Question on very simple free fall concepts

[brood910]

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I know that two objects will fall + hit the ground at the same time regardless of their masses.
However, according to TBR, since equal height = equal PE = equal KE, heavy ones have smaller v. I do not understand how they can have different velocities with same vertical acceleration (g) when they hit the ground at the same time..

Am I mixing something up here?

 

[rueby25]

I know that two objects will fall + hit the ground at the same time regardless of their masses.
However, according to TBR, since equal height = equal PE = equal KE, heavy ones have smaller v. I do not understand how they can have different velocities with same vertical acceleration (g) when they hit the ground at the same time..

Am I mixing something up here?

I think you're forgetting to account for gravity being an acceleration, and PE is also dependent on mass. Delta PE = - Delta KE. Taking into consideration the force acting on the mass is g in both cases, the masses cancel each other out, thus velocity is no different.

This all assumes no friction or other forces.

 

[brood910]

I think you're forgetting to account for gravity being an acceleration, and PE is also dependent on mass. Delta PE = - Delta KE. Taking into consideration the force acting on the mass is g in both cases, the masses cancel each other out, thus velocity is no different.

This all assumes no friction or other forces.

Apparently, you didnt read my question carefully.
That's exactly what I said. I am asking how they can have two diff velocities as TBR says.

Also, how the heck two diff masses can have the same PE when they are at the same height?
It is impossible as PE = mgh, where g and h are constant.

 

[reising1]

I know that two objects will fall + hit the ground at the same time regardless of their masses.
However, according to TBR, since equal height = equal PE = equal KE, heavy ones have smaller v. I do not understand how they can have different velocities with same vertical acceleration (g) when they hit the ground at the same time..

Am I mixing something up here?

They cannot have different velocities. If you want to calculate velocity using conservation of energy for a falling mass, you'll get mgh = (1/2)mv^2, the "m" cancels on both sides, and you see that velocity is only dependent on height (and gravity). But...be very sure (I don't have TBR and can't check) that what you are reading assumes no air resistance, friction, etc.

 

[reising1]

Apparently, you didnt read my question carefully.
That's exactly what I said. I am asking how they can have two diff velocities as TBR says.

Also, how the heck two diff masses can have the same PE when they are at the same height?
It is impossible as PE = mgh, where g and h are constant.

You'll have to give us the excerpt from TBR because as you correctly pointed out, this doesn't seem correct...

 

[brood910]

I dont remember from which problem I got this, but I am pretty sure it is from chapter 4.
I guess this is another uncommon typo.

Thanks, everyone. Im glad I didnt get it wrong.

 

[navho77]

Everything that has been said is true in a vacuum. But if there is air resistance (and I don't think it's too out of the scope of the MCAT for that to be the case), the heavier object will be more likely to be at a higher velocity right before it lands than the lighter one. This is because air resistance results in a terminal velocity (no acceleration) when the force of the air resistance is exactly equal to the weight of the object. Because g is constant, a larger force from air resistance is needed to keep the more massive object from ceasing to accelerate. Thus, if we compare a 1kg object and a 10kg object of equal surface area falling, say, 100m, the force of the air resistance becomes equal to the weight of the 1kg object sooner than for the 10kg object, and so the 1kg object stops accelerating at a time the 10kg object is continuing to accelerate. So, the 10 kg object is able to attain a higher final velocity than the 1kg object.

 

[FeinMS]

delete please