Bevægelse med luftmodstand | SRO

Bevægelse med luftmodstand - 2 - Studieretningsopgave Abstract The following scientific report is about movement with air resistance. Newton’s second law of motion tells us that if an external force acts on a body, the body accelerates in the same direction as the force. The force equals the mass of the body times the acceleration. The magnitude of the air resistance of low speed is approximately proportional to the body’s speed: F = kv, where k is a constant that depends on the shape and size of the body and the properties of the surroundings. But the air resistance of high speed is approximately proportional to v rather than to v: F = kv , where k depends on the shape and size of the body and on the density of the air. Now Newton’s second law gives: ΣF = mg + (-kv) = ma As the speed increases, the resisting force also increases, until it equals the magnitude of the weight, and then you have mg=kv.

To prove this theory, I made an experiment by measuring the speed of a falling cake tin and I discovered that F = kv describes the movement the best.

I concluded that the movement of a body depends on its weight, and the more it weighs, the more time it will use on accelerating and therefore it will have a higher maximum speed. Formål Formålet er at redegøre for bevægelse med luftmodstand med udgangspunkt i Newtons 2. lov, samt at redegøre for den matematiske sammenhæng mellem funktionerne s(t), v(t) og a(t). Teori Newtons 2. lov går ud på at summen af de kræfter, der virker på systemet, er lig bevægelsesmængden, p, over tidsrummet.

F = p t (m  v) t = m  v t = m  a Man får så at den resulterende kraft er lig massen gange med accelerationen. Når et legeme falder, er det påvirket af to kræfter: tyngdekraften, der presser os ned, og luftmodstanden, der retter opad.

Stokes gnidningslov går ud på at F = kv, hvor k er en konstant, kaldet Reynolds tal, der afhænger aflegemets form, omgivelsernes viskositet, diameteren og densiteten. Denne formel angiver, hvordan luften strømmer omkring legemet. Formlen gælder kun for små legemer med forholdsvis små hastigheder, hvor strømningen foregår i forskellige lag Men for større hastighederbliver strømningsmønsteret omkring kuglen for turbulent, da der opstår hvirvler.