Yeah. I’m feeling like an idiot here.
I prefer my physics in a vacuum - who cares whether or not the parchutist can breathe, so long as I have my ideal conditions? 
I’ve got one word for you: “mathematics”.
That’s true – at a given time the iron ball will be traveling at a greater speed, and thus experiencing a greater force of air resistance. However, I don’t like the way the teacher just said “a heavier iron ball falls faster through the air.” That could give students the impression that the acceleration due to gravity is greater on a heavier object, which is false. Really what’s happening is that the upward accelaration due to air resistance is less for the heavier object (at a given velocity) than for the lighter object.
I’d say a better explanation would be this:
Both balls experience an approximately constant downward acceleration due to gravity for their entire fall, and it’s the same between the two balls. However, as they begin to accelerate downwards they experience an upward force due to air resistance. Early in their fall the two balls have roughtly the same velocity, so the force of air resistance is the same for each. However, from the equation F=ma we know that the acceleration due to air resistance is less for the heavier ball. Thus, the heavier ball experiences a greater net downward acceleration, meaning it starts to fall faster than the lighter ball. Because of the dependence of air resistance on velocity, the heavier ball then feels a greater force of air resistance.
That’s right. It sometimes takes students a while to understand that velocity can be increasing even though acceleration is decreasing. Velocity continues to increase so long as the acceleration is positive (where in this case by “positive”, I mean “downwards.”)
When it’s moving at constant speed, yes. As has been said, the friction went from equal to P (when it wasn’t moving), to less than P (when it was accelerating), to equal to P (when it’s moving with constant velocity).
Yeah, I think it’s unfortunate that physics teachers will sometimes make casual statements like “The formula for friction is mu times N” (where mu is the coefficient of friction and N is the normal force.) Really, this formula only gives the maximum possible force of friction that the surface can apply under those conditions – not necessarily the force of friciton that it does apply.
Having not read everyone else’s answers, here are mine, but bear in mind that I went into law solely because I didn’t get the science gene:
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C. Same
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A. increases
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a. less than
b. greater than 0
The proper thing to do- give a reasonable interpretation of the question to make each of the answers correct. My responses in Bold.
Question 1 :
Quote:
Two smooth balls of exactly the same size, one made of wood and the other of iron, are dropped from a high building to the ground below. The ball to encounter the greater force of air resistance on the way down is the:
a) wooden ball- not possible, AFAIK
b) iron ball- since it’s heavier, it has a greater terminal velocity, and thus experiences more resistance at highest speeds.
c) both the same- at any given velocity, yes.
Question 2:
Quote:
accompanied by a picture of a parachutist free-falling
As she falls faster and faster through the air, her acceleration
a) increases- ** Total acceleration, yes. Gravity remains the same, and acceleration due to drag increases**
b)decreases- Net acceleration, for the reasons mentioned above.
c)remains the same- Though “through the air” makes vaccum difficult to assume, it still applies
Question 3 ( a two-parter):
Quote:
A crate filled with delicious junk food rests on a horizontal floor. A slight pull P is exerted on the crate, which does not move due to friction f. Pull P is increased until the crate begins to move. It is pulled so that it moves with constant velocity across the floor.
a) Friction f is less than (initially, before the crate moves or the force is increased), equal to**(When moving at a constant velocity), or greater than(When the initial movement is obtained)** P (pick one)
b) Net force on the crate is less than**, equal to, or greater than zero (pick one)-** same as above, and you can reverse less than & greater than freely by redefining the positive direction.**
There might be one of two problems in there, but I like the general theme of “you worded your questions senselessly.”
You are confusing force with acceleration. It’s the aerodynamic force that counteracts the force of gravity. The acceleration of the parachutist can only be upward if the net force is upward.
/me sighs
The force of air resistance gives rise to an acceleration. This acceleration is added to that due to gravity to get the net acceleration, which is still downwards.
Q1: There is not enough information to answer this question since the relative masses of the balls are not given. It can be argued that the question is implying that the iron ball is heavier but I see no reason to jump through hoops making various assumptions when the teacher did not take care to ask the question properly. Typically I would take the question to the teacher during the test and ask for the pertinent information. Or, if I was spoiling for a fight, I would make a smart aleck remark about assuming that the balls were both “solid” in which case the iron ball would encounter greater resistance since it would achieve the greater velocity in a given time interval.
Q2: There are actually three accelerations in the equations for this situation; that towards the ground due to gravity, away from the ground due to air resistance and the net acceleration due to the forces at work. Her net acceleration in the direction of the ground decreases, her acceleration away from the ground increases with speed until terminal velocity is achieved and her acceleration due to gravity stays the same (well that’s not exactly true but the change is insignificant for problems of this sort… yet another unspoken assumption one must make). Without information as to which of these quantities the teacher is referring to it is impossible to answer the question… a case could be made that any of the three answers could be correct and I was just the type of student to try and make that case. 
So far the teacher is 0 for 2. BTW you always have to define the direction you are interested in when dealing with vector quantities… which is why we use mathematics as a short-hand for these type of questions so that we don’t end up trying to divine the original intent of the question.
Q3: I was flummoxed by the formatting of this question. The crate has two steady states with an acceleration in the middle. Since three possibilities were given as answers I originally assumed that I was to match each of the possibilities with a particular state… square peg meets round hole. After yet another trip to the teacher’s desk during the test I came up with net force = zero.
I think Hyperelastic was talking about when you said “the more upward acceleration from resistance counteracts the force of gravity”–acceleration doesn’t counteract a force. 
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The friction would depend on ball size and surface roughness. Assuming same roughness, then since the size is the same both balls would get the same friction, reach the floor at the same time etc (oh, Galileo Galilei, where art thou!)
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Aceleration is the same through the length of her fall, unless you want to go and calculate g to the nth decimal figure.
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If the crate is moving at constant speed, the forces are equilibrated (neat force zero, and that’s answer b). So the two forces exerted (pull and friction) are identical.
Normalize the measurements to unit mass.
For both the wood and the iron ball?
Hello.
My name is glee.
I failed physics at School :eek: (the teacher certainly failed to help me!).
May I ask for clarifications:
- Assume two identically shaped solid balls, one of heavier mass (wood / iron if you like) falling through air from a simulataneous drop.
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Doesn’t gravity increase with mass?
(Which is why we can jump higher on the Moon?)
So doesn’t the iron ball fall faster? (Though presumably the difference is infintesimal?) -
Is the force of air resistance purely dependent on shape and speed?
(Because parachutists can vary their stance to vary their acceleration. And if air resistance didn’t increase with speed, how would terminal velocity ever occur?)
Next, presumably the same force of air resistance affects the denser mass less, so the iron ball thus meets less resistance and therefore loses less acceleration than the wooden ball?
Although both balls are moving downwards, their accelerations are negative and thus eventually they achieve terminal velocity?
Actually that will do for now.
I’ll see if this is the right place to ask.
Always the right place.
In this idealized thought experiment, their accelerations (in the direction of fall) would always be positive, then zero at terminal velocity–their fall rate does not slow.
Ya know its hard enough for some people to undertsand physics answering with blatantly wrong information doesn’t help. If you don’t know your answers are correct don’t answer!
The answer is b. The iron ball will fall faster becuase it experiences a larger force from gravity than the wooden ball. Since the force due to air resistance increases with velocity the iron ball will experience ‘the greater force of air resistance’.
The answer is b again. The force due to gravity is constant throughout the parachutists fall (ignoring the change in distance from the center of the earth). The force from air resistance which opposes gravity will increase as the parachutists speed increases. As the parachutist falls the net force on the parachutist decreases and since the mass of the parachutist doesn’t change the acceleration decreases.
a) less than. The crate accelerates in the direction of the pull therefore we know there is an unbalanced force in that direction. Since only f and P are acting in the horizontal direction we know f is less than P.
b) The crate is moving with a constant velocity therefore there is no net force. Since only f and P are acting in the horizontal direction we know f and P are equal.
if we knew we were wrong…
That’s easy for you to say!
I think you are confusing a few things here.
[ul]
[li]Yes, the gravitational force on the ball is proportional to its mass.[/li][li]However, acceleration is inversely proportional to mass. So if there was no air, the acceleration would be the same.[/li][li]But very strictly speaking, not only does the ball fall towards the earth, but the earth also moves towards the ball by an infinitesimal amount. So the heavier the ball, the sooner it meets the ground.[/li][*}But if you dropped two balls simultaneously, the earth would be pulled by both balls. So the balls accelerate towards the earth at the same rate, and there’s only one earth to move towards the balls. Both balls hit the ground at the same time.
[li]All that infinitesimal effect goes out the window when you introduce air. If the two balls experience the same air drag, it has less effect on the heavier ball. (Much like two identical brakes, one installed on an 18-wheeler and the other on a motorcycle. Same force, but big difference in effectiveness.[/li][/ul]
Air resistance depends on size (frontal area), shape, speed and air density. Also keep in mind that “shape” also includes orientation.
Parachutists can change their own shape and orientation, which changes their air resistance.
Accelerations aren’t negative. Acceleration is the rate of change of speed. Acceleration simply decreases asymptotically to zero, at which point there’s no more change of speed.
Acceleration becomes zero where downward force is balanced (cancelled out) by the upward force. Downward force is gravity, so it depends on the mass of the ball. Upward force is air resistance, so it depends on the speed of the ball (assuming same shape and size). For a heavier ball, it takes more speed to generate enough air resistance to balance out the gravity. So the heavier ball reaches a higher terminal velocity.
Did that make any sense? If not, keep asking more questions.
Not quite. Both balls (assuming the same size and roughness) would have the same coefficient of friction. But not necessarily the same frictional force. That force (Drag) depends on the drag coefficient, C[sub]D[/sub] and the velocity (actually, the square of velocity). Since C[sub]D[/sub] is the same for both balls, they experience the same force any time they have the same velocity.
Now we also assume the iron ball weighs more (it’s pretty implicit based on the presumed intent of the problem). If this is the case, the same drag force will slow it down less than it would the wooden ball.
So as each ball falls, it pick up speed. As it picks up speed, the drag starts to rise, and adds an upward piece of acceleration that partially cancels gravitational acceleration. Each ball still experiences a net downward force, it’s just getting smaller the faster it goes. Eventually each ball will reach a speed at which the drag force equals its own weight. Then, the net force is zero, and it stops accelerating. At that point it is falling with constant velocity, known as its terminal velocity.
Since the wooden ball weighs less than the iron one, it needs less drag to balance its weight. This lower value of drag occurs at a lower velocity, and so the wooden ball has a lower terminal velocity than the iron ball. The iron ball keeps speeding up past that speed, and end up going faster before the drag can balance its weight.
Since the iron ball end up falling faster than the wooden one, they won’t hit the ground at the same time. In a vacuum however, they would. And that’s regardless of the size, weight, or texture.
Re-reading this I realize that I didn’t make it clear what I was saying and someone might get the wrong information.
Let me try again:
Initially the iron ball and wooden ball will experience the same force from air resistance becuase they are the same size. However becuase the iron ball is more massive it experiences a greater force due to gravity. Since acceleration in this case is [Fg (force due to gravity) - Far (force due to air resistance)]/mass the larger Fg is the greater the acceleration. Since the iron ball experiences a higher acceleration it will have a greater velocity than the wooden ball. Since Far increases with velocity the iron ball will experience ‘the greater force of air resistance’.