# kinetic energy Definition and Topics - 248 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. ### Exponential potential energy state diagram

It is my second "energy state diagram problem" and I would want to know if I am thinking correctly. First I have done some function analysis to get a glimpse of the plot: - no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0## - y interception: ##U(0)=-U_0## - even...
2. ### I Question about n rotating parallel cylinders

There are n vertical identical parallel identical cilinders rotating around their length axes with the same angular velocity. The are somehow fixed wrt to Earth and brought together (on a rail?). After the contact there is no slipping and the cilinders are coupled to their neighbor cilinders. It...
3. ### Lagrangian mechanics - rotating rod

Hello, It might sound silly, but when I try to calculate the kinetic energy of a rotating rod to form the Langrangian (and in general), why it has both translational and rotational kinetic energy? Is it because when I consider the moment of Inertia about the centre I need to include the...
4. ### Why can I not use the work-kinetic energy theorem for this falling elevator problem?

As stated, part (a) says that the work done by the gravitational force ##\vec{F_g}## is 59 kJ. If ##W_T## is the work done by the elevator cable during the 12 m fall, then using the work-kinetic energy theorem, \begin{align*} K_f -K_i &= W_g + W_T\\ \frac12m({v_f}^2 - {v_i}^2) &= 59000 + W_T\\...
5. ### Why the temperature of a car does not increase with velocity?

We know temperature is a measure of average kinetic energy of molecules/particles of a system. Now if a car starts to move, its velocity increases so does its kinetic energy. Therefore all the molecules are gaining velocity too. Shouldn't this increase the temperatre as average kinetic energy of...
6. ### What is the temperature change of a bullet upon impact?

Summary:: What is the temperature change of a bullet upon impact. I have this problem to solve but I'm kinda stuck, would apricate any feedback. We fire a silver bullet with a muzzle speed of 200 ms−1 into a sack of sand. What is the temperature change of the bullet, if 40 % of its kinetic...
7. ### Confusion about tidal locking and rotational kinetic energy

Hello! I was reading two things: 1) tidal locking (as explained in the Wikipedia article:https://en.wikipedia.org/wiki/Tidal_locking where it is stated that, because of internal friction caused by the body of water being attracted to the moon and deforming, the kinetic energy of the system...
8. ### Using Orbital Energy to Calculate Velocity

So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m. Then I found change in potential energy, -5.597*10^11 m. Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial...
9. ### At what size is kinetic energy no longer related to temperature?

Hi all, I've read so many times that "temperature is a measure of the average kinetic energy of the molecules in a substance," or sometimes "particles" to encompass atoms and ions too. But how big can "molecules/particles" be before their kinetic energy is no longer relevant to temperature? If...
10. ### A Degrees of freedom of thin rods

(Note: I had this question posted at the intermediate level of difficulty for 11 days, but got only one, cryptic (to me) response that was rather quickly removed. So, I figured perhaps it's actually an advanced question, requiring more than a cursory understanding.) Assuming they've had an...
11. ### Physics momentum problem -- Collision between 2 blocks that stick together

So far I found the answer for a and b, but when I attempted to do the other ones I was completely lost. A.) P= MV M = 25g = .025kg V = 18 .025 * 18 = .45kg*m/s B.) KE= 1/2 mv^2 1/2 (.025)(18)^2 4.05 J

13. ### Finite quantum well, multiple choice question

Homework Statement:: Consider an electron trapped in a one-dimensional finite well of width L. What is the minimum possible kinetic energy of the electron? A) 0 B) Between 0 and h^2/8mL^2 C) ≈h^2/8mL^2, but it is not possible to find the exact value because of the uncertainty principle D)...
14. ### Kinetic energy as a function of time

I got acceleration by dividing force by m then replaced a by dv/dt and then integrated it to get velocity as a fxn of time and hence got kinetic energy but problem is my ans does not match with any option can someone please compare their ans
15. ### Estimating the damage to a material based on force or kinetic energy

I'm programming a game in which I'd like to simulate the real world physics of an attack using primarily medieval style weapons. Think dwarf fortress, but rather than assigning damage numbers we're calculating force or kinetic energy. Getting that much is easy enough since I can find the mass of...
16. ### Man jumping onto a see-saw to launch bricks vertically

I drew a diagram for the a) part The person is h meters high So GPE= 100 x 9.8x h GPE= 980h j KE = 980h when the person hits the see saw KE=1/2mv² 980h=0.5 x 5 x v² Now it v²=u²+2as For the brick going up to 10m v = 0 u=? a=-9.8ms-² s=10m u²=2 x 9.8 x 10 u=14m/s We can assume that u=14m/s is...

18. ### Kinetic Energy of Protons

So first I tried to use KE=1/2 x m x v^2 but then realised I didn’t have the velocity and I can’t figure out a way to obtain it. I then tried to work out the energy using a different equation, W= q x v but that left me with 1.28x10^-14 J which seemed too small. I also then have to calculate the...
19. ### Confused by the relationship of work and kinetic energy

So the equation for work is W = F * s F = m * a, so W = m * a * s Transferring this to units of measurement gives us: J = kg * m * s-2 * m Or simplified: J = kg * m2 * s-2 Transferring back to units of quantity: W = m * v2 How can that be correct? Obviously Ekin = 1/2 * m * v2. Where did that...
20. ### 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...
21. ### 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...
22. ### 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...
23. ### 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...
24. ### 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...
25. ### 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...
26. ### 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...
27. ### 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...
28. ### 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. ### 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. ### Moving down a ramp

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...