Falling Objects (With air resistance)

In summary, two individuals are having an argument about falling objects with varying masses. One believes that heavier objects will hit the ground first due to air resistance, while the other believes they will hit at the same time. The argument is based on the example of two identical jugs, one filled with water and the other without, being dropped at the same time. The first individual agrees that they will fall at the same time in a vacuum, but not in the presence of air resistance. The second individual seeks a second opinion and provides a detailed explanation of the relationship between mass, gravity, air resistance, and acceleration. In conclusion, the heavier jug will hit the ground first due to its greater acceleration and speed. The individuals involved have come to an
  • #1
Morcam
4
0
So, I've been having a bit of an argument with a guy about falling, identical items, with varying masses.

Homework Statement



For the sake of the argument, we've been using the example of two identical jugs, one filled with water, and the other without. They are dropped at exactly the same time. I believe the one filled with water will hit the ground first, due to air resistance. He believes they will hit at the same time. I agree that they will, in a vacuum.

Homework Equations



Force of Air Resistance = Constant
Fg = m * g

The Attempt at a Solution



http://www.physicsclassroom.com/class/newtlaws/u2l3e.cfm

In situations in which there is air resistance, more massive objects fall faster than less massive objects. But why? To answer the why question, it is necessary to consider the free-body diagrams for objects of different mass. Consider the falling motion of two skydivers: one with a mass of 100 kg (skydiver plus parachute) and the other with a mass of 150 kg (skydiver plus parachute). The free-body diagrams are shown below for the instant in time in which they have reached terminal velocity.

I'm not entirely sure why we're still having this argument, but he's very insistent, so I'd like a final answer from someone who knows this firsthand.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Yes, the heavier jug will hit the ground faster. There's absolutely no room for an argument to the contrary. To take an extreme case, a paper jug would take seconds to fall to the ground from eye level.
 
  • #3
As the (possibly mentally defective) friend from morcams above post, I'd like to ensure I'm totally wrong by asking for a second opinion.
 
  • #4
DarthPJB said:
As the (possibly mentally defective) friend from morcams above post, I'd like to ensure I'm totally wrong by asking for a second opinion.

Until the second opinion comes, I'll expand a bit on my answer. The force of gravity is mg, and air resistance is kAv^2. k is a constant, A is the cross-sectional area, and v is speed. Newton's second law says F=ma, so mg-kAv^2 = ma and a=g-kAv^2/m. Solving this equation will yield a position vs. time equation, but it's not necessary to go that far. Just examining the equation will do.

Go through this in your head: A jug is dropped. Gravity accelerates it at 9.8 m/s: that's the "g" in the equation a=g-kAv^2/m. If the mass is tiny, kAv^2/m would be huge, and acceleration would immediately drop. If the mass is high, kAv^2/m would be tiny, and acceleration would decrease slowly.

So the conclusions are:

(1) At every point in time during the fall, the heavier jug has a greater acceleration than the light one.
(2) At every point in time during the fall, the heavier jug has a greater speed than the light one.
(3) At every point in time during the fall, the heavier jug is closer to the ground than the light one.
 
  • #5
I think perhaps I should have drunk a little less at the weekends while at collage, somehow I managed to have an hour argument over something so very obvious.
I was so sure I was right, I suppose this is how wars get started!
I'm going to accept my utter stupidity and ignorance in this matter and thank you kindly for your reply.

Now all I have to do is survive morcams jokes :/
 

FAQ: Falling Objects (With air resistance)

How does air resistance affect the speed of a falling object?

Air resistance is a force that opposes the motion of a falling object. As an object falls, it pushes against the air molecules in its path, causing the air to push back. This force increases as the object's speed increases. As a result, the object will eventually reach a terminal velocity, where the force of air resistance is equal to the force of gravity pulling the object down. At this point, the object will no longer accelerate and will fall at a constant speed.

How does the size and shape of an object affect its rate of descent?

The size and shape of an object can greatly affect its rate of descent due to air resistance. Objects with a larger surface area, such as a parachute, will experience more air resistance and therefore fall at a slower rate. Objects with a smaller surface area, such as a bullet, will experience less air resistance and fall at a faster rate. The shape of an object also plays a role, as streamlined objects will experience less air resistance compared to irregularly shaped objects.

How does air density affect the motion of falling objects?

Air density is a measure of how many air molecules are present in a given volume of air. In general, higher air density will result in greater air resistance, leading to a slower rate of descent for falling objects. This is because the air molecules are more tightly packed together, creating more resistance for the falling object. On the other hand, lower air density will result in less air resistance and a faster rate of descent for falling objects.

Can air resistance ever cause a falling object to move upwards?

No, air resistance can never cause a falling object to move upwards. Although air resistance can slow down the rate of descent for a falling object, it will never be strong enough to overcome the force of gravity pulling the object down. Therefore, the object will always continue to fall downwards, even if its descent is slowed by air resistance.

How does the speed of a falling object change over time?

At the beginning of its fall, an object will have a high acceleration due to the force of gravity pulling it down. However, as the object falls and its speed increases, the force of air resistance will also increase until it eventually reaches a terminal velocity. At this point, the object will fall at a constant speed with no further acceleration. Therefore, the speed of a falling object will increase until it reaches its terminal velocity, at which point it will remain constant.

Similar threads

Launching a Projectile with Air Resistance
Replies
13
Views
2K
Why air resistance has less force than gravitation force in free fall?
Replies
4
Views
1K
Vertical flight with air resistance
Replies
11
Views
2K
B Do Objects in Free Fall Encounter Air Resistance?
Replies
10
Views
900
Finding Force of Air Resistance on Parachutist Falling at 55km/h
Replies
17
Views
2K
Free falling ball with and without air resistance
Replies
3
Views
2K
What is the velocity of a falling object with air resistance?
Replies
11
Views
3K
Solving for Velocity of Falling Object with Air Resistance
Replies
2
Views
1K
Why Does It Take 200 N to Slow Down a 10 kg Mass in Free Fall?
Replies
12
Views
2K
Free falling with air resistance question
Replies
12
Views
1K

Hot Threads

Recent Insights

Back
Top