^2 = (m1+m2)Vf - m1v1 Or totally wrong? Thanks!
42. ### Momentum conservation inelastic collection

If a car crashes with a stationary tree and comes to stop, we could say that the kinetic energy of the car was converted to heat and that the collision was inelastic. However, conservation of momentum dictates that momentum is still conserved. How would that be possible given that neither the...
43. ### Solve questions on oscillations and kinetic energy

A spring of spring constant k sits on a frictionless horizontal table, one end of the spring is attached to a wall the other end to a block of mass M= 2kg, also resting on the frictionless table. Another block of mass m=450g moving at a speed of 7m/s collides in-elastically with the block of...
44. ### Finding displacement using net work?

Homework Statement The question is: A 2 kg particle is moving in the positive x direction with the speed of 5 m/s. As it passes the origin, a force F = (30 N - 2N/s*t)i is applied to it. Where does the particle come to a stop? Homework Equations F=ma W = integral F(x)dx K=.5mv^2 The Attempt...
45. ### Inelastic Collision - Kinetic Energy

A 6.0kg metal ball moving at 4.0m/s hits a 6.0kg clay ball at rest and sticks to it. The two move at 2.0m/s. a. calculate the kinetic energy of the metal ball before it hits the clay ball. b. calculate the kinetic energy of the metal ball after it hits the clay ball. c. calculate the kinetic...
46. ### Finding relativistic mass and energy of an electron

Homework Statement A resting electron was sped up to 0.5 of the speed of light. Find: A. relativistic mass of the electron, B. total energy of the electron, C. kinetic energy of the electron. Homework Equations K = mv^2/2 E=mc^2 The Attempt at a Solution Let’s first find the kinetic energy...
47. ### Calculate height and velocity given kinetic and potential?

Homework Statement I have a table that needs to be filled out. In each column, potential and kinetic energy are given, but height and velocity are left blank. Ex: PE = 20 J, KE = 0 J, h = ?, V = ? Homework Equations KE = 1/2mv^2 U = mgh The Attempt at a Solution I'm totally stumped. How can I...
48. ### Kinetic Energy and Collision Question

Homework Statement Why is there more heat and sound energy produced with a larger collision? Homework Equations The Attempt at a Solution Honestly no clue. I would really appreciate any help! Any videos would also help!
49. ### Kinetic Energy and Collision Question

Is there a threshold of maximum kinetic energy lost when kinetic energy is transferred between two objects through collision? I just cannot find any information on this, any help would be VERY much appreciated.
50. ### Kinetic Energy from a Simple Harmonic motion and spring

Homework Statement A 0.26-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes...