# M1 vs M2 on a frictionless surface

I was wondering, if I had a frictionless surface and I had an M1 that was 100kg and an M2 that was 1kg and I pushed each separately with an equal force F would they move at the same speed or am I assuming incorrectly?

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$$Force = Mass \times Acceleration$$

or since you're asking what happens when you push on the objects a quick rearrangement gives:

$$Acceleration = \frac {Force}{Mass}$$

So if you feed in the force you're pushing with and the mass (1kg or 100kg) you can work out how fast the mass will accelerate. For the same force the 1kg mass is going to accelerate 100 times as fast as the 100kg mass.

You asked "would they move at the same speed", and of coures because the masses are accelerating at a constant rate the speed is continually increasing. If you want to know the speed after some time you simply multiply the acceleration by the time:

$$Speed = \frac {Force}{Mass} \times Time$$

If you choose some time to measure the speed you'll find the 1kg mass is moving 100 times as fast as the 100kg mass.

Your question seems a bit odd given that common experience suggests it's a lot easier to push a 1kg mass than a 100kg mass. I wonder if you were thinking about why the 1kg and 100kg masses fall at the same speed under gravity.

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+ Right, and you could try pressing equally hard on a toy boat versus a real boat. –  Mike Dunlavey Feb 15 '12 at 20:40
Thought it would be more fun to drive both off a cliff and measure the acceleration :-) –  John Rennie Feb 15 '12 at 20:41
Yeah, or maybe go up in the space shuttle and launch two satellites, one being a little rock, and one being a great big rock. That way, you could kill two stones with one "bird" :) –  Mike Dunlavey Feb 15 '12 at 20:49