What determines the rate at which an object falls to the Earth? Is it the object's shape or the mass

[Peter Check]

I had come across a question in AS level P2, where two raindrops(spherical) were falling, one had a greater radius,lets say that is raindrop A. The question was which raindrop would fall to the ground first. I reasoned that, since A has a greater surface area, it will experience more air resistance, and hence B will fall first. The actual answer was A, because A having a greater volume, will have a greater mass(same density), so it will fall first? So I am having a hard time exactly grasping this concept.

 

[kirashinagami]

Do they state that air resistance is negligibe? If so, A is the correct answer.

 

[Peter Check]

I dont remember, but what if its not? is it B then?

 

[kirashinagami]

Yes. Imagine 1 kg of feathers and 1 kg of a metal ball falls from a top building.
With air resistance, the metal ball will reach the ground first.
Without air resistance, they will reach the ground at the same time.

 

[anonymous123]

I had come across a question in AS level P2, where two raindrops(spherical) were falling, one had a greater radius,lets say that is raindrop A. The question was which raindrop would fall to the ground first. I reasoned that, since A has a greater surface area, it will experience more air resistance, and hence B will fall first. The actual answer was A, because A having a greater volume, will have a greater mass(same density), so it will fall first? So I am having a hard time exactly grasping this concept.

9702 s11 qp 22
Q2 b

by littlecloud11 :
ok, the question says that the radius of the second raindrop is less than the first.
and F=6pi*D*R*v
if the radius for the second is less the frictional force acting on it is also less.
and Density=m/v
both the rain drops have the same density but the mass if the second is approx one-cube of that of the first bcoz the radius is less.

the difference in mass is much greater than the difference in frictional force. so, when if the equation
mg-f=ma
the acceleration of the second will be less than the first. so the slope of the second graph will be below that of the first. and as the mass of the second drop is less the weight (downward force) will b less and it will reach terminal velocity earlier than the first. so the graph will reach a lower constant value earlier.

 

[Peter Check]

9702 s11 qp 22
Q2 b

by littlecloud11 :
ok, the question says that the radius of the second raindrop is less than the first.
and F=6pi*D*R*v
if the radius for the second is less the frictional force acting on it is also less.
and Density=m/v
both the rain drops have the same density but the mass if the second is approx one-cube of that of the first bcoz the radius is less.

the difference in mass is much greater than the difference in frictional force. so, when if the equation
mg-f=ma
the acceleration of the second will be less than the first. so the slope of the second graph will be below that of the first. and as the mass of the second drop is less the weight (downward force) will b less and it will reach terminal velocity earlier than the first. so the graph will reach a lower constant value earlier.

When you say,"both the rain drops have the same density but the mass if the second is approx one-cube of that of the first bcoz the radius is less.", how can you relate/compare mass with radius?

 

[littlecloud11]

When you say,"both the rain drops have the same density but the mass if the second is approx one-cube of that of the first bcoz the radius is less.", how can you relate/compare mass with radius?

radius is used to find the volume and you use the volume to find the mass using the formula density= mass/volume
so when the radius is less, the volume is also less, and as per the formula the mass of the object is less.

 

[Peter Check]

radius is used to find the volume and you use the volume to find the mass using the formula density= mass/volume
so when the radius is less, the volume is also less, and as per the formula the mass of the object is less.

okay, got it, so thats why the ball with lower radius falls first! thnx a tonne

 

[leosco1995]

I have another (somewhat related) question: if two objects of the same nature, but different masses, fall to the ground which one would achieve terminal velocity first and why?

 

[littlecloud11]

I have another (somewhat related) question: if two objects of the same nature, but different masses, fall to the ground which one would achieve terminal velocity first and why?

By same nature, do you mean they have similar surface area? when you say terminal velocity, we're assuming that air resistance is not negligible.

if they have the same SA the object with the greater mass would reach terminal velocity later, because it's weight would be greater, so the downward force would be greater. the upward force (air resistance) on both would be the same as they have similar SA.
The weight of the smaller mass will be balanced by the air resistance earlier and so it'll reach terminal velocity earlier.