NancyF wrote:my 2 cents:
If you and the object are both on the frictionless surface, and if you have no momentum yourself you can move only objects with less mass than you, by adding muscle force like straightening your arm at the elbow. You would move backwards as the object moved forward. The total momentum of you and the object would equal the force you supplied. If the object had more mass than you, you would just push yourself off of it. Tyg can move objects heaver than her (and so can all of us, because we use things to increase the friction between our feet and the ground and to decrease it between the object and the ground. Examples: furniture glides, putting a rug under the object, wearing sneakers with stick soles.
NancyF (not a physicist - only an engineer)
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).