25/01/2014. Chapter 4: Work, Energy and Power. Work of a force. Chapter 4: Work, Energy and Power (First part) Work = Force x Displacement

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1 5/0/04 Chapter 4: Work, Energy and Power King Saud University College o Science Physics & Astronomy Dept. Phys 45 (General Physics) Chapter 4: Work, Energy and Power (Part ) Week n 5 This presentation has been prepared by: Pr. Nabil BEN NESSIB We will learn in this chapter 4: Work and Energy Kinetic energy Potential energy Dissipative orces Power Chapter 4: Work, Energy and Power (irst part) We will learn in this irst part o chapter 4: Work and Energy Kinetic energy Potential energy Work o a orce The work done by a orce is deined as the product o the orce component and the displacement. Work = orce x Displacement In the S.I., work is in Joule (J), J = N xm. θ 3 Δx W(). x cos() x i and x are in the same direction: W() x 4

2 5/0/04 Work o a orce Example 5. Work o a orce Example 5. When a man carries a bucket o water دلو من الماء) ) horizontally at constant velocity, the orce does no work on the bucket: Displacement is horizontal and orce is vertical. cos 90 = 0 so W = 0 Work can be positive or negative: θ = 0, W > 0 Δx θ = 80, W < Work done against gravity Work done by multiple orces Example 5.3 Work (joules) W = mgh Mass (kg) Height object raised (m) W() mg. mg x mgcos(90) x 0 W() R. R x R cos(90) x 0 R θ Gravity (m/s ) W(). x cos() x m g Δx W W()()() mg W Rcos() W x net 7 8

3 5/0/04 Video 0 o Week 05: Work and energy Kinetic energy The total work done on an object by all the orces acting upon it is equal to the variation o its kinetic energy. W() net KE KE KEi We have: v a x v v so a x and W x ma x vi i i net net The kinetic energy o an object having a mass m and a velocity v is: KE 9 0 Kinetic energy Remember that: So: The KE is always positive. KE I the mass is doubled the KE is also doubled, but i the velocity is doubled the KE is quadrupled (KE is proportional to the square o the velocity). Kinetic energy Example 5.4 I the surace is smooth what is the speed o the block at the bottom o the incline? We have: W()() W0() R W mg sin(38) W mg mgl net KE KEi 0 L So: v glsin(38) gh m/s 3

4 5/0/04 Potential energy An object can store energy as the result o its position. Energy is the ability to do work, so one o the energy orm is the potential energy. This stored energy o position is reerred to as potential energy. Potential energy is the stored energy o position possessed by an object. Gravitational potential energy is the energy stored in an object as the result o its vertical position or height. The energy is stored as the result o the gravitational attraction o the Earth or the object. Reerence level or potential energy The reerence level is a location where the gravitational potential energy is zero. It must be chosen or each problem. The choice is arbitrary since the change in the potential energy is the important quantity. Once the position is chosen, it must remain ixed or the entire problem. PEgrav mgh where h is the height o the object. h 3 4 Total mechanical energy (TME) The total amount o mechanical energy is merely the sum o the potential energy and the kinetic energy. This sum is simply reerred to as the total mechanical energy (abbreviated TME). TME KE PE mgh Law o conservation o energy The total amount o mechanical energy is merely the sum o the potential energy and the kinetic energy. Or: TME i TME KEi PEi KE PE No new energy is created and no existing energy is destroyed. This is the principle o conservation o energy

5 5/0/04 Law o conservation o energy Example 5.5 I the surace is smooth what is the velocity at B i the initial velocity at A is zero? Video 0 o Week 05: Work and energy We will treat the problem with the law o conservation o energy: TMEA TMEB A mgha 0 mghb v g h h 4 m/s A B 0 m B 7 8 Conservative orce Video 03 o Week 05: Kinetic and potential energies Any orce that has the property that the work it does is the same or all paths between any two given points is said to be conservative orce. Gravitational, electrical and spring orces are examples o conservative orces. riction and many other orces are not conservative

6 5/0/04 Summary o week 05 Quiz or week 05 Work o a orce is: W(). x cos() x Kinetic and potential energies are respectively: KE PEgrav mgh A orce is conservative when its work between two points is independent o the path between the two points. Gravitational orce is conservative but riction is not. 6