Work, Energy, Power and Conservation Laws. In this week we will introduce the following concepts: o Kinetic energy of a moving object o Work done by a force o Power o Potential Energy o Conservative and non-conservative forces o Mechanical Energy o Conservation of Mechanical Energy The conservation of energy theorem will be used to solve a variety of problems (7-1)

o In addition we will develop the work-kinetic energy theorem and apply it to solve a variety of problems o This approach uses scalars such as work and kinetic energy rather than vectors such as velocity and acceleration. Therefore it simpler to apply. o It cannot be used to solve all problems, particularly those which demand an answer involving position as a function of time. But it is best to try to use it first.

Kinetic Energy: We define a new physical parameter to describe the state of motion of an object of mass m and speed v We define its kinetic energy K as: We can use the equation above to define the SI unit for work (the joule, symbol: J ). An object of mass m = 1kg that moves with speed v = 1 m/s has a kinetic energy K = 1J Work:(symbol W) If a force F is applied to an object of mass m it can accelerate it and increase its speed v and kinetic energy K. Similarly F can decelerate m and decrease its kinetic energy. We account for these changes in K by saying that F has transferred energy W to or from the object. If energy it transferred to m (its K increases) we say that work was done by F on the object (W > 0). If on the other hand. If on the other hand energy its transferred from the object (its K decreases) we say that work was done by m (W < 0) (7-2) m m

(7-3) m m

m m (7-4)

m m Work-Kinetic Energy Theorem (7-5)

A B (7-6)

(7-7) A B m.

Work Done against Friction So work done is W = Force x distance =   R d Where    is the coefficient of dynamic friction  R = mg is the force down (due to gravity)  d is the distance pushed 10kg F d Push a weight at constant speed against friction over a surface

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(7-10) O(b) xixi x O(c) xfxf x O (a) x

O x y z A B path (7-11)

.. O x-axis x dx F(x) AB m (7-12)

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(7-14) v