H2 Work Energy and Power Lecture Notes

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 1 Chapter 5 WORK, ENERGY AND POWER Content  Work  Energy conversion and conservation  Potential energy and kinetic energy  Power Learning Outcomes Candidates should be able to: (a) show an understanding of the concept of work in terms of the product of a force and displacement in the direction of the force. □ □ □ (b) calculate the work done in a number of situations including the work done by a gas which is expanding against a constant external pressure: W p V . □ □ □ (c) give examples of energy in different forms, its conversion and conservation, and apply the principle of energy conservation. □ □ □ (d) show an appreciation for the implications of energy losses in practical devices and use the concept of efficiency to solve problems. □ □ □ (e) derive, from the equations for uniformly accelerated motion in a straight line , the equation 21 2 kE mv . □ □ □ (f) recall and use the equation 21 2 kE mv . □ □ □ (g) distinguish between gravitational potential energy, electric potential energy and elastic potential energy □ □ □ (h) deduce that the elastic potential energy in a deformed material is related to the area under the force-extension graph. □ □ □ (i) show an understanding of and use the relationship between force and potential energy in a uniform field to solve problems. □ □ □ (j) derive, from the definition of work done by a force, the equation pE mgh for gravitational potential energy changes near the Earth’s surface. □ □ □ (k) recall and use the formula pE mgh for gravitational potential energy changes near the Earth's surface. □ □ □ (l) define power as work done per unit time and derive power as the product of force and velocity in the direction of the force. □ □ □

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 2 5.1 WORK The way we use the term “work” in physics is different from the way it is used in everyday life. Work is done by a force on a body when the force causes a displacement of the body in the direction of the force.  Force exerted  Force exerted  Force exerted  Weights displaced by force X Wall not displaced by force  Wall displaced  Work is done X No work done  Work is done 5.1.1 WORK DONE BY A CONSTANT FORCE Symbol: W Unit: Joules (J) Calculating work done If a body is displaced by a constant force F at an angle θ from the displacement s, then the work done by the force, W, is cosW Fs  Definition of work done Work done by a force on a body is the product of the force and the displacement in the direction of the force. Graphical representation Graphically, the work done is given by the area under the Fs graph. Note: The component of the force perpendicular to displacement, sinF  , does not do any work.

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 3 Example 1 Calculate the work done by the 10 N force in each case.   = ____0____ ° Work done = ____20____ J   = ____30____ ° Work done = ____17____ J   = ____180____ ° Work done = ____-20____ J Work done by a force can be positive or negative. The significance of the sign for work done will be discussed in 5.2 Work Done and Energy. 5.1.2 WORK DONE BY A VARYING FORCE Determining work done when force is not constant If a body is displaced by a varying force, the work done by the force on the body is given by sW F ds Where Fs is the component of the force in the direction of displacement. Graphical representation Graphically, the work done is given by the area under the Fs graph. Example 2 Calculate the work done in each case. Work done = ___42___ J Work done = ___30___ J Work done = ___25.5___ J 10 N 2 m 10 N 2 m 30° 10 N 2 m

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 4 5.1.3 WORK DONE BY AN EXPANDING GAS Consider a gas enclosed in a chamber of cross sectional area A and fitted with a light frictionless piston. If the gas expands at constant pressure p, such that the volume changes by an amount ΔV, the force exerted by the gas on the piston, Fgp, is gpF pA and the displacement of the piston, Δx, is given by Vx A  The work done by the gas on the piston, Wgp, is ( )( ) gp gpW F x VpA A   Hence, gpW p V Determining work done by gas If the pressure is not constant, the work done by the gas is given by: Area under - graphgpW p dV p V Graphical representation Graphically, Wgp is given by the area under the p-V graph. Note: as the gas does positive work on the piston in expanding, the atmosphere is doing negative work on the piston. 5.1.4 WORK DONE AND ENERGY CHANGE When work is done, energy is converted from one form to another as a result. +W, positive work done –W, negative work done  Force is exerted on a body in the direction of its motion  Positive work is done on the body  Body gains energy.  Force is exerted on a body opposite to the direction of its motion (e.g. friction)  Negative work is done on the body  Body loses energy When body A does 100 J of work on body B, A loses 100 J of energy and B gains 100 J of energy. When body A does –100 J of work on body B, B loses 100 J of energy and A gains 100 J of energy. x A F p / Pa V / m3 Vi Vf p / Pa V / m3 Vi Vf

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 5 Example 3 Determine whether positive or negative work was done in each case. Superman exerts a force of 3.0 × 104 N on a passenger jet to tow it down a runway at a constant speed. What is the work done on the passenger jet when Superman tows it a distance of 10 m? Work done by Superman on the plane, WS on P S on P 4 5 cos30 (3.0 10 )(10)(0.866) 2.6 10 J W Fs    Superman has done ___________ J of work on the jet. Superman _________ energy and the passenger jet _________ energy. Work done by friction on the plane, Wf on P Since passenger jet is being pulled at constant speed, totalcos30Ff  f on P total 4 5 () ( 2.6 10 )(10) 2.6 10 J W f s       Friction has done ___________ J of work on the jet. The passenger jet _________ energy which is converted to heat energy due to friction. 5.2 ENERGY Energy is an indirectly observed property of a body; that means it cannot be directly measured with any instrument, and must be determined from other measurements. It is the ability or capacity of the body to do work on another body (causing it to lose energy in the process). Energy is a scalar quantity wi th no associated direction. Bodies in a system may possess the following types of energy. F s 30° s f f 30°

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 6 5.2.1 POTENTIAL ENERGY A body possesses potential energy when it has the potential to do work. Potential energy can be either positive or negative; the point of zero potential energy is used as a reference and depends on the definition of the specific type of potential energy. Hence, when analysing the change in energy of a body or system between two points, it is often more useful to talk about the change in potential energy rather than the value of potential energy. 5.2.1.1 ELASTIC POTENTIAL ENERGY When work is done by a force on an elastic body, it deforms and its shape changes. When the force is released, the deformation is restored. This allows the object to store elastic potential energy as a result of its deformation. In a spring, the change in length caused by a force is known as the extension. Both compression and extension of the spring are able to store elastic potential energy. The elastic potential energy is given by (More detail can be found in Chapter 4 Forces.) Example 4 Shade the area which represents the work done on the