Heavier objects fall faster than lighter objects? G481

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#1
If Galileo dropped a heavy object and a light object and found that they hit the ground at the same time, why is it that heavier objects reach a greater terminal velocity, ( if this is true a heavy object would hit the ground before the lighter one?)
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7 years ago
#2
The force on the object due to air resistance does not depend on the object's mass, whereas the force on the object due to its weight does. Does that give you a clue?
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#3
Still don't understand
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7 years ago
#4
(Original post by MrChemKid)
If Galileo dropped a heavy object and a light object and found that they hit the ground at the same time, why is it that heavier objects reach a greater terminal velocity, ( if this is true a heavy object would hit the ground before the lighter one?)
It's not true in general that heavier objects reach a greater terminal velocity. You could make a very heavy parachute if it were very large, but a pebble (which may be very un-massive) will drop like a stone.

It's not even true if the objects are the same shape. A cannonball made out of lead will fall at the same speed as a cannonball made out of balsa wood. (EDIT: in the absence of wind.)

The classic thought experiment is to connect your two objects with a string, and drop them simultaneously. Suppose for contradiction that it were true that heavier objects hit a higher terminal velocity than lighter objects. Then the heavier one would eventually pull the string tight and drag the lighter one down with it. However, the system as a whole (two objects plus string) is heavier still than the heavier cannonball, and so the system should fall at a higher terminal velocity than the heavier cannonball. That's a bit of a problem given that the thing which is driving the motion is the weight of the heavier cannonball. (It also contradicts common-sense: in freefall, you'd expect to be able to separate a sphere into two hemispheres without causing the hemispheres to suddenly slow down because their terminal velocity has decreased because they are individually lighter than the sphere.)
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#5
Ok, basically heavier objects sometimes fall faster , sometime not?
thanks
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7 years ago
#6
(Original post by Smaug123)
It's not true in general that heavier objects reach a greater terminal velocity. You could make a very heavy parachute if it were very large, but a pebble (which may be very un-massive) will drop like a stone.

It's not even true if the objects are the same shape. A cannonball made out of lead will fall at the same speed as a cannonball made out of balsa wood. (EDIT: in the absence of wind.)

The classic thought experiment is to connect your two objects with a string, and drop them simultaneously. Suppose for contradiction that it were true that heavier objects hit a higher terminal velocity than lighter objects. Then the heavier one would eventually pull the string tight and drag the lighter one down with it. However, the system as a whole (two objects plus string) is heavier still than the heavier cannonball, and so the system should fall at a higher terminal velocity than the heavier cannonball. That's a bit of a problem given that the thing which is driving the motion is the weight of the heavier cannonball. (It also contradicts common-sense: in freefall, you'd expect to be able to separate a sphere into two hemispheres without causing the hemispheres to suddenly slow down because their terminal velocity has decreased because they are individually lighter than the sphere.)
That's only true in a vacuum, in which case there would be no terminal velocity. When in air, the terminal velocity is given by:

where m is the object's mass, ρ is the density of air, A is the cross-sectional area of the object in the direction of motion, and Cd is a coefficient which depends on the object's shape. This can be easily derived by taking the equations for weight and drag, and stating that the terminal velocity is reached when they balance each other. This makes sense, because a heavy object is going to be less affected by its environment than a light object.

In the case of the hemispheres, what you'll find is that each hemisphere shields the other from air resistance to some extent. If the hemispheres became separated by a larger distance then you would indeed find that their terminal velocity drops.
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7 years ago
#7
(Original post by Arbolus)
That's only true in a vacuum, in which case there would be no terminal velocity. When in air, the terminal velocity is given by:

where m is the object's mass, ρ is the density of air, A is the cross-sectional area of the object in the direction of motion, and Cd is a coefficient which depends on the object's shape. This can be easily derived by taking the equations for weight and drag, and stating that the terminal velocity is reached when they balance each other. This makes sense, because a heavy object is going to be less affected by its environment than a light object.

In the case of the hemispheres, what you'll find is that each hemisphere shields the other from air resistance to some extent. If the hemispheres became separated by a larger distance then you would indeed find that their terminal velocity drops.
OK, instead of spheres, go for a downward-pointing arrow of some fractal description. Split the arrow to make two identical half-size arrows, which have half the cross-sectional area each and half the mass.

I may be being really silly, but isn't OP's question wrong? That is, "heavier objects reach a greater terminal velocity" is false?
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7 years ago
#8
(Original post by Smaug123)
OK, instead of spheres, go for a downward-pointing arrow of some fractal description. Split the arrow to make two identical half-size arrows, which have half the cross-sectional area each and half the mass.

I may be being really silly, but isn't OP's question wrong? That is, "heavier objects reach a greater terminal velocity" is false?
If you split the arrow then the drag coefficient would change slightly to account for the change in total surface area.

The experiment that OP is referencing isn't actually to do with terminal velocity at all, but instead with acceleration due to gravity. Galileo found that "heavy objects fall faster" is false when assuming that weight is the only force involved, because in the examples he gave the objects were travelling slow enough that air resistance could be considered to be negligible. You can't consider it to be negligible when talking about terminal velocity, though, because the definition of terminal velocity requires that air resistance be exactly equal and opposite to weight.
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7 years ago
#9
Basically, F=ma Only force acting is W, W=mg

mg=ma

m's cancel, g=a
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