The change in velocity divided by the change in time is the definition of the acceleration a. For a constant mass m, Newton’s second law looks like: F = m * (V 1 – V 0) / (t 1 – t 0) But if we were discussing the flight of a bottle rocket, then the mass does not remain a constant and we can only look at changes in momentum. If we were discussing the flight of a baseball, then certainly the mass remains a constant. The weight of the fuel is probably small relative to the weight of the rest of the airplane, especially if we only look at small changes in time. This assumption is rather good for an airplane because the only change in mass would be for the fuel burned between point “1” and point “0”. Let us assume that the mass stays at a constant value equal to m. We only know how much product (m * V) changed. So at this point, we can’t separate out how much the mass changed and how much the velocity changed. Newton’s second law talks about changes in momentum (m * V). Let us just take the difference between the conditions at point “1” and the conditions at point “0”. Newton’s second law can help us determine the new values of V 1 and m 1, if we know how big the force F is. The mass and velocity of the airplane change during the flight to values m 1 and V1. The airplane’s new location is X 1 and time t 1. An external force F to the airplane shown above moves it to point “1”. The airplane has a mass m 0 and travels at velocity V 0. Let us assume that we have an airplane at a point “0” defined by its location X 0 and time t 0. His second law defines a force to be equal to change in momentum (mass times velocity) per change in time. Momentum is defined to be the mass m of an object times its velocity V. Newton’s Second Law: Force The acceleration of an object depends on the mass of the object and the amount of force applied.
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