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
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...
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...
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...
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...
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...
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?
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...
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...
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) =...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
"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...
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...
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...
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...
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...
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.
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...
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...
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 ?
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...
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...
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
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...
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...
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...
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 =...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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)...