Projectile Motion and Mass

[grayfalcon89]

From my lab this week, I analyzed that the projectile motion is independent from the mass of the object and that it's not a factor in any equation for projectile motion. I said this based on my lab results.

 

But I find it difficult to believe that it's true with my eyes. I don't know.. I just feel like heavier object, like car, will have less steeper projectile motion than soccer ball.

 

Can anyone tell me if I'm right (and that my eyes, just like in other scenarios of physics, are deceptive)?

[Bignose]

If you did this in your lab, what do you think was flawed with the lab, then? Shouldn't you believe your own experiments? and their results?

 

Intuition is a valuable thing mankind developed. The more intuitive members of our species learned to trust their intuition, and not go into the deep grasses when intuition said that there was a tiger in there. But, just because our intuition says that there is a tiger there, doesn't mean that there actually is a tiger -- intuition can be wrong.

 

Intuition is not fact, and that's why experiments are performed... to test whether your intuition is correct or not. And, if your intuition doesn't agree with the experiment, there are really only two choices: the experiment was flawed in some way, or your intuition is wrong and needs to be righted.

 

Don't feel too bad. Not many people are born with a true physics intuition. Many, many people will argue how the heavier object should fall faster than the lighter one... until the experiment is done. To be a good physicist, however, you will have to abandon those first instincts and learn to accept the physics ones. It's not easy, but worthwhile because your intuition will be more in tune with how nature really acts.

[swansont]

Big objects usually don't travel at the same speeds as small objects, which can make direct comparisons more difficult. And of course there are confounding effects like air resistance, which depend on surface area.

 

But in the idealized case, mass doesn't matter.

[thedarkshade]

Idealized case... That's a thing I have problems with. The calculations and the theoretical procedure goes just fine, but there's just one problem. It does not fit reality, and that is something I do not like.

 

Why do they have to be just for idealized cases? But how can they be for realistic cases, when our world is messily complexed.

 

What an irony!

[insane_alien]

well, do you ant to have to consider aerodynamic drag(complete with a full model of the local atmosphere), nonuniform gravitational field, changing magnetic field, radiation pressures, buoyancy, quantum effects etc. just to estimate how far a ball is going to be thrown.

 

idealized cases are only used in the teaching of something. they assume that the rest of the parameters are zero. if it is the only major force involved then the model will be correct to a reasonable degree.

[grayfalcon89]

Thanks for the feedback. Yeah, I know I should believe my results (which are usually right, assuming I followed the procedures) but I'm just not born with "physics" intuition.

 

From my AP book, I found that:

 

Horizontal motion:

[math]\Delta x = v_{0x} t[/math]

[math]v_{x} = v_{0x}[/math]

[math]a_x = 0[/math]

 

Vertical motion

[math]\Delta y = v_{0y} t + \frac{1}{2} (-g) t^2 [/math]

[math]v_y = v_{0y} + (-g)t[/math]

[math]a_y = -g [/math]

 

So, now it hits me clearly ( ) that mass is not necessary!

 

COOL!

[Bignose]

Idealized case... That's a thing I have problems with. The calculations and the theoretical procedure goes just fine, but there's just one problem. It does not fit reality, and that is something I do not like.

 

Why do they have to be just for idealized cases? But how can they be for realistic cases, when our world is messily complexed.

 

What an irony!

 

dark, do you learn to solve differential equations before you learn to take a derivative? For that matter once you learned the number system, did you jump right to multiplication, division, fractions, decimals? When you take a new job, are you expected to work at 100% maximum immediately or are you given some training first? When you leaned how to read, did you then immediately pick up War and Peace?

 

Of course not to all off that -- you work your way up, dealing with simpler problems and build up a repertoire of knowledge. No one jumps right to the hardest problems first. So, you do idealized problems with no drag, no friction, to start with the simpler problems. Simpler problems also you to check yourself to make sure that you have the basic concepts down before you move on to to harder problems. Many, many of the problem threads on this forum and others could be resolved if the authors/OPs knew the basics before trying the complicated.

 

There are others, but here: ( http://www.scienceforums.net/forum/showthread.php?t=25275 ) is the one I specifically remember. The author there had really had a poor grasp of the basics before he was trying to do more complex things.

 

Using idealized situations allow one to learn to walk before they learn to run. Sure, real life has many, many additional complications. But, you don't throw all those in at the beginning -- you learn the basics and then learn how to include those additional complications later.

[swansont]

Exactly. It's necessary to keep things simple at first, and only look at one or two concepts at a time. Once you get comfortable with the ideas of basic kinematics, and with energy and momentum, then you can tackle more advanced situations.

[thedarkshade]

Of course Bignose, I completely agree with you!

 

The problem is that i think they make you fell not so close to the reality, but it's still science and I love it!

 

Cheers,

Sh8

[swansont]

Well, labs should be designed to minimize the confounding factors. If you want to study kinematics without friction, you use an air track and not a block on an inclined plane.

[Mr Skeptic]

Well, labs should be designed to minimize the confounding factors. If you want to study kinematics without friction, you use an air track and not a block on an inclined plane.

 

But it is very close to reality if the assumptions are close to reality. If your projectile is in space, or massive with an aerodynamic shape, those equations will match extremely closely with reality.

[thedarkshade]

But it is very close to reality if the assumptions are close to reality. If your projectile is in space, or massive with an aerodynamic shape, those equations will match extremely closely with reality.

Yet you're idealizing the case:rolleyes:...

[Cap'n Refsmmat]

Friction is negligible in most basic physics labs anyway, so the assumptions hold true.

 

Remember that the equations don't purport to just "work" -- they purport to describe the motion of an object being acted upon by one force: gravity. That situation just doesn't exist most of the time.

[Bignose]

Yet you're idealizing the case:rolleyes:...

 

shade,

 

idealizations occur all the time... and incredibly accurately, too. Where should we draw the line? Do we model a golf ball flying through the air, or should we model each layer in the construction of the ball, or should we model every molecule of the golf ball and their interaction with every molecule of air? Heck, that's still an idealization, because really we should be modeling each atom in each molecule, and each proton, neutron and electron in each atom, and each quark in each neutron and proton and each lepton in each electron, right? Shoot, even those may be idealizations of strings, so, once we figure string theory out we won't have to use idealizations at all any more, unless there are substrings or something like that.

 

What the heck is the problem with some idealizations? That is where a lot of the true experience in physics comes in -- when it is okay to make an idealization/assumption and when it isn't and when to go back and double check that your assumptions are valid.

 

It really all comes down to what level of exactness do we need. Do we need to know within one yard of where the golf ball came down? Then we better have a good model of the drag and lift and good initial data on its spin rate and initial velocity. Do we only need within 10 yards? Then maybe treating it as a smooth (non-dimpled) sphere might be okay.

 

Or, do we need to know approximately where Mars is so we can locate it with our telescopes tonight? -- use Kepler's laws of planetary motion. Or, do we need to know where it exactly is like if we wanted to land a probe at a specific place on Mars? -- then more exacting calculations will be needed. It really all comes down to how exacting do you need to be, or how exacting your measuring instruments can be.

 

There are always idealizations in every single problem, where do you draw the line? Even in the unbelievably accurateness of landing a probe on Mars, there are still idealizations -- The gravitational influence of the far away planets are included in the calculations, but they are treated as a point source, not as a full sphere. That idealization turns out to be very, very accurate in certain cases. Is it really that bad to treat it as such?

 

How about an ideal gas like Helium at higher temperatures and pressure? If you treat the molecules as points and derive their properties from that idealization, you get very, very accurate results. Idealization in this case, as well, is perfectly fine.

 

There is nothing wrong with idealizations, when the assumptions behind the idealizations are valid. Why do you think that they are so bad? Why should we insist on dramatically increasing the difficulty of problems when there isn't any significant increase in accuracy? Where does the need or reward or even the desire for that come from? If the easier, simpler problems give the same answers, then they are just as good.

[swansont]

It really all comes down to what level of exactness do we need. Do we need to know within one yard of where the golf ball came down? Then we better have a good model of the drag and lift and good initial data on its spin rate and initial velocity. Do we only need within 10 yards? Then maybe treating it as a smooth (non-dimpled) sphere might be okay.

 

Or, do we need to know approximately where Mars is so we can locate it with our telescopes tonight? -- use Kepler's laws of planetary motion. Or, do we need to know where it exactly is like if we wanted to land a probe at a specific place on Mars? -- then more exacting calculations will be needed. It really all comes down to how exacting do you need to be, or how exacting your measuring instruments can be.

 

 

Yep. The calculations for satellite/space vehicle paths are based on Newtonian gravity rather than GR, for exactly the reason that the GR corrections are so small it's not necessary — it all reduces to Newton anyway.

 

And, as the joke goes, cows are approximated as spheres, but not always.

[thedarkshade]

OK Bignose, fair enough!

And, as the joke goes, cows are approximated as spheres, but not always.

I've heard of "consider a spherical cow"! That's just a joke to refer to oversimplification!