Momentum is always conserved

glueball8

I don't understand how I can be at rest and then start walking or when a ball hits the wall it bounces back while the wall get no momentum at all?

Ed Aboud

As far as I know, conservation of energy underlies conservation of momentum, so therefore if a ball hits a wall and bounces back some of its kinetic energy is converted to other forms such as heat and sound which appear in the wall.

mathman

In the cases you mentioned there is momentum transfer to the earth (via the wall in the second case). Since you and the ball are a lot less massive than the earth, the velocity effect on the earth is extremely small.

aerospaceut10

In either case, momentum is conserved. It's just that the wall is rigidly connected to the ground/Earth and likewise for your walking scenario. Remember that it's mass times velocity to get that momentum figure, so if you have such a large mass, the Earth, it'll have to have an insignificant velocity, essentially, when your tiny mass moves at the given velocity.

glueball8

So what about that I can walk from rest? How is the momentum conserved here?

Doc Al

As you move forward with momentum +P, the ground/Earth is pushed back with momentum -P. Since the ground/Earth is so massive, you won't notice its backward movement. (As mathman and aerospaceut10 already explained.)

Phlogistonian

When you walk, you push against the earth. Theoretically, this gives it a very slight velocity in the opposite direction, but it's too small to be detected.

rockerdoctor

here is another way to think about it. think of someone driving a car. the car has momentum. when the car comes to a stop at a stop sign, all the momentum in the car is pushed into the road. this is why you frequently see ripples in the road at places where there are frequent stops. all the momentum must go somehwere so it goes into pushing up the road. momentum is always conserved

Cyrus

"Theoretically"?.......... "velocity in the opposite direction?" ..........."To small to be detected"...........? ............

Hint:
[tex]m_ev_{e,1}+m_pv_{p,1}=m_ev_{e,2}+m_pv_{p,2}[/tex]

Do some algebraic manipulation and get this"

[tex]v_{1,e}-\frac{m_pv_{p,2}}{M_e}=v_{e,2}[/tex]

Now, how did you deduce the earth moves "in the opposite direction?" Something should have yelled to you, wait a minute, that doesnt make sense by the sound of what I just wrote.

Phlogistonian

The OP phrased the question as starting from rest. Whenever I answer a question, I take the OP's conditions as implicitly given. I'm sorry if this confuses you.

Actually, I'm not sorry. You're just an annoying nitpicker.

And how do you propose to measure the motion of the earth due to a person walking around upon it?

Cyrus

The initial velocity of the person was set to zero as part of the algebraic manipulation.

Please explain how the earth goes in the 'opposite direction'.

Phlogistonian

Cyrus,

Ah, I see your point now. I didn't see it at first. Your point is still stupid.

I have to specify that the earth is moving before I take a step? Why? What absolute reference frame are you using?

Cyrus

As long as you see my point, im happy. Statements like "very slight velocity in the opposite direction" sound very, very wrong.

D H

It's not nice to be rude.

Particularly when you are wrong.

Loren Booda

If (for an elastic collision) momentum of a ball incident upon a wall is equal and opposite to its resultant momentum, would it be correct to assert that the mass and rigidity of the wall approach infinity?

Cyrus

Ok, sorry if I was rude.

DH, I read what they wrote. They were using a reference frame of the earth being stationary, I did not. In the case where its not stationary, the earth does NOT move backwards.

I just showed this using the simple conservation of momentum equation. I have no problems with you stating im wrong, but then show me where my equation is incorrect.

D H

Conservation of energy, linear momentum, and angular momentum are three distinct concepts. Suppose you take a drive in your car down the freeway, and wham, your car instantaneous reverses its velocity vector, throwing you against the steering column at 120 mph. The car's speed is 60 mph before and after the velocity reversal, so kinetic energy is conserved. Fortunately, that never happens because of conservation of momentum.

The three conservation laws are related through Noether's theorem. Some quantity is conserved for a system in which the Lagrangian exhibits a symmetry. Energy is conserved if the Lagrangian is temporally symmetric. Linear momentum is conserved if the Lagrangian is symmetric with respect to position. Angular momentum is conserved if the Lagrangian is rotationally symmetric.