Few simple classical physics conceptual questions

[random_soldier1337]

And one practical one. Hope this is the right place since these are mostly beginner questions.

1. When can we treat objects as point masses/behaving like particles for the sake of simplification of calculations? I ask this question because my physics textbook said that a stiff pig sliding down a slide could be treated as one whereas a tumbleweed could not which I'm not quite sure about. I would think that the pig's limbs and snout jutting out would cause changes in its motion due to the collisions with the slide. Likewise, isn't the tumbleweed a relatively cohesive mass? Maybe if one were to analyze the movement of the tumbleweed itself, I would think it would matter more then but not when its motion is being analyzed relative to a surrounding. Anyway, what can you guys tell me about this?

2. If two objects are in freefall in an ideal vacuum and ideally constant gravitational field, is it absolutely true that the two objects will fall at the same rate? As in nothing short of a constant force applied in the opposite direction will change it's rate? Maybe I've been conditioned to look at objects falling in our atmosphere but is there really nothing like an associated rotational motion to the object or anything that would change its rate of freefall? Or is that just a beginner's simplification/concept?

3. When do we observe the negative x-axis? I ask this question because a question asked me to find the maximum positive distance achieved by a particle with motion defined by the equation x = 12(t^2) - 2(t^3). Graphically, that would be +infinity at the time -infinity. But the answer is a finite value at t = 4, which is 64. Hence, my question.

4. How were instantaneous velocities, accelerations and forces measured before modern times i.e. without any digital indicators or industrial machinery and the products thereof? And did these give numerical values or only a qualitative indication?

[Sriman Dutta]

For 2, there is same rate of acceleration due to gravity as long as the gravitational field is constant.

[swansont]

1. Rotating objects can't be point objects; that's why a tumbleweed can't be one. Simple kinematic problems with linear motion can be solved with this approximation.

[random_soldier1337]

1. Rotating objects can't be point objects; that's why a tumbleweed can't be one. Simple kinematic problems with linear motion can be solved with this approximation.

 

So in general, it will not work for more practical cases, where one is trying to describe the motion of most realistic objects?

[swansont]

So in general, it will not work for more practical cases, where one is trying to describe the motion of most realistic objects?

Virtually all of physics involves approximation. It's a matter of how close to reality you need to be. That's what dictates how complicated the model needs to be.

[Bender]

3) I assume that with "x-axis" you mean "t-axis" and are talking about a negative time? In that case, it depends on the question, which should make it clear in which time interval you should look. I would guess in this case they are looking for a positive time, because that is where the local maximum is.

 

4) instantaneous velocities and accelerations weren't measured . In fact quite often they aren't measured even now and instead derived the position measurement (or position and velocity from the acceleration measurement). As far as I know, Galileo was the first to measure acceleration indirectly by positioning bells in such a way that a passing ball would cause a constant rhythm. It depends of course how far back you want to go. Rotational velocity could be measured with the centripetal force or induced voltage.

Force could be measured the same way as it is measured now: deformation of a spring (or elastic structure).

I don't really know much about the history of measurement techniques, to be honest. It would probably have depended greatly on the application. Are you looking for anything specific?

Edited January 15, 2017 by Bender

[random_soldier1337]

Virtually all of physics involves approximation. It's a matter of how close to reality you need to be. That's what dictates how complicated the model needs to be.

 

Well, to put it differently, is there ever a practical physics problem where the model of simple kinematics in linear motion apply?

 

 

3) I assume that with "x-axis" you mean "t-axis" and are talking about a negative time? In that case, it depends on the question, which should make it clear in which time interval you should look. I would guess in this case they are looking for a positive time, because that is where the local maximum is.

 

4) instantaneous velocities and accelerations weren't measured . In fact quite often they aren't measured even now and instead derived the position measurement (or position and velocity from the acceleration measurement). As far as I know, Galileo was the first to measure acceleration indirectly by positioning bells in such a way that a passing ball would cause a constant rhythm. It depends of course how far back you want to go. Rotational velocity could be measured with the centripetal force or induced voltage.

Force could be measured the same way as it is measured now: deformation of a spring (or elastic structure).

I don't really know much about the history of measurement techniques, to be honest. It would probably have depended greatly on the application. Are you looking for anything specific?

 

3) Well... it didn't specifically say the time period. I'm guessing unless otherwise specified or needed to be observed (as in that is where the answer is), 0 to +infinity is the time period to observe.

 

4) If even now instantaneous velocities and accelerations are derived from either graphs or other indirect methods, then how do speedometers work? I have a hunch it is the same indirect way either with some sort of spring mechanism as you said or electrical transducer or the like.

 

Well I'm just curious how one without access to industrial machinery of any sort would do their own experiments, back then or even now, like say measuring the force required to bend an iron rod of some specific dimensions or the force required to cause a fracture in a rectangular baked clay brick.

[Bender]

Well, to put it differently, is there ever a practical physics problem where the model of simple kinematics in linear motion apply?

Of course. e.g. a gps uses it to calculate the estimated time of arrival given the average speed on each road and the length of those roads.

 

When looking at accelerating or breaking of a vehicle, it is often safe to ignore any rotational effects (not always)

 

...

 

3) Well... it didn't specifically say the time period. I'm guessing unless otherwise specified or needed to be observed (as in that is where the answer is), 0 to +infinity is the time period to observe.

As long as you are aware that this is not a general rule, the frame of reference is an arbitrary choice and that in practical problems, you should look at the relevant time frame.

) If even now instantaneous velocities and accelerations are derived from either graphs or other indirect methods, then how do speedometers work? I have a hunch it is the same indirect way either with some sort of spring mechanism as you said or electrical transducer or the like.

 

Well I'm just curious how one without access to industrial machinery of any sort would do their own experiments, back then or even now, like say measuring the force required to bend an iron rod of some specific dimensions or the force required to cause a fracture in a rectangular baked clay brick.

Speedometers can work in several ways. One is magnetic, where the voltage increases with velocity (much like how a dynamo works). Another is with encoders: discs with either optical or magnetic marks. The amount of marks passing a detector is counted to know the distance driven. Divide by time and you have velocity.

On a bike, the disk is replaced by a magnet on the wheel, so the speedometer counts the revolutions of the wheel.

 

In the examples, the required force was not measured. It was determined by experience and trial and error what was required for a specific task.

Edited January 15, 2017 by Bender

[swansont]

Well, to put it differently, is there ever a practical physics problem where the model of simple kinematics in linear motion apply?

 

Yes.

 

I used it in calculating the trajectory of atoms launched in my atomic fountain clock. I needed to know when to expect when the atoms would be in a region where they could be detected. (Also did a similar calculation in my thesis)

[random_soldier1337]

In the examples, the required force was not measured. It was determined by experience and trial and error what was required for a specific task.

 

So basically, it was qualitative? And people would basically say that, "So and so has been seen to bear this much weight but I can't say about more." Or something to that effect I take it.

 

 

Yes.

 

I used it in calculating the trajectory of atoms launched in my atomic fountain clock. I needed to know when to expect when the atoms would be in a region where they could be detected. (Also did a similar calculation in my thesis)

 

But don't atoms have angular momentum? Also I never actually asked why rotating objects can't be point objects. Why is that so?

[swansont]

But don't atoms have angular momentum? Also I never actually asked why rotating objects can't be point objects. Why is that so?

 

 

Yes, but they aren't rotating. The linear impetus does not go into rotation. QM is a different beast than classical mechanics; suffice it to say that the problem I solved can be treated classically.

 

A point object, classically, can't have mass, and how fast would it be rotating? There's no circumference to use; the linear speed of the surface must be infinite for any rotation. How would you figure a moment of inertia for it? Those terms (and probably others) diverge for a point particle.

[Bender]

So basically, it was qualitative? And people would basically say that, "So and so has been seen to bear this much weight but I can't say about more." Or something to that effect I take it.

Yes. It obviously went wrong sometimes. Hundreds have died under collapsing churches during construction.