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What is the final velocity of a particle accelerated from 8 E8 meters per second so that its momentum doubles when the acceleration is over?
Very sneaky. Your particle is starting out at 2.67 times the speed of light, so
in order to do this whole thing, we must borrow some math from Dr. Einstein.
-- First of all, if your particle was ever at rest, what was its mass ? Call it M0 kgm.
We have no idea how it ever reached 2.67 times the speed of light, but however that happened, the particle's speed, before we begin to mess with it, is 8 x 108m/s .
The easiest way to approach this whole thing is to tunnel directly to the relativistic
momentum formula, without passing GO or any intermediate stages: Momentum = (rest mass)times(speed)/D kgm-m/sec ' D ' is the dimensionless factor that pops up everywhere in special relativity.
I call it ' D ' because it's so Difficult to type in a straight-text presentation.
' D ' is the square root of [1 minus (speed of the particle/speed of light)2].
Be that as it may, the mass of your particle at its initial speed ... speed1 ... is
M = M0/D1 . (That would be j 0.4045 M0 kgm, which is interesting, but we don't need it
just now.)
Its momentum is P1 = M1 x speed1 = M0/D1 x (speed1) (That would be j 323,615,934 M0kgm-m/sec , which is interesting, but we don't need
it just now.)
Notice that both the particle's mass and its momentum are imaginary. But that's OK.
This whole peculiar exercise is imaginary.
You want to double the momentum by changing the particle's speed.
Seems to me it needs to go down like this: P2 = 2 x P1
M2 x speed2 = 2 x (M1 x speed1)
M0/D2 x (speed2) = 2 x M0/D1 x (speed1) Happily, each side may be divided by M0. The particle's rest mass no longer appears, meaning that it has no effect on the answer.
From here, the rest is just a matter of excruciating algebra. The answer you want
is speed2 . It's right out there in the open on the left side of the equation, but the
square of it is also buried in a square root inside of D2 . The worst part about all of
this is that it's almost impossible to solve for speed2 while typing. So if you'll excuse
me for a few minutes, I'll do it on scratch paper, and I'll be back when I have it in a
form that I can just hand over to you.
===================
Well, I'm back. I worked it 3 times, and got the same answer the last 2 times,
so I'll propose that one as my solution.
The particle's speed must be reduced to 3.386 x 108 m/s , about 42% of its initial
speed, and now only about 13% faster than light, in order to double its momentum.
The mass and momentum both remain imaginary.
It all strikes me just as weird as it does you. But I'm confident that you won't need
this answer to enhance the progress of your research anytime soon, so I decided
that I've done my part, and I'm not to spend any more time on it.
What else can I help you with?
What is the momentum of a resting particle?
Momentum = (mass) x (velocity)If the particle is at rest, velocity = 0, and momentum = 0.
Does a body moving with uniform acceleration have momentum?
Yes, a body moving with uniform acceleration has momentum. Momentum is the product of an object's mass and its velocity, and acceleration is the rate of change of velocity. As long as the object is moving and has mass, it will have momentum.
Do acceleration and momentum mean the same thing?
No, acceleration and momentum are not the same. Acceleration refers to the rate of change of an object's velocity, while momentum is the product of an object's mass and velocity. Acceleration measures how quickly an object's velocity is changing, while momentum is a property that depends on both an object's mass and how fast it is moving.
Is momentum is another term for acceleration?
No, momentum is not another term for acceleration. Momentum is a vector quantity that describes an object's motion, taking into account both its mass and velocity, while acceleration is the rate of change of velocity of an object.
When the velocity of a particle is constant its acceleration is also constant?
When the velocity of a particle is constant, it means there is no change in speed or direction. Therefore, its acceleration is zero because acceleration is the rate of change of velocity. If the velocity is constant, there is no change to be measured, so the acceleration is constant at zero.
What is the momentum of a resting particle?
Momentum = (mass) x (velocity)If the particle is at rest, velocity = 0, and momentum = 0.
Does a body moving with uniform acceleration have momentum?
Yes, a body moving with uniform acceleration has momentum. Momentum is the product of an object's mass and its velocity, and acceleration is the rate of change of velocity. As long as the object is moving and has mass, it will have momentum.
What is one similarity to speed velocity acceleration?
Speed, velocity, and acceleration all have momentum.
Do acceleration and momentum mean the same thing?
No, acceleration and momentum are not the same. Acceleration refers to the rate of change of an object's velocity, while momentum is the product of an object's mass and velocity. Acceleration measures how quickly an object's velocity is changing, while momentum is a property that depends on both an object's mass and how fast it is moving.
What does acceleration do to an object?
increases its velocity and momentum
What are Drift velocity and momentum relaxation time?
Drift velocity refers to a particle's average velocity being influenced by its electric field. Momentum relaxation time is the time required for the inertial momentum of a particle to become negligible.
Is momentum is another term for acceleration?
No, momentum is not another term for acceleration. Momentum is a vector quantity that describes an object's motion, taking into account both its mass and velocity, while acceleration is the rate of change of velocity of an object.
Which of these is the rate of change in velocity momentum speed friction or acceleration?
The rate of change in velocity is called acceleration.
Momentum of the particle?
mass times the velocity of the body.
When the velocity of a particle is constant its acceleration is also constant?
When the velocity of a particle is constant, it means there is no change in speed or direction. Therefore, its acceleration is zero because acceleration is the rate of change of velocity. If the velocity is constant, there is no change to be measured, so the acceleration is constant at zero.
What affect momentum?
force and acceleration
Is momentum another term for acceleration?
No, momentum is not another term for acceleration. Momentum is the product of an object's mass and velocity, and it is a measure of how difficult it is to stop the object's motion. Acceleration, on the other hand, is the rate at which an object's velocity changes over time.
