Math/Physics Project Help!!

[XSlingerX]

Hello. I am in grade 11 Pre-Calculus and as a project, each of us have to think of a problem that we have no idea how to solve, and solve it. Though, I'm having alot of trouble with mine and I could use some help to get on the right track.

My problem is this:
How much force would it take, firing on the hull of a USS Bradley (FF-1041), to tip it on its side. I basically have to figure out how much force it will take to push it off its centre of gravity.

My knowledge of physics caps off a linear kinematics, dynamics, and a little bit of non-linear kinematics. I done some research on centre of gravity.

This project is due soon and I would really appreciate some help!

Thanks

[Lee1026]

It is quite undoable, unless if you know the way that the ship is designed. You will need to know stuff like exactly how heavy the keel is. And I am willing to bet everything that I owned that this will not be a piece of easy information to find. Chances are, it is classified, so you can't use it on a class project even if you do know it. Also, there is no such thing as force to turn over a ship. You can talk about torque, but not force. To make matters worse for you, you have to discuss how long that force would be applied.
And of course, you would need to worry about water reistence for any vaguely accurate guessimate. Get a new problem.

[XSlingerX]

Thanks lee. I could do just a basic boat shape and drop the USS Bradley (FF-1041) idea.
Would this be possible? Because its too late to get a new problem, and this project is meant to replace an exam!

[Lee1026]

No. Even if it is a solid block (the easiest thing to tackle in this case) sitting on top of flat ground, the problem would still involve in a decent bit of calculus. Assuming that your teacher would let you say that you applied a certain amount of Joules or Newton-seconds instantly (otherwise this problem would get really nasty), then we would still need to do a intergral across the block to figure out the torque that would come from gravity.

[DarkKnight]

Well lets start with what we know. Start with a free body diagram.

Forces on COM of boat
Force of gravity= 9.8 m/s downwards
Bouyant force from water= Fg= 9.8 m/s upwards

Forces applied elsewhere on the boat
Force applied= X to the left or right(what were trying to find)
Resistance from the water= equal to the force applied when in static equilibrium


*Since I dont know how to use greek letters on this forum I will represent torque as T and Theta as 0
T=rFsin0
You will recieve the maximum amount of torque if the force is applied perpendicular to the radius, so we assume that 0=90 (remember 0 is representing theta)
sin90=1
T=rF
In order to recieve the maximum torque, the radius would have to be its maximum. So we would need to know how far the distance from the COM to the highest point on the ship is.

Now we're finding the minimum force required so that allows us to find the maximum force that can be applied in this situation while keeping the ship in equilibrium. Then we know any force greater than that will tip the ship.

So we can say
T(from the applied force)=T(from the resistance)
Now this is a physical nightmare to figure out the amount of resistance or "drag" the water creates. It would all depend on the water pressure, how deep the hull is underwater, how much water the ship displaces, and a buch of crap.
So if this could be found or given, then you could plug that value in for T in T=rF. Then like I said before, if you found the dimensions of the ship and found the COM and found the distance from the COM to the tallest point of the ship you would know r and could use that equation to solve for F, which of course is what you are trying to find.

In conclusion, go call your teacher a :wub: moron for giving you a problem that is impossible to do because there are so many missing variables.

[Wild Bill Kelso]

Moved to Physiologia.. kind of sounds like it belongs there WBK

[Lee1026]

Figuring out the amount of force required, however, is one tricky bit of calculus.

[XSlingerX]

Thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou thankyou DarkKnight, this gives me something to work with!

[DarkKnight]

Ive been doing some thinking and maybe this might work. If you think about it, in essence, the resistance offered by the water is technically friction. The force of friction is calculated by the formula
F=uFn
*u representing the greek letter mew as the coefficient of friction and Fn representing the normal force

The normal force in this case would be the bouyant force. The easiest way to calculate this would be to find the force of gravity f=mg since the force of gravity equals the bouyant force in this case. However I couldnt find the mass of the ship. However I did find on a site that the ship displaces 2620 tons of water, approximately 2381818.2Kg. The boyant force is calculated using Archimedes Principle that the bouyant force equals the weight of the displaced fluid. Therefore the bouyant force is 2381818.2N.

So now we know
Ff=2381818.2u
If you could come up with the coefficient of friction for water you could use that to find the "force of friction" which we are using to represent the "drag" caused by the water.

I am kinda reaching for straws here, but maybe that will give you something to work with.

[Lee1026]

I sincerely hope you are aware that formula for friction only work when the two objects in discussion are both solid.

Otherwise, a ship would encounter the same amount of resistance no matter what shape it is. As we know from looking at ships, they design those sharp bows from a reason, you know.

Also, the proper formula is C * V^2
where C is a constant, determined by the shape of the boat in question. V is the speed with which the ship is moving.

To make matters worse, we are discussing tipping over the boat, which involves in torque, which involves rotational inertia, which is one hell of a physics problem. (it will require triple intergration, a techique that I am assuming that you do not know)

To make matters even worse, we have to remember that the resistence force in question here is not friction, after all, that is C V^2, and we can take a limit as V approaches 0. The restoration force here is from the little fact that the bottom of the ship is considerablely heavier then the top, which means that as the ship rotate, the center of gravity of the ship will rise, and it will want to return to the orginal place. However, if we can just get a ship to lean so far off that water can get in, then the ship will sink.

Hence, you will need to figure out just how far you are rising the center of gravity to tip it over that badly, and that should give you the amount of energy required to tip the darn thing over. Doing that, however, is still one hell of a calculus problem.

[DarkKnight]

Lee what level of physics have you taken?
I am curently in AP Physics B and it sounds like you have a much better understanding of physics than me.

[Lee1026]

Currently on my first year in college of a program toward mechical engineering.
Anyway, the AP test in Physics is easy. I got a 5 on both parts of the C test, and I spent a grand total of 3 weeks studying for the E&M section.

[DarkKnight]

Im planning on going into mechanical engineering. Right now Im on my junior year taking AP Physics B and PreCalculus Honors and next year taking AP Physics C and AP Calculus BC.

[Lee1026]

Coward, I took the C test in junior year while I was in a honors physics class.

[XSlingerX]

Ah, thanks for you suggestions DarkKnight and Lee. The purpose of this project is to explore a topic, and therefore, I can get 90% for just understand the factors involved in solving it, but not actually solving it. You both have given me a better perspective as to the physics of this question. Even though I won't be able to solve the question, due to my lack of calculus and more advanced physics knowledge, thanks for giving me something to work with. I appreciate it!

[wcwraymond]

Which teacher tells you to do this project without giving you any data?? I If you want to find the force, you must know presicely where the centre of gravity is. That's hard even for the designer himself to tell you exactly. Also, this is not practical to tip it over with a cannon: to tip it you are talking about high speed cannon. that would penetrate the hull. To tip it, you use ropes to pull it over.
Also attacking the hull is impossible to overthrow it. The center of mass of a ship is usually at the lower hull around middle of the hull. You need ultra-ultra-ultra-ultrasonic cannon with very very very high speed, since the point of impact is too close to the rotational center.
Of course if you are interested in how to sink it, a torpedo woulf be more advisable. Ever played Silent Hunter III?