Explaining Why a Bullet Hits Lower than a Laser Beam

[kirsten_2009]

Homework Statement

A riffle barrel and a laser point directly towards a target some distance away. General relativity says that the bullet and the light experience the same downward acceleration during horizontal travel, yet the bullet hits the target well below the laser beam. Explain.

Homework Equations

The Attempt at a Solution

While the downward acceleration is acting on both the bullet and the laser beam at the same rate; this downward acceleration actually has more time to work on the bullet that on the laser beam since the laser beam is traveling a lot faster (speed of light) than the bullet. Also, the bullet has more mass to be acted on downward than the laser beam. Consequently, the laser beam will arrive faster to the target as it has less time and mass to be acted on by downward acceleration forces compared to the bullet and the added downward forces experienced by the bullet will drag it down; hitting the target after and below that of the laser beam...correct?

Thanks for the help :)

 

[haruspex]

While the downward acceleration is acting on both the bullet and the laser beam at the same rate; this downward acceleration actually has more time to work on the bullet that on the laser beam since the laser beam is traveling a lot faster (speed of light) than the bullet. Also, the bullet has more mass to be acted on downward than the laser beam. Consequently, the laser beam will arrive faster to the target as it has less time and mass to be acted on by downward acceleration forces compared to the bullet and the added downward forces experienced by the bullet will drag it down; hitting the target after and below that of the laser beam

You have advanced two arguments, one based on time and one based on mass. One is right, one is wrong. Can you identify which and why? Hint: Pisa.

 

[kirsten_2009]

Hello!

Thanks for the reply. I've been thinking about it...and the time one has to be right since the difference in speed of the two traveling objects is so significant. Mass has to be wrong because it wouldn't be of importance in outer space which is where I assume this is taking place...right?

 

[PeroK]

Hello!

Thanks for the reply. I've been thinking about it...and the time one has to be right since the difference in speed of the two traveling objects is so significant. Mass has to be wrong because it wouldn't be of importance in outer space which is where I assume this is taking place...right?

Why would it be taking place in outer space?

You could think about two rifles: one fires a large, heavy bullet; the other a smaller bullet. Imagine they fire their bullets at the same speed. What can you say about the tracetory of the two bullets?

 

[kirsten_2009]

Hmmm...well if this was happening here on Earth...(I just automatically assume every thought experiment happens in outer space because my textbook never deals with stuff on Earth)...the heavier bullet would hit the target lower than the smaller bullet...so speed has nothing to do with it?

 

[PeroK]

Hmmm...well if this was happening here on Earth...(I just automatically assume every thought experiment happens in outer space because my textbook never deals with stuff on Earth)...the heavier bullet would hit the target lower than the smaller bullet...so speed has nothing to do with it?

So, you've never heard of poor Galileo climbing all the way to the top of the leaning tower of Pisa to demostrate that a heavy object and a light object fall at the same rate?

 

[kirsten_2009]

No...actually, I haven't. I thought however, that two objects of different mass fell at the same rate in a vacuum...so this also holds true in "real life"?

 

[PeroK]

No...actually, I haven't. I thought however, that two objects of different mass fell at the same rate in a vacuum...so this also holds true in "real life"?

Yes. It's true for all objects in a vacuum. The complication in "real life" is air resistance. Similar objects (same density and shape) will fall with the same acceleration. Normally you would think of a light object (feather) falling more slowly than a heavy object (canonball). But, take a woman with an open parachute. She's heavier with the parachute than without it, but falls more slowly. In this case, the heavier object falls more slowly.

In general, unless the effects of air resistance are significant, objects accelerate at the same rate due to gravity. So, in real life, the trajectory of a bullet is not dependent on its mass.

 

[haruspex]

two objects of different mass fell at the same rate in a vacuum

Quite so, but how does that lead you to conclude

the heavier bullet would hit the target lower than the smaller bullet

?

 

[kirsten_2009]

Hello,

Thanks for the excellent explanation! I think my confusion arose from the fact that the conditions in a vacuum are different than in "real life" since I figured the heavier bullet would have more 'drag' (if that's even the appropriate term) since it was heavier...but I see what you guys are saying. Thanks as always for the help! :)

 

[haruspex]

the heavier bullet would have more 'drag'

It generally would, but in proportion to its inertia less drag than the lighter bullet. So in air the lighter bullet would hit the target lower. Imagine throwing a rock at a target, then throwing a feather.