The difference between mass and weight causes a lot of confusion amongst a lot of people. Put simply, weight is a measure of gravity's effect on something. Mass is the amount of matter in an object. Move to a different planet and an object's weight will change, but its mass will be the same. There are a couple of ways to measure mass. The most common method is to use a balance. Hey, wait a minute! (you should be saying) People weigh stuff all the time with a balance! Think about it. If you go to a different planet, the balance weights change by the same factor as the object you are measuring. Your mass measured with a balance would be the same on the moon as it is on Earth. There are a couple of other neat tricks, but they only really work perfectly in no-gravity, no-friction environments. For example imagine a big rock floating in space. Give it a slap with a calibrated hand so you know exactly how much energy you gave it. Now measure how fast the rock is moving. That new speed is proportional to its mass. In space you weigh nothing, but your mass is the same, so a space bully can still shove the 98 pound weakling even though they both weigh 0 pounds.
The balls collide in a completely inelastic collision, in other words they have the same velocity after the collision, this velocity has a magnitude V.
We need to use the conservation of momentum Law, the total momentum is the same before and after the collision.
