i realise that this answer was supposed to be in a vaccum (no air resistance), i’d like to point out though that if you were to add in the air (which if you were outside dropping things off a building would be present) while the acceleration would be the same, 9.8m/s/s approx. the terminal velocities would be different. because the hammer has a larger mass, or prehaps simply because it is more dense, it would exert more force downward(F=am) thus it would require a higher opposing force to counter act the force of acceleration. if we are assumeing that the density of the air is more or less constant then the hammer would have a higher terminal velocity and thus hit first.
i also realise that surface area and aerodynamics play a role but, i believe the effects would be minimal.
i only posted this because my roomate and i had this argument and it took a while for us to figure out what exactly determines terminal velocity.
What are you trying to say here? That a hammer hits the ground before a feather does if dropped in Earth conditions? That’s what Ian said too. Am I missing something?
I don’t think terminal velocity would be the biggest factor, though. Imagine dropping a feather and a hammer from a height of five feet; the hammer would still hit the ground first by a wide margin, without having reached its terminal velocity.
Terminal velocity is determined by drag. In a falling object, the force of gravity will cause it to accelerate to a point where it’s weight is countered by the resistance of the air flowing around it. So, aerodynamics don’t just play a role, they are the role.
If you drop a feather and a lead pellet of the same weight, the pellet will still fall faster due to the lesser amount of air resistance.
that would be because the feather reached terminal velocity very early. i realise that aerodynamics play a large role, that doesn’t mean mass does not however. like i said force= mass * acceleration. therefore an object with larger mass produces a greater force downward, which must be couterbalanced with a greater force upward (the normal), the force that air would provide would be determined by friction due to rate of fall. therefore an object with larger mass would have a higher terminal velocity, falling faster would create more friction producing more force to balace the add force downward. aerodynamics still play a large role, but to things of equal size and shape with different densitys (determined by MASS and volume) will have different terminal velocities.
See what happens? The mass of the body released drops out of the equation. So the mass of the feather and the hammer and the lead pellet and anything else is irrelevant. All will fall at exactly the same rate.
The only variable here is air resistance. Take that same mass of lead and beat it into a very thin sheet and drop it and air resistance will slow it down compared to a pellet of lead.