Conservation of Momentum, Frame of Reference
Date: Summer 2013
The question is about the conservation of momentum.
Imagine that we have two objects with equal masses and volumes. Let's call the first ball X and second ball Y.
I am an observer (call me OBS1) and from my frame of reference,X moves towards Y with a constant speed and bumps into Y. The momentum is conserved, so Y starts moving with the same speed and same direction as X. Nothing wrong here.
Now imagine that I am in the ball X. My frame of reference is in X,and I can see outside.(I am OBS2)
Because my speed is constant, I cannot tell whether I am moving towards Y, or Y is moving towards me. Since both situations can be true, I am free to assume whatever I choose. All I can observe is that the distance between X and Y decreases, then increases again.
Now, like OBS1, I can assume that X moved towards Y and bumped into it, transferring all its momentum.
But, I can also assume that X bumped into Y, and then bounced back with the same speed, since I am in the ball X and I cannot know which ball is moving towards which.
So according to the second assumption,there is no thing such as "conservation of momentum". The ball X just bounced back off Y, defying the "law of conservation of momentum."
But the laws of physics are the same everywhere, are they not? They do not change in any frame of reference.
Then what about the OBS2 guy?
Thanks for the question. Voyager 1 has electrical power courtesy of radioisotope thermal generators which utilize Plutonium-238. At present, after accounting for the decay of Pu-238, Voyager 1 has about 225 W of electrical power. Voyage 1 is about 200 AU units of distance from Earth at present. Since, the intensity follows an inverse square law, use the equation
I = P/(4*pi*R^2) where I is the intensity in W/m^2, P is the power output of the Sun in W, and R is the distance from the Earth to Voyager in m. You will need to convert AU (astronomical units) into meters.
I hope this helps. Please let me know if you have more questions.
Both balls accelerate when they collide. The reference frames of the balls are not ?inertial? reference frames during the collision. If you ride along with either ball, it is NOT the case that all you can observe is that the balls move together and then apart. You will observe a jarring force while the balls are in contact. If you define your reference frame to be either of the balls, you will need to include a non-inertial force in your reference frame during the time of the collision.
Another way to put it is that if you observe the balls from any constant-velocity reference frame, you will see them exchange momentum during the collision. It is only in a non-inertial frame of reference that momentum is not conserved.
The reference frame of the ball is inertial at all times EXCEPT during the collision. It is not a coincidence that, in that reference frame, the momentum of the system is conserved at all times except during the collision.
Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy
University of Wyoming
Thank you for your question.
I would like to point out that the scenarios you describe can happen if you have a very elastic collision such as between billiard balls. In that case, energy will be conserved, and ball X "stops" (that is relative) when it hits ball Y. All momentum and energy is transferred to ball Y. If the collision is not so elastic (such as between balls of soft clay) then energy is converted to heat during the collision. In that case the two balls will continue moving after the collision, but at reduced speed. Momentum is conserved in either case.
When the observer observes the collision, he or she needs to assume that momentum is being conserved and interpret what he or she sees accordingly. Given that, if the balls have equal mass, then either ball must be moving before the collision or after the collision or both.
If you think that this explanation does not help enough, please re-explain your problem as carefully as possible. In a lifetime of experience, it is amazing how often a careful explanation of a problem will almost by itself illuminate the answer. I will be willing to try again if you can re-state the problem very carefully.
Great question. Relative frames of reference are tricky. Try looking at it this way.
Regardless of what is going on in the external frame of reference, if you were riding in the first ball, you will see ball Y getting closer at a relative velocity of V. You cannot tell who is moving in the external frame of reference. All you can see is that other ball is getting awfully close and is about to collide with mine! Whether you are parked or moving you really all you want to do about now is avoid the collision. (I mean, what are your parents going to say if you wreck the family ball?)
During the collision, you will experience an acceleration as either your ball stops or begins to move (to the outside observer). To you in either case, the acceleration is the same. What you do see after the collision is ball Y receding at relative velocity V.
There is no contradiction as far as you are concerned, and no loss of momentum within the two ball system whichever way you choose to look at; either we just got hit or we just hit something. You also realize that your collision was totally elastic, there is no damage to your ball and you are off the hook with your folks. Congratulations!
Hope this helps.
The laws of physics apply when the observer is not accelerating. Newtonian physics assumes all measurements are made from a non-accelerating reference frame. The observer cannot tell whether the frame of reference has velocity, but self-acceleration is quite easy to detect. We see this every time we ride an elevator. When the elevator starts upward, we feel pressed to the floor. When the upward elevator slows down, we feel a lifting effect. When in a rotating frame of reference, such as a car turning the corner quickly, we feel an outward push. These pushes and lifts are the forces causing our bodies to accelerate. For an observer riding an object that changes speed or direction, that observer?s measurements will not agree with the laws of physics. The measurements will have to be adjusted for the observer?s acceleration.
Dr. Ken Mellendorf
Illinois Central College
The first observer is in an unaccelerated reference frame. This problem
is easy in an unaccelerated reference frame, because all you have to
think about are the initial and final speeds. The second observer is
in an accelerated reference frame. There is nothing wrong with being in
an accelerated reference frame, but you do have to include the acceleration
in what you observe.
When you collide with ball Y, you decelerate, and you can measure the
deceleration you experience to find out the total change of velocity you
experience. Accelerations are not relative in the same way speeds are.
You cannot do any experiment to find out if you are moving toward Y or if
Y is moving toward you, but there's no question about who is experiencing
what acceleration, because you feel it.
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