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An object of mass m is traveling with an initial speed v. The object is brought to a rest by a variable force that acts over a distance d for a time t. There are two ways to calculate the magnitude of the “average” force, F av = mv/t Or F av = mv 2 /2d. Are the two methods equivalent? Under what conditions, if any, will they yield the same average? Will one method tend to produce a larger result, and, if so, which method?
No, the two methods are not equal. The magnitude of average force in the first method comes from the momentum of the particle and the second method comes from change of kinetic energy.Yes, the two methods will give the same average when the particle has initial momentum and final momentum have same magnitude and also have same direction.Yes, one method tends to produce a larger method. Suppose a particle has initial momentum pi and final momentum also - pi but the final direction is just opposite to the initial direction. The change in momentum in this case is 2 pi. But the change in kinetic energy is zero. Thus the average force using first method will have the larger result than the second method.
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