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.
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...
Homework Statement
The position of an object of mass 2 kg is changing as a function of time by the formula x(t) = 4t^3-6t. (a) find the work done by the forces acting on the particle between t=1 and t=3s. (b) What is the object's velocity when the force on it is zero?
Homework Equations
is...
I am really confused here. I have studied that if the kinetic energy of a moving body is not changing then the net work being done on the object is equal to zero. But when we are talking about a body moving upwards at constant velocity there is no change in its kinetic energy but there is still...
I'm confused; forgive me if this dumb.
I'm trying to reason what "force" is, on a molecular level. I'm only concerned about normal forces here (pushes and pulls), not field forces. Forces in Newtons are vector quantities and only represent relationships between two things right? It isn't...
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.
Hello everybody,
A special problem constrain me to make a variable change in my Hamiltonian operator, so with the kinetic energy operator, I have a doubt.
The variable change is: ## \theta \longrightarrow (\theta + k) ## (where ##k## is a constant).
And the kinetic energy operator...
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...
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...
College-level introductory physics textbooks usually devote a chapter to special relativity. Peter J. Riggs in his article appearing in the February 2016 issue of The Physics Teacher (pp 80-82) derives a couple of expressions for the kinetic energy of a massive (as opposed to massless) particle...
basically, as far as I know we can derive 1/2mv2 from
∫F⋅ds=1/2mv2=(p2)/2m
for wave equation we use Hamiltonian H=P2/2m+V where P and V are both operators
However, I wonder how we can say that P2/2m is the term for kinetic energy because
∫F⋅ds=∫(dp/dt)⋅ds=1/2mv2 is saying that knowing F and...
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...
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...
Homework Statement
You push a blob of gelatin with a constant force of 2.4 F across a wet table on which it slides easily. Because the blob shape distorts, its center of mass moves only 33 mm during the time interval in which the point of application of your force moves 53 mm .
By how much does...
Homework Statement
Two 0.50-kg carts are pushed toward each other from starting positions at either end of a 6.0-m low-friction track. Each cart is pushed with a force of 2.9 N , and that force is exerted for a distance of 1.0 m.
What is the kinetic energy of the center of mass of the system...
Homework Statement
In solid state physics,we know all the states of free electrons can be expressed by the First Brillouin Zone. We know the $$E(k+K)=E(k)$$ where K is reciprocal lattice vector. We also know that the kinetic energy of the electron is $$E_{k}=\frac{\hbar^2k^2}{2m}$$. [/B]...
I saw another post about this but i didn't quite find what i was looking for there so i thought i'd give it a go instead with a thread.
Homework Statement
Calculate the exact value of the kinetic energy of the hydrogen atom in its ground state. No more information is given, we are referred to...
Homework Statement
A 120 kg hoop rolls along a horizontal floor so that its center of mass has a speed of 0.240 m/s. How much work must be done on the hoop to stop it?
Homework Equations
I of hoop=MR^2
The Attempt at a Solution
KE=0.5*m*v^2+0.5*(mR^2)(v/R)^2...
Homework Statement
A.What is the change in kinetic energy of the crate? Answer in units of J.
B.What is the speed of the crate after it is pulled 5.79 m? Answer in units of m/s
Magnitude of work done by gravity= 200.786
Work done by applied force= 822.18
mass=8.91kg
force pulling on box= 142N...
Homework Statement
A 410 g particle in a semi-spherical bowl of radius 0.9 m is released from rest at point A at the level of the center of the bowl, and the surface of the bowl is rough. The speed of the particle at B is 2.6 m/s. The acceleration of gravity is 9.8 m/s 2 . What is its kinetic...
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...
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...
Homework Statement
Consider a gas of molecules of mass m at equilibrium at temperature T. Obtain an expression for the fraction of molecules having kinetic energy e = 1/2mC2 in the range e to e + de.
This is problem 5.3, page 48 of Vincenti and Kruger's Intro to Physical Gas Dynamics
Homework...
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)...
Homework Statement [/B]
An ice skater executes a spin about a vertical axis with her feet on a frictionless ice surface. In each hand she holds a small 5kg mass of which are both 1m from the rotation axis and the angular velocity of the skater is 10rad/s. The skater then moves her arms so that...
I've added 'in classical physics' in the thread title because all the differences between them that I found on the internet involved relativistic physics. It was something like both momentum and kinetic energy being components of a four-momentum or something like that. But I cannot understand...
Homework Statement
A disk of mass m1 is rotating freely with constant angular speed ω. Another disk of mass m2 that has the same radius is gently placed on the first disk. If the surfaces in contact are rough so that there is no slipping between the disks, what is the fractional decrease in the...
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...
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...
I'm having a bit of trouble conceptualizing this. I've looked all over the Internet, and I've been seeing that in completely inelastic collisions the reason that kinetic energy is not conserved is because energy goes into deformation, sound, propelling shrapnel, and especially heat (among other...
Homework Statement
I have the decay
K+ → μ+ + νμ
Calculate:
1. Momentum of μ+
2. Total energy of νμ
3. Mass of K+
4. Speed of μ+
5. Speed of νμ
Homework Equations
The only thing we get are the kinetic energy of μ+ so Kμ+ = 152.53 MeV
and the mass of mμ+ = 105.658 MeV/c2
The Attempt at a...
Homework Statement
Not actually a homework question but is an exercise in my lecture notes.
Homework Equations
I'm following this which demonstrates that the momentum operator is Hermitian:
The Attempt at a Solution$$KE_{mn} = (\frac{-\hbar^2}{2m}) \int\Psi_{m}^{*} \Psi_{n}^{''} dx $$
$$...
Homework Statement
A wooden toy mouse of mass (m) is attached to a spring with constant (k) and suspended vertically as shown below. The toy is released at the point the spring is unstretched at position x = +A, passes through equilibrium at x = 0 and the spring’s maximum extension occurs at x...
How should I look at the problem at stopping a moving object with the following conditions
1) mass m and speed v
2) 0.5 m and 2v
3)0.5m and sqrt 2 v
Simple math tells me the number 2 would require more energy to stop it. I can relate to energy better in terms of how to stop a moving mass...
Homework Statement
Ball 1 has an inertia of 0.500 kg and ball 2 has an inertia of 0.600 kg . Ball 1 is moving away from you at 5.0 m/s, and you decide to throw ball 2 at it to make it go faster. The balls collide head-on, and the coefficient of restitution for the collision is 0.95.
Part A)How...
1. The problem statemees and given/known data
A ball has a potential energy of 200J. Once the ball reached the ground, it's kinetic energy was 175J. Is this possible and does this defy the conservation of energy?
Homework Equations
KE = PE
The Attempt at a Solution
I am not sure. Being in high...
Homework Statement
Homework Equations
ΔKE=W+FcosΘd
KE=.5mv^2
Final Vel^2=initial Velocity^2+2ax
The Attempt at a Solution
So calculate the force at x=2.6 to -5.356N, set 2.6(-5.356)=1.3Vf^2-1.3(0^2) which seemed to prove a problem as the square of the final velocity was negative, but just...
Homework Statement
I need to accommodate a dashpot in an intentionally simple work-kinetic energy analysis method. For example, for a box being dragged up a ramp via a rope while attached to a spring, I can deal with the work done by gravity, rope tension, spring force, and friction via the...
Hi, I'm a high school science teacher. Most textbooks classify EM radiation as kinetic energy. But this doesn't seem right to me. As a photon is massless it's hard to see how it can have kinetic energy which is 1/2 mv^2.
It could be said that it has energy hf and therefore mass hf/c^2. Then its...
When I learned about operators, I learned <x> = ∫ Ψ* x Ψ dx, <p> = ∫ Ψ* (ħ/i ∂/∂x) Ψ dx. The book then told me the kinetic energy operator
T = p2/2m = -ħ2/2m (∂2/∂x2)
I am just think that why isn't it -ħ2/2m (∂/∂x)2
Put in other words, why isn't it the square of the derivative, but...
1. Problem Statement:
A worker lifts a heavy crate vertically 1.0 m in 2.0 s. If she lifts the same crate the same distance in 1.0 s, the work was done by her is
A
the same.
B
two times as great.
C
half as great.
D
four times as great.
E
one-fourth as great...
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...
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 =...
Homework Statement
"In Fig. 8-33, a runaway truck with failed brakes is moving downgrade at ##130\frac{km}{h}## just before the driver steers the truck up a friction-less emergency escape ramp with an inclination of ##θ=15°##. The truck's mass is ##1.2⋅10^4kg##. What minimum length L must the...
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...
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...
Homework Statement
Show that the largest possible change in the kinetic energy , ##\Delta E_{kin}##, of a particle of mass ##m## running into another particle of mass ##M## at rest in the lab coordinate system is
\Delta E_{kin} = \frac{-4AE_{kin}}{(1+A)^{2}}, where ##A = \frac{M}{m}##...
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 =...
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...
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...