Weight of Horizontal Projectile

[skulliam4]

Hi, I am 12 years old and sort of a noob to physics due to, well, me being in the 8th grade. I need to find the weight of this spherical projectile given just about every other factor, I know the Angle in which it was fired (32.2°), the gravity of the planet this takes place on (12m/s²), the drag (0.2/s), the fire power (16.656 m/s), traveling at 14 1/6 m/s, the distance it goes (51 meters on perfectly flat, level ground), and terminal velocity of 60m/s. The equation needed to find this is really what I need (along with which variable is which), but if you happen to want to take me through the steps, I would appreciate it. I still need the answer if it turns out negative! Thank you for your help.

 

[skulliam4]

Oh, and the density of the object is 2.71.

 

[Nathanael]

Suppose you had an object that was launched at the same angle on the same planet with the same initial speed. If there is no air resistance, it would be impossible to tell the mass of the object. (All objects would behave the same.)

The useful information is the drag (air resistance) along with the distance travelled. A certain distance traveled with same drag will uniquely define the mass (I won't go into detail but feel free to ask questions).

A simpler approach, though, would be to use the terminal velocity. Please explain to me your understanding of terminal velocity and how it relates to drag.

(P.S. what are your units for drag? 0.2 Newtons per second?)


Edit:
Sorry if I made it a little confusing, I know you're only in 8th grade. Ask as many questions as you need to though. (I'm assuming you want to actually learn and not just the answer)

 

[Nathanael]

Oh, and the density of the object is 2.71.

Do you know the radius of the spherical object? That would make things very simple :)P.S.
What are your units of density?

 

[skulliam4]

I am sorry, I truly do not knnow the unit of measurement the drag is used. And I need either the mass or weight because I have the density, but if I had the radius I could easily determine the size.

 

[skulliam4]

And density is kg per m³

 

[Nathanael]

Yes if you had the radius you could find the volume, and multiply it by the density to find the mass

(Density is defined as "mass per volume" so, volume times density equals mass)Air resistance (drag) is a force so there's a good chance the units are Newtons (they didn't tell you the units?)Do you know what "terminal velocity" means? Have you ever heard about it before?

 

[Nathanael]

Actually, I just realized that terminal velocity makes no sense with a constant drag. (Usually drag increases while speed increases, and that results in a "terminal velocity")

Do you mind if I ask what this is for? Is this a school assignment?

It's possible to find the mass, but I think it might be a bit complicated for your level.

 

[skulliam4]

Terminal velocity is the speed of descent where the wind resistance is powerful enough to cancel out any further acceleration.

 

[skulliam4]

This is simply a question that I asked myself, and I truly wanted to find the answer.

 

[Nathanael]

Terminal velocity is the speed of descent where the wind resistance is powerful enough to cancel out any further acceleration.

Yes, exactly. But this can only happen when the wind resistance increases with speed (but you said wind resistance is a constant 0.2)

 

[skulliam4]

My souce labeled the denominator as per second, but not he numerator. I can only guess this is meters, but I am not really sure what units resistance is measured in. So it is 0.2 x per second.

 

[Nathanael]

Do you have any ideas how you may be able to figure this out?

What if air resistance was zero? Then are you able to figre out how far the object would travel?

 

[skulliam4]

The projectile travels at 51 meters no matter what. Of all the variables I know about, I know the least about drag, and I now notice that drag might lessen the distance, but I know that 51 meters is an undeniable fact that cannot be altered; it is an independent variable.

 

[Nathanael]

The projectile travels at 51 meters no matter what. Of all the variables I know about, I know the least about drag, and I now notice that drag might lessen the distance, but I know that 51 meters is an undeniable fact that cannot be altered; it is an independent variable.

Ok but I'm talking about in theory. Suppose that you had no idea what the distance traveled was, but you knew that the drag was zero. Would you know how to figure out the distance travelled?
(You'll need to be able to do this before you can solve this problem.)

I think the understanding behind the solution to the problem you're asking is beyond your level (it's a little tricky)

You'll need to understand trigonometry

If you don't know how to figure out the distance based off the launch angle and launch speed, then I would suggest looking up some videos on projectile motion (although I suggest knowing basic trigonometry first)

 

[skulliam4]

So it's not as simple as solving for weight, plugging in the variables, and getting an "x=?"?

 

[Nathanael]

I could just write a formula for this sort of situation that would give you the weight of the object (you would have to plug in launch angle, launch speed, horizontal distance travelled, and gravitational acceleration) but there's really no reason in giving you that formula (I haven't even wrote it yet) if you don't understand why and how it was created.

 

[skulliam4]

So, if you start with a downright universal, mathematical law of projectile motion, then solve for mass/weight and plug in the known variables you should get a "law" about how the weight/mass correlates to the different conditions. If you could simply name off the equation that shows one variable (such as distance) and the procedure needed to calculate that using certain key variables, it shouldn't be too hard to solve for mass/weight as long as no imaginary number is involved. Depending on your location, I am either 1 or 2 years ahead in just math, and am beginning to take Geometry.

 

[Bandersnatch]

If I may interject, this problem has got impossible setup. Even without any air resistance, and at 45 degrees, 16m/s muzzle velocity won't carry the projectile farther than 22-ish metres.

 

[skulliam4]

If I may interject, this problem has got impossible setup. Even without any air resistance, and at 45 degrees, 16m/s muzzle velocity won't carry the projectile farther than 22-ish metres.

It is 32.2 degrees, and the gravity is different on the planet in which the projectile is being fired. I realize the end result will be negative, but since it is all about them mathematic theories, I am taking into account negative mass, which, in case you're thinking, is not antimatter; antimatter still has a weight in the positive.

 

[Bandersnatch]

It is 32.2 degrees, and the gravity is different on the planet in which the projectile is being fired. I realize the end result will be negative, but since it is all about them mathematic theories, I am taking into account negative mass, which, in case you're thinking, is not antimatter; antimatter still has a weight in the positive.

None of that matters. I took the higher gravity into account, and 45° is merely the angle at which you have to shoot to achieve the greatest range(which is 22m). 32 will net you a few metres closer than that.

Negative mass would make the problem impossible to solve, as the projectile would never fall, but rather shoot into space at ever increasing pace.

You simply can't have the values you've chosen.

 

[skulliam4]

Ok, this is a little weird to say, but this is a different reality. More like, it isn't reality. It fires at 51 meters tops, and that is achieved at 32.2°. And If you are referring to infinitely going into space by the "chase" that happens between negative mass and normal mass, then please do tell me the force that the negative mass is repelled by the normal mass, then please tell me the exact force of the repulsion. The only way for it to go on forever is if that force is greater than the gravity.

 

[Nathanael]

So, if you start with a downright universal, mathematical law of projectile motion, then solve for mass/weight and plug in the known variables you should get a "law" about how the weight/mass correlates to the different conditions.

Yeah, pretty much. They wouldn't be considered laws (the math would come from more fundamental "laws," such as Newton's).
If you understand the relationship between the variables (speed, angle, gravity, time, drag, etc.) then you're able to write an equation that describes the situation.

If you could simply name off the equation that shows one variable (such as distance) and the procedure needed to calculate that using certain key variables, it shouldn't be too hard to solve for mass/weight as long as no imaginary number is involved.

Do you know anything about the sine and cosine functions? The equation would involve those functions. (Those are trigonometric functions, you'll learn about them in the coming years.)

I am not really a big fan of people using math that they don't understand. I could tell you the equation but I'd also have to tell you details about sine and cosine functions and you'd end up just typing things in on a calculator (namely sine and cosine of an angle) that you don't even understand.

Preferablly, you should understand the entire equation and how it was created.

But at least you should understand the math involved in the equation (specifically trigonometry).

 

[skulliam4]

I don't like to do math without understanding it either. I will either research it and notify you when I trust I know it well, or you can tell me the equation and I will sure as heck make sure that everything about it I understand crystal clear. I don't know if you get notifications when people comment on something you too have commented on, but I will say so (if you prefer me do the first) when I learn the ways of Trig.

 

[Bandersnatch]

45 degrees will always be the most efficient angle range-wise. To say otherwise is akin to saying that squares don't have all of their sides equal.
Also, the projectile can't reach 51 metres with that setup. If you world doesn't agree, then it's of little use to ask for physcially-plausible answers.As for the negative mass - look at Newton's law of gravity. $F=GMm/R^2$
If you use a negative value for one of the masses, you end up with gravity being repulsive rather than attractive(the force will have an opposite sign to what it would have with two positive masses). It's not some other force that would overcome gravity, it's the gravity itself that would push away the projectile into space.

 

[skulliam4]

As for the negative mass - look at Newton's law of gravity. $F=GMm/R^2$
If you use a negative value for one of the masses, you end up with gravity being repulsive rather than attractive(the force will have an opposite sign to what it would have with two positive masses). It's not some other force that would overcome gravity, it's the gravity itself that would push away the projectile into space.

That is why positive mass is repulsed by negative mass, but negative mass is attracted to positive mass. The positive mass has and provides gravity, and the negative wants to follow gravity. But the positive mass doesn't want to be near the negative, so it repels it. But if the force of gravity is stronger than the force of repulsion, it will indeed hit the ground.

 

[Nathanael]

Feel free to private message me at any time (private messages do give notifications) and I'll talk with you about it.

I can't tell you the equation because I don't have it. But I am thinking about it ("writing it") right now, because I think it's an interesting problem. (I'm changing your drag units to Newtons, since it's a force.)

But even after perfectly understanding Trig, you will not understand the equation crystal clear. In fact, no one will understand the equation crystal clear unless they write it themselves (or at the least, have a good understanding of how they would go about writing it themselves)


But feel free to private message me whenever. I plan on being on these forums for a long time (I learn a lot from them) so I should still be here and willing to talk with you even if it's been a long time.

 

[Nathanael]

That is why positive mass is repulsed by negative mass, but negative mass is attracted to positive mass.

No, they would both repel each other.

The positive mass has and provides gravity, and the negative wants to follow gravity.

No, they both are sources of gravity.

But the positive mass doesn't want to be near the negative, so it repels it.

They both don't want to be near each other.

But if the force of gravity is stronger than the force of repulsion, it will indeed hit the ground.

The gravity IS the "force of repulsion." There are not two seperarte forces.

 

[sophiecentaur]

So, if you start with a downright universal, mathematical law of projectile motion, then solve for mass/weight and plug in the known variables you should get a "law" about how the weight/mass correlates to the different conditions. If you could simply name off the equation that shows one variable (such as distance) and the procedure needed to calculate that using certain key variables, it shouldn't be too hard to solve for mass/weight as long as no imaginary number is involved. Depending on your location, I am either 1 or 2 years ahead in just math, and am beginning to take Geometry.

From what I have read in this thread, it strikes me that you may not know (or don't accept) that the trajectory of an object does not depend upon its mass - in the absence of air resistance. If you are 12 years old then the Physics of projectiles with air resistance is probably too difficult and, in any case, you should start with the ideal case of no atmosphere.

The only things that count are the value of g, the speed and the direction of launch. This Wiki Link says it all and you can see the equations do not include mass. Read that article carefully and you should find the answer in there.

 

[jbriggs444]

As for the negative mass - look at Newton's law of gravity. $F=GMm/R^2$
If you use a negative value for one of the masses, you end up with gravity being repulsive rather than attractive(the force will have an opposite sign to what it would have with two positive masses). It's not some other force that would overcome gravity, it's the gravity itself that would push away the projectile into space.

Negative passive gravitational mass means that it is repelled by gravity. Negative inertial mass means that it accelerates toward the source of a repulsive force. It works out that negative mass projectiles follow the same arc as positive mass projectiles -- if you blindly follow the mathematical model where ever it leads.