No, as Martin says, the total momentum of you and the object will be zero (taking into account that momentum is a vector quantity). I can show this from basic principles, but it probably won’t make it any clearer.
Suppose you apply a force F to the object. (Then there is an equal and opposite force -F applied to you). Suppose, as a result of these forces, the object has a momentum MV (mass times velocity) and you have a momentum mv. Then according to Newton’s second law, F = d(MV)/dt, and -F = d(mv)/dt, where d( )/dt denotes the time derivative. Now add those two equations.
F + (-F) = d(MV)/dt +d(mv)/dt
Simplifying the right hand side, and noting that the left hand side is 0, we get
0 = d(MV + mv)/dt
Since the time derivative of the total momentum is 0, this means that the total momentum MV + mv of the system is constant in time. Since the initial momentum of the system was 0, we must have MV + mv = 0. I.e.,
MV = -mv.
Hence if one velocity is non-0, so is the other. I.e., if one object moves, so must the other.
Another way to see that both must move is that if the system starts out at rest, then the center of mass of the system must be stationary unless an external force is applied to the system. Therefore if one mass moves, the other must also move; otherwise, the center of mass would be moving (in the direction of the moving mass).
Just to make sure I am absolutely clear on this: The mass on the frictionless surface is in a vacuum and not surrounded by Jell-O or something that is clinging to the surface I am standing on, right?
You can assume a vacuum if you like. We didn’t take it quite that far in the original discussion.
Also one thing brought up then which hasn’t been addressed here yet (or at least, I don’t think so…forgive if I’m mistaken or overlooked it):
Say you are standing beside (not on) the frictionless surface, and you have a 500,000-ton chunk out of a mountain on the frictionless surface. You reach out and slap the rock. Will your slap actually suffice to start that much mass moving, or will the energy from the slap be absorbed or dissapated by the rock in another way, without the rock actually moving? Or would the entire rock from one end to the other actually start to move across the surface, albeit at an almost infinitely slow pace? Or would the rock actually flex a minute amount to absorb your blow without the whole mass moving?
My company has a fountain that consists of a globe floating (and spinning) on a very thin layer of water. Now, this particular globe is made of marble and is about 8 feet in diameter, so it has some pretty considerable mass to it. The fun thing about it is to go up to it and push. You can change the direction and speed of the spin with relatively little effort, although it might take a while to do it.
Of course, this doesn’t really help to answer the original question, but I just think it’s cool.
I’ve moved 30-ton pieces of iron on an air sled. It needs to be done very carefully. And, you might need a very sophisticated piece of equipment to measure the velocity, but, yes, the huge mass would still move.
A momentum can never equal a force, because the force is the time derivative (rate of change) of the momentum. They’re apples and oranges.
I believe it would move, even if it had some “other way” of absorbing the force. It would move excruciating slowly, but it would move. If there’s some “other way” for it to absorb the force, I believe you would set up some kind of more complex motion (e.g. sound waves bouncing around inside the rock, etc.) but it would move. All the more excruciatingly slowly perhaps, and with some other internal dynamics going on while it moves, but I believe it would move.
Martin, you have proven me correct.
Let’s suppose that, instead of a sneeze of .01 grams at 100 miles per hour, you spit one fourth gram (I weighed some spit, and this is plausible) at ten miles per hour (I have no way of performing this measurement). If you could do this ten times, you would moving a little more than six inches per hour, if I’ve applied your calculations correctly. If you could do it twenty times, you would be moving more than one foor per hour. At that rate, in ten hours, you would have moved ten feet. Not inconsequential.
If, sometime during the ordeal, you had to urinate, and you were able to pee 250 ml (250 grams) in the correct direction at two miles per hour, you would increase your speed by another 100 feet per hour, if I’ve done the arithmetic right.
I also believe there’s a way you could move yourself simply by breathing.
Thank you for setting me straight on the physics you guys. I knew momentum didn’t equal force, just trying to say something too complicated in too simple of terms. Also, hadn’t considered an anchored fulcrum, just me and and an object on the surface. And yes, I agree that the heavier-than-me object (most objects are heavier than me, lol) would move very slowly if I pushed off of it, in exactly the same way I would move backward slowly if I pushed an object lighter than me.
Now if I could only find a way to move a very light object to somewhere with an Irish music scene…
You’re driving in your car with the windows closed. There’s a helium balloon in the back of the car, floating freely. You make a right turn. What does the balloon do?
Jerry, an empirically noted wintertime phenomenon: I’m in the car, dashboard vents blowing heated air. Executing a close right turn (Japanese, Brits, etc. please note that my U.S. driver position is at the usual left), I consistently feel a mass of warmth collide into me (although it may be more accurate to say that I collide with it), and then everything goes back to normal (as far as can be said in my case ). I presume that the opposite happens on left turns…
The helium balloon moves to the right, as the air in the car moves to the left toward the outside of the turn. Same thing if you come to a sudden stop–the balloon would move to the rear of the car as the air mass “bunches up” momentarily in the front.
You’re driving in your car with the windows closed. There’s a helium balloon in the back of the car, floating freely. You make a right turn. What does the balloon do? Relative to the interior of the car, does it stay where it is? Does it move to the left, or does it move to the right?
). I presume that the opposite happens on left turns…
