What is Conservation of momentum: Definition and 756 Discussions
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum is
p
=
m
v
.
{\displaystyle \mathbf {p} =m\mathbf {v} .}
In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).
Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry.
Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is generalized momentum, and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle.
In continuous systems such as electromagnetic fields, fluid dynamics and deformable bodies, a momentum density can be defined, and a continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids.
Homework Statement
A 100 kg person in space throws a 1kg sphere away from their body. The sphere starts from rest and ends up traveling 10 m/s away from the person. What is the kinetic energy of the person and the kinetic energy of the sphere? Is kinetic energy conserved?[/B]Homework Equations...
Hello! I'm new to this forum but ok let's get this started,
First I'll revisit the definition I know as physics; the study of nature in order to provide a reasonable(radical/rudimentary) explanation/reason. This I believe in is not quite how things are today, at school, with my teachers or at...
Homework Statement
A block of mass ##m## slides down a wedge of mass ##M## and inclination ##\theta## whose surfaces are all frictionless. Find the velocity of the block when it just reaches the bottom of the wedge.
Homework EquationsThe Attempt at a Solution
I was told that to solve this...
Homework Statement
a trailer with a mass of 150 kg happen to roll away with the speed 20 m/s. 450 kg cement fall staight down into the trailer! which speeds does the trailer get when the cement fall into it?
Homework Equations
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I know how to solve it but I don't know why it works. Is...
Homework Statement
A block of mass M=2kg with a semicircular track of radius R=1.1m rests on a horizontal frictionless surface.A uniform cylinder of radius r=10cm and mass m=1kg is released from rest from the top most point .The cylinder slips on the semicircular frictionless track.The...
Homework Statement
Hi everybody, I was studyng a photon disintegrating in one electron and one positron in the presence of a heavy atomic core; I want to find the final momentum of the atomic core
Homework Equations
Conservation of energy: Eγ=2me+Sqrt(Mn2+Pn2)
Conservation of momentum Pγ=Pn...
Homework Statement
Two identical buggies 1 and 2 of mass ##M## with one man of mass ##m## in each, move without friction due to inertia towards along two parallel rails. When the buggies are opposite to each other, the men exchange positions by jumping in a direction perpendicular to motion of...
Suppose a block of 10kg at 10m/s collides into a block of 5kg at 0m/s.
Does a given percent of energy loss in the collision affect the final velocity of the blocks after the collision?
For instance, if there is no energy lost in the collision, would the final velocities be faster than if...
Hi,
I googled 2d elastic collisions to see if I could find a problem where two objects are approaching each other from different directions before collision and then moving away from each other at different directions after collision, but I noticed that all the problems I've found have 1 of two...
Homework Statement
Three identical balls (of equal masses) are connected by light inextensible strings and kept on a smooth horizontal surface. The middle ball B is given a velocity ##v_0## at ##t=0##. Find the velocity of ball A when A collides with C.
Homework Equations
Impulse ##J=\Delta...
Homework Statement
hello. i tried to solve for the problem, which was quite difficult for me and I'm not sure whether i approached it correctly, so if someone will help me figure it out thank you!
the problem:
1. a 2 kg firework is shot vertically, at v=50 m/s
a. what is the velocity and...
Hey guys, this is not really a h/w question but I thought this would be the best place to get a relevant answer.
So I was doing physics h/w last night and found that I could spin on my chair (a standard office swivel chair) by moving my arms in the opposite direction to the way I wanted to...
Homework Statement
During an explosion, a bomb explodes into 3 pieces. Two fragments, whose masses are 0.8kg and 0.5kg fly off with velocities of 10m/s and 16m/s respectively along the paths at right angles to each other. If the third fragment goes off with a velocity of 24m/s, then find its...
Homework Statement
A plane with an initial velocity of (225m/s ŷ + 325m/s Ẑ) intercepts a 20kg piece of luggage with initial velocity of (-75m/s ŷ - 15m/s Ẑ). After, plane is moving at speed 400 m/s. What is the mass of the plane?
Homework Equations
momentum y: Mplane(225m/s) + 20kg(-75 m/s) =...
Homework Statement
Im stuck on this question please help. =/
a 50.0g bullet travels right and becomes embedded in a 7.00kg stationary block. the block and embedded bullet moves off at a velocity of 5.00m/s right. what was the initial velocity of the bullet? the answer is 706m/s right.
Homework...
Homework Statement
Hey everyone! I'm new to these forums so I apologize in advance if I do something wrong! I just had a quick question about the momentum in one direction equation m_1v_1o +/- m_2v_2o = m_1v_1f +/- m_2v_2f; I'm just not sure when I'm supposed to add these values and when I'm...
Homework Statement
An astronaut is pushed from her ship at a velocity of 2m/s. Her weight including her tool belt is 120kg. Remembering Newtons 3rd law, she takes 5 seconds to decide to detach her belt and throw it away from her. The 20kg tool belt leaves her suit as she throws it in front of...
Homework Statement
One end of a spring is attached to a wall to a block of mass X= 2kg (on a frictionless horizontal table). Another mass M of 150g moving at a speed of 7m/s collides (inelastic). This takes 0.4s to compress the spring to its max compression.
I have to find the max force of...
Homework Statement
A flywheel and shaft have a moment of inertia of 600kg and is rotating at 5 rev/s. Another flywheel and shaft, on the same axis, is suddenly connected by means of a clutch. If this flywheel and shaft has a moment of inertia of 620kg and is initially at rest, calculate:
a)...
Hey! :o
I am looking at the conservation of momentum.
The force at $W$ from the tensions at the boundary $\partial{W}$ is $$\overrightarrow{S}_{\partial{W}}=-\int_{\partial{W}}p \cdot \overrightarrow{n}dA=-\int_{W}\nabla p dV$$ where $p(\overrightarrow{x}, t)$ the pressure and...
Hi
I recently got some weird feedback on homework. It said that "..momentum is only conserved componentwise..". The problem involved Compton scattering, and I had used p_{\lambda,1} = p_{e,2} + p_{\lambda,2} to find p_{e,2} for collision between an electon and a photon. I had used the...
So I've found several instances in which Bernoulli and Conservation of momentum (in Reynolds transport theorem form) give different answers for the study of an inviscid fluid.
Let's consider a simple situation as described in my diagram attached.
Basically a tap/faucet is releasing fluid, which...
if a nice fuzzy block is stationary on a frictionless surface and is hit by a high velocity bullet in such a way that the bullet cleanly penetrates and exits the box leaving the box stationary but the velocity of the bullet slightly changed, what can one say about the conservation of momentum of...
Homework Statement
A stationary atom releases a photon when it goes from excited state n to lower state n. Delta(E) is the energy difference between initial state En and final state En', consider kinetic energy of recoiling atom. Apply conservation of energy and momentum and solve for the...
Hey everyone,
I have a little physics space problem I can't manage to solve, so I hoped someone would be able to help me here.
This is the problem:
We have an object with mass m and speed v1 approaching an other object with mass M and speed U1. The two objects are moving in opposite direction...
In Leonard Susskind's the theoretical minimum, he says, "For any system of particles, if the Lagrangian is invariant under simultaneous translation of the positions of all particles, then momentum is conserved". For a system of two particles moving under a potential which is a function of the...
Homework Statement
A firework at rest with a mass of 0.90kg explodes into 3 pieces. One piece has a mass of 0.25kg and moves horizontally at 36m/s [N]. Another has a mas of 0.35kg and moves horizontally at 32m/s [S50°W]
Find the velocity of the third peice[/B]Homework Equations
SOH CAH TOA...
Homework Statement
There are two trolleys traveling in the same direction which are about to collide.
Trolley 1 is traveling at 4 metres per second and has a mass of 2kg
The other, Trolley 2, (which is in front) is moving a 1 metre per second and has a mass of 4kg.
After the impact, they...
Homework Statement
A lorry of mass 20,000kg is traveling at 20.0 metres per second. A car of mass 900kg is traveling at 30.0 metres per second towards the lorry.
What is the magnitude of the total momentum?
1. 209 kNs
2. 373 kNs
3. 427 kNs
4. 1045 kNs
2. Homework Equations
Linear Momentum...
Homework Statement
Cart 1 and cart 2 are initially at rest, and after the explosion the momentum of the two carts was the same. If the two carts were moving at some initial speed v0 before the explosion: would the momentum of the two carts still be equal?
Homework Equations
Momentum. mvi=mvf...
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A frog sits on the end of a long board of length L=5m . The board rests on a frictionless horizontal table. The frog wants to jump to the opposite end of the board . What is the minimum take-off speed (in s.i. Units) i.e.,relative to ground 'v' that allows the frog to do the...
Homework Statement
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Three masses are positioned on a frictionless surface, as shown. Initially, mass m1 (1.0 kg) moves with a velocity of 2.0 m/s to the right, mass m2 (2.0 kg) is at rest, and mass m3 (3.0 kg) moves to the left with a velocity of 0.50 m/s. First, mass m1 collides...
Homework Statement
I was given a chart to figure out the different momentum and kinetic energies of different collisions (elastic and inelastic) and in the lab he posed the question "Calculate the percent elasticity for each of the collisions."
Homework Equations
conservation of momentum...
Homework Statement
A frog of mass m jumps from the edge of a plank of mass M of length L to the other edge. The plank is on water and is free to move, assume no friction whatsoever. What is the minimum value of the speed of the frog ?
Homework Equations
Conservation of momentum and energy
Some...
Homework Statement
A photon with of 13600eV energy interacts with a hydrogen atom at rest and ejects the electron (photoelectrically) in the direction in which the photon was travelling. If 13.6 eV is required to eject the electron, find the speed of the photoelectron and the momentum and...
Three High energy Photons spontaneously convert into electron positron pairs, The electron on the left marked A is created and and destroyed within a short interval, sending an electric field burst towards electron B shortly after it's created, just enough so that Electrons B's electric field...
Homework Statement
A uniform 4.00kg square solid wooden gate 2.00m on each side hangs vertically from a frictionless pivot at its upper edge. A 1.30kg raven flying horizontally at 4.50m/s flies into this door at its center and bounces back at 2.50m/s in the opposite direction.
What is the...
Homework Statement
A 500 g billiard ball is going at 10 m/s [E] when it impacts 2 other identical billiard balls. Afterwards, you observe 2 of the balls moving at 2 m/s [30 W of S] and 3 m/s[45 N of E] respectively. Calculate the Energy lost in the collision.
Homework Equations
KE = 1/2mv^2...
Homework Statement
A ball with mass 2kg is traveling 2m/s. It impacts and sticks to a hanging, stationary 4kg pendulum. How high will the pendulum + ball go?
Homework Equations
KE = 1/2mv2
PEg = mgh
mava = m(a+b)v(a+b)
The Attempt at a Solution
I tried to solve this question assuming...
Homework Statement
Homework Equations
Conservation of linear momentum for fluids
The Attempt at a Solution
This seemingly simple problem has me confused. First of all, I want to set up the sum of the foces as:
-Min + Mout -Fx = 0
So first of all, not only does my Fx term have the wrong...
We all know that momentum is conserved in a system. But I am confused of one thing.
Suppose we have a system containing a wall with very large mass and a ball and use a classical x-y coordinate axis.
If I swing the ball at an angle of 45 degrees from the horizontal, upwards to the huge wall...
ABSTRACT:
I have a collection of springs and disks (masses) to choose from. I have a solid rod fixed to the ground. I slide a piece of sheet metal into the rod to act as a base. I now slide a disk into the rod. Then a spring. Then another disk. Then another spring. And one final disk. I now lift...
Homework Statement
A diesel engine weighs 8 times as much as a freight car. This diesel engine, moving on a horizontal track at 3 km/h, crashes into the freight car (which was moving at 2 km/h in the same direction). What is the velocity, in km/h, of the now linked together engine/car...
Homework Statement
A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown. If the first ball moves away with angle 30° to the original path, determine
a. the speed of the first ball after the collision.
b. the speed and direction of the second...
Homework Statement
A 59.8kg person holding two 0.902kg bricks stands on a 2.14kg skateboard. Initially, the skateboard and the person are at rest.
Calculate the final speed of the person and the skateboard relative to the ground if the person throws the bricks one at a time. Assume that each...
Homework Statement
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Two rocks collide in outer space. Before the collision, one rock had mass 14 kg and velocity ‹4450, −2950, 2250› m/s. The other rock had mass 7 kg and velocity ‹−600, 1900,3600› m/s. A 1 kg chunk of the first rock breaks off and sticks to the second rock. After the...
Homework Statement
An 82-kg lumberjack stands at one end of a 380-kg floating log, as shown in the figure (Figure 1) . Both the log and the lumberjack are at rest initially.
If the lumberjack now trots toward the other end of the log with a speed of 2.7 m/s relative to the log, what is the...
Homework Statement
A plate drops onto a smooth floor and shatters into three pieces of equal mass. Two of the pieces go off with equal speeds v at right angles to one another.
1. Find the speed of the third piece.
2. Find the direction of the third piece. Assume the motion of the two pieces...
I know that momentum is conserved if there are no external forces.
But, can you tell me what external forces are ?
The site http://www.physicsclassroom.com/class/energy/Lesson-2/Internal-vs-External-Forces says that internal forces are force of gravity and force of spring.
But, I think that...