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Impulse and Momentum
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Impulse Newton s second law of motion, F ma, can be rewritten by using the definition of acceleration as the change in velocity divided by the time needed to make that change It can be represented by the following equation: F ma m
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Multiplying both sides of the equation by the time interval, t, results in the following equation: F t m v Impulse, or F t, is the product of the average force on an object and the time interval over which it acts Impulse is measured in newton-seconds For instances in which the force varies with time, the magnitude of an impulse is found by determining the area under the curve of a force-time graph, such as the one shown in Figure 9-1 The right side of the equation, m v, involves the change in velocity: v vf vi Therefore, m v mvf mvi The product of the object s mass, m, and the object s velocity, v, is defined as the momentum of the object Momentum is measured in kg m/s An object s momentum, also known as linear momentum, is represented by the following equation Momentum p mv
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The momentum of an object is equal to the mass of the object times the object s velocity
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Momentum and impulse vectors are orange Force vectors are blue Acceleration vectors are violet Velocity vectors are red Displacement vectors are green
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Recall the equation F t m v mvf mvi Because mvf pf and mvi pi, this equation can be rewritten as follows: F t m v pf pi The right side of this equation, pf pi, describes the change in momentum of an object Thus, the impulse on an object is equal to the change in its momentum, which is called the impulse-momentum theorem The impulse-momentum theorem is represented by the following equation Impulse-Momentum Theorem F t pf pi
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The impulse on an object is equal to the object s final momentum minus the object s initial momentum
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9 Momentum and Its Conservation
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If the force on an object is constant, the impulse is the product of the force multiplied by the time interval over which it acts Generally, the force is not constant, however, and the impulse is found by using an average force multiplied by the time interval over which it acts, or by finding the area under a force-time graph Because velocity is a vector, momentum also is a vector Similarly, impulse is a vector because force is a vector This means that signs will be important for motion in one dimension