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# lecture-ch7 - Contents 7 Work-Kinetic Energy Theorem 1 7.1...

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Unformatted text preview: Contents 7 Work-Kinetic Energy Theorem 1 7.1 What is Energy? . . . . . . . . . . . . . . . . . . . . . . . . . 1 7.2 Kinetic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 1 7.3 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7.3.1 Net work done by several forces . . . . . . . . . . . . . 2 7.4 Work-Kinetic Energy Theorem . . . . . . . . . . . . . . . . . . 3 7.5 Work Done by the Constant Gravitational Force . . . . . . . . 4 7.6 Spring Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 7.6.1 The Work Done by a Spring Force . . . . . . . . . . . 6 7.6.2 The Work Done by an Applied Force . . . . . . . . . . 6 7.7 Work Done by a General Variable Force . . . . . . . . . . . . 7 7.7.1 One-Dimensional Analysis . . . . . . . . . . . . . . . . 7 7.7.2 Three-Dimensional Analysis . . . . . . . . . . . . . . . 9 7.8 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 7 Work-Kinetic Energy Theorem 7.1 What is Energy? Loosely speaking, energy is a number that we associate with a system of one or more objects. If a force changes one of the objects by, say, making it move, then the energy number changes. After countless experiments, scientists and engineers realized if the scheme by which we assign energy numbers is planned carefully, the number can be used to predict the outcomes of experiments and even more important, to build machines. This success is based on a wonderful property of our universe: Energy can be transformed from one type to another and transferred from one object to another, but the total amount is always the same (energy is conserved .) No exception to the principle of energy conservation has ever been found. In this chapter, we focus on only one type of energy ( kinetic energy ) and on only one way in which energy can be transferred ( work ). 7.2 Kinetic Energy Kinetic Energy K is energy associated with the state of motion of an object. For an object of mass m whose speed v is well below the speed of 1 light c , K = 1 2 mv 2 The SI unit of kinetic energy is the joule (J), named for James Prescott Joule, an English scientist of the 1800s. It is defined in terms of the units for mass and velocity 1 joule = 1 J = 1 kg · m 2 /s 2 7.3 Work If you accelerate an object to a greater speed by applying a force to the object, you increase the kinetic energy K ( 1 2 mv 2 ) of the object. Similarly, if you decelerate the object to a lesser speed by applying a force, you decrease the kinetic energy of the object. We account for the change in kinetic energy by saying that your force has transferred energy to the object from yourself or from the object to yourself. In such a transfer of energy, work W is said to be done on the object by the force . If the force vector F is applied to an object which moves a distance specified by the displacement vector Δ vectorx , the amount of work Δ W that is done on the object is defined to be Δ W = vector F · Δ vectorx = vextendsingle vextendsingle...
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lecture-ch7 - Contents 7 Work-Kinetic Energy Theorem 1 7.1...

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