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Transcript
Ch5 Energy 5.1,2 Work and Energy Theorem. Work has different meaning in physics. Definition: work is proportional to the mass and the square total energy of the system remains the same at of the speed. This is definition of the kinetic all time. energy. Conservative force: 1 W Fd cos KE mv 2 1.Conservative force keeps the total energy of a 2 system constant at all time. It only transforms F d Then, work-energy theorem can be deduced the energy from one form(i.e potential energy) F from the definition of work. to the other forms(i.e. Kinetic energy). 2. the work it does moving an object between Wnet KE two points is the same no matter what path is d Work doesn’t happen by itself. Work is done by This implies that net work changes kinetic taken. something on the object of interest. energy of the object of interest. W2 Work is a scalar quantity. W2 SI unit is J (joule) Here we used equation of motion under a W1 W1 The U.S. customary unit is the foot-pound. constant acceleration to derive work-energy Work can be positive or negative. theorem. But this is a valid under all W1 W2 If a force and a displacement are in opposite circumstances and if we use calculus, we can If work done by a force is different in the two directions, work is negative. derive the theorem for the case of a variable different paths shown above(left diagram), If a force and a displacement are perpendicular force as well. Energy is not conserved in the closed to each other, work is zero. system(right diagram). If a force and a displacement are in the same 5.3 Gravitational Potential Energy. 3. All fundamental forces are conservative direction, work is positive. Work done by gravity. forces. Also spring force is conservative. Wg mg ( y f yi ) Now from the definition of work, lets use some When we define upward is positive direction, Nonconservative force: tricks then from the work-energy theorem, 1.generally dissipative. 2.the work is path dependent. Wnet mg ( y f yi ) KE Wnet Fnet x 3. friction and external force by a person are 2 2 examples of nonconservative force. ( KE f KEi ) mg ( y f yi ) 0 v v0 (ma )( ) Strictly speaking, all forces are conservative. 2a from this equation we can deduce that PE mgy However, the nonconservative force transforms 1 1 Finally mv 2 mv02 energy to a form that is hard to measure. So, we 2 2 KEi PEi KE f PE f can not keep track of the energy transfer due to When work is done on a object, the speed is Thus, in any isolated system of objects the nonconservative forces. changing. The equation above shows that the interacting only through gravitational force, the 5.4 Spring Potential Energy Spring force is also a conservative force. According to Hooke’s law, Fx kx Where k is spring constant and its unit is N/m 5.6 Power Power: rate at which energy is transferred. Average power: P W Fv t Instantaneous Power: P Fv The work done by the spring force is 1 Ws kx 2 2 1 Ws k ( x 2f xi2 ) 2 KE From this equation, 1 PE kx2 2 When we include gravitational force and nonconservative force to the equation, Wnc Wg Ws KE Wnc ( KE f KEi ) ( PE gf PE gi ) ( PE sf PE si ) This is the key equation we will use in this chapter. This is the equation of the conservation of mechanical energy. At this point, we can now know that work transfers energy from one object to the other object. SI unit W(watt) Unit in the US horsepower(hp) 1hp = 746 W 5.7 Work done by a varying force. Area under F vs. x curve is the work done by the force. An Eskimo returning from a successful fishing trip pulls a sled loaded with salmon. The total mass of A 1.00 x103-kg elevator car carries a maximum load of the sled and salmon is 50.0 kg and the Eskimo 8.00 x 102 kg. A constant frictional force of 4.00 x exerts a force of magnitude 1.20 x 102 N on the 103 N retards its motion upward. What minimum sled by pulling on the rope. How much work does power, in kilowatts and in horsepower, must the he do on the sled if θ=30.0° and he pulls the sled motor deliver to lift the fully loaded elevator car 5.00 m at a constant speed of 3.00 m/s? A 0.500 kg block rests on a horizontal, frictionless surface as in the figure below. The block is pressed back against a spring having a constant of k=625 N/m, compressing the spring by 10.0 cm to point A. Then the block is released. (a) find the maximum distance d the block travels up the frictionless incline if θ=30.0°. (b) how fast is the block going at half its maximum height?