Under what conditions can you just add velocities? For example if I throw a paper ball in the air in a 1m/s wind the ball should move in that direction at 1m/s as it falls according to relative velocities. However what if I throw a bowling ball like this, common sense says it will just fall straight down, why doesn't relative velocity work in this case? Thanks
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$\begingroup$ When learning physics, common sense often leads to common misconceptions that are VERY difficult to overcome. It's best to learn the key concepts well, and to apply those key concepts consistently, regardless of what "common sense" would dictate. $\endgroup$– David WhiteCommented Sep 28, 2020 at 15:43
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2 Answers
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The difference in observed behavior has to do with the applicability of the simplifying assumptions made.
In many introductory examples we assume there is no air resistance. This is a good assumption if the force of air resistance is much smaller than the other forces. For example, a projectile would experience forces from the air and from gravity. The force of air depends on the relative speed of the air and the object, and the force of gravity on the object's mass.
No air resistance is a good approximation for massive things moving slowly. To good approximation the motion of the bowling ball is dominated by gravity. The air barely affects it.
The relative motion assumption states that the object flows perfectly in synch with the air. The force of the air on the paper ball will rapidly speed it up until it moves at the same speed as the air. Once you release it, it almost instantaneously flows with the air. The co-moving assumption is a good fit to this situation.
The air colliding with the bowling ball imparts a small force, and eventually the bowling ball will speed up and flow with the air, but it will take much longer than the paper ball.
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$\begingroup$ Am I correcet in saying that when we simplying add velocities like that we assume the acceleration is instant then? $\endgroup$ Commented Sep 28, 2020 at 16:12
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$\begingroup$ That is one way of thinking about it. Because the mathematical techniques of physics like continuous systems without sudden jumps, I think it is more helpful to say that the paper ball is already co-moving with the air when we start calculating what it does. $\endgroup$– Paul T.Commented Sep 29, 2020 at 12:50
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There are two reasons. Inertia is the physical resistance of any physical object to any change in its velocity and the larger a mass the larger it’s inertia. The second reason is density. The bowling ball is much denser than the paper. If you were to squeeze the sheet of paper down to the same density as the bowling ball it too would drop to the ground as quick as the bowling ball.
answered Sep 28, 2020 at 15:53