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Momentum and Impulse Momentum: A measure of how difficult it is to stop a moving object. Momentum = mass x velocity p = mv m Unit for momentum: kg s Can a VW bug have the same momentum as an ocean liner? Can a bullet have the same momentum as an Army tank? If the boulder and the boy have the same momentum, will the boulder crush the boy? Hint: Which would have the larger speed? Momentum of a system of particles P m i v i Mv cm i Which also yields the formula to calculate the velocity of the center of mass: v cm mv i M i Calculus Connection! dv d mv d p F ma m dt dt dt Kinetic Energy in terms of momentum– MEMORIZE!! 2 mv (mv )(mv ) K 2 2m 2 p K 2m Honestly, this could save you a lot of time on occasions! How do you change the momentum of an object? PUSH on it for a period of TIME. Impulse: the product of the force exerted on an object and the time interval during which it acts. Impulse = Force x time J = Ft Some texts symbolize impulse with “I”, but AP uses “J” Example: Wall exerts a force of 100,000 N. The contact time is 0.2 s. -----------------------------Impulse = F t = 20000 N-s The impulse given to an object is equal to the change in momentum of the object. Ft = D mv = mvf – mvo Change in Momentum = Impulse D(mv) = Ft mv = Ft The same change in momentum may be the result of a SMALL force exerted for a LONG time, or a LARGE force exerted for a SHORT time. Varying Forces If the force exerted on an object is NOT a constant force, finding the impulse/change in momentum is a little more difficult. As the saying goes, “If the forces varies… You must integrate!” In most cases dealing with collisions, the varying force is shown to be a function of time. The impulse is defined as the integral of the force over the time interval during which the force acts. It equals the total change in momentum of the particle. F( t )dt impulse Dp F ( t ) dt D p For example: If F(t) = 4t2 + 2, J = 4/3 t3 + 2t (+ C) Which will equal the CHANGE in momentum And, of course, on a Force vs time graph, The impulse/change in momentum, Is the “area under the curve”