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View Full DocumentChapter 7 Review and summary\ Print this page REVIEW & SUMMARY Kinetic Energy The kinetic energy K associated with the motion of a particle of mass m and speed v , where v is well below the speed of light, is (7-1) Work Work W is energy transferred to or from an object via a force acting on the object. Energy transferred to the object is positive work, and from the object, negative work. Work Done by a Constant Force The work done on a particle by a constant force during displacement is (7-7,7-8) in which is the constant angle between the directions of and . Only the component of that is along the displacement can do work on the object. When two or more forces act on an object, their net work is the sum of the individual works done by the forces, which is also equal to the work that would be done on the object by the net force of those forces. Work and Kinetic Energy For a particle, a change K in the kinetic energy equals the net work W done on the particle: (7-10) in which K i is the initial kinetic energy of the particle and K f is the kinetic energy after the work is done. Equation 7-10 rearranged gives us (7-11) Work Done by the Gravitational Force The work W g done by the gravitational force on a particle-like object of mass m as the object moves through a displacement is given by (7-12) in which is the angle between and . Work Done in Lifting and Lowering an Object The work W a done by an applied force as a particle-like object is either lifted or lowered is related to the work W g done by the gravitational force and the change K in the object's kinetic energy by (7-15) If K f = K i , then Eq. 7-15 reduces to (7-16) which tells us that the applied force transfers as much energy to the object as the gravitational force transfers from it. Spring Force The force from a spring is (7-20) where is the displacement of the spring's free end from its position when the spring is in its relaxed state (neither compressed nor extended), and k is the spring constant (a measure of the spring's stiffness). If an x axis lies along the spring, with the origin at the location of the spring's free end when the spring is in its relaxed state, Eq. 7-20 can be written as (7-21) A spring force is thus a variable force: It varies with the displacement of the spring's free end. Work Done by a Spring Force If an object is attached to the spring's free end, the work W s done on the object by the spring force when the object is moved from an initial position x i to a final position x f is (7-25) If x i = 0 and x f = x , then Eq. 7-25 becomes (7-26) Work Done by a Variable Force When the force on a particle-like object depends on the position of the object, the work done by on the object while the object moves from an initial position r i with coordinates ( x i , y i , z i ) to a final position r f with coordinates ( x f , y f , z f ) must be found by integrating the force. If we assume that component F x may depend on x but not on y or z , component F y may depend on ... View Full Document
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