MadSci Network: Physics |
Hallo, Jeremy, and thanks for the question! I will split this answer in two parts. First part will be the (more or less) straight answer to the question, along with some comments on how to obtain that answer. The second part will be a comment of rather philosophical nature, but I believe that you will find it more helpful than the first part. So, the beehive hangs suspended from the isolated old oak-tree on a lovely meadow carpeted with flowers... (this rustic setting is just to help you understand that physics is not just some weird science done exclusively in sealed and heavily guarded underground labs, but is rather a way of looking at the real world around you, and as such can be applied even to the trees and meadows!) A young lad passes by, resting a while from his study (he's got a physics exam in two days and is just studying collisions), and he wonders what would happen to the beehive if he hit it with a stone (he'd like to see some physics in action, because seeing it just in the books can bore you to death). SO he runs back home, picks up a paper and a pencil, and dashes off back to the meadow and sits himself in the shadow of the old oak. First he has to model the process, so he needs to make some assumptions about the quantities he can and needs to measure in order to calculate the ones he can't directly measure. He picks the 'known' quantities to be the masses of the stone and beehive. He also simplifies the whole process of hitting-the-bee-hive-with-a-stone by just considering a beehive to be a pendulum, i.e. a mass suspended on a string. Also he considers a stone to be the point-mass object. Further he assumes that he knows the speed the stone attains when he throws it and finally, he assumes that when the stone hits the beehive, it penetrates it from one side and doesn't pass through, but instead gets stuck in it. This is just a sort of process you have inquired about. It is called TOTALLY INELASTIC COLLISION, and there certainly IS a way on how to calculate the speed of the compound object (beehive with a stone in it) that resulted from the collision. I will not solve it for you, but instead give you the hint on how to do it yourself (an old Chinese proverb says 'do not give the fish you have caught to the hungry - teach them how to catch the fish themselves instead'). Two physical quantities you can consider are the total energy and the total linear momentum at moments just before and just after the collision. Since beehive and the stone constitute the closed physical system, both these quantities are conserved throughout the collision process. But alas, the main characteristic of the inelastic collision, as opposed to the elastic one, is that the part of the initial kinetic energy (due to the motion of the stone before the collision) is transformed to heat. This transformation comes about due to the friction between the stone and the inside of the beehive which acts as to halt the stone's motion with respect to the beehive. Effectively, when considering just the kinetic energies in the system, their sum is not conserved. So conservation of energy cannot help us much... (unless we can somehow accurately measure all the energies that are transformed, such as heat and sound) Hence we turn to the conservation of (linear) momentum. Before the collision, the total momentum of the system is contained in the motion of the stone (you should know that the expression for the linear momentum of a point mass m moving with the known velocity v is m*v). After the collision the total momentum is equal to the (M+m)*v', where M is the mass of the beehive and v' is the unknown velocity of the compound object, a beehive with a stone stuck in it. Now what you get when you use the conservation of momentum principle is one equation (momentum before equals momentum after the collision) with one unknown (velocity of the compound object) that you can solve. Hence the unknown velocity... Now to the philosophy... PLEASE, DO NOT THINK OF PHYSICS IN TERMS OF FORMULAE. Formulae are just algerbra, number-letter juggling. Think of it rather as the multitude of processes that go on around you (and within you). Do not ask for a formula - that is something you can work out yourself. Ask for the description of the process - what you can measure, what you can't measure, which quantities are relevant for the given process, which are obsolete. I'm saying this because I know that just memorizing formulae makes physics dull and gray, and the final result is not that you actually learn something new but instead you become unable to think of the phenomena without your formula-booklet in your hand. Hope you are satisfied with the answer, and hope you'll enjoy your future journeys into the world of physics.
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