RI 2022 Work, Energy and Power

Chapter 5 RAFFLES INSTITUTION YEAR 5-8 PHYSICS DEPARTMENT WORK, ENERGY AND POWER Content • Work • Energy conversion and conservation • Potential energy and kinetic energy • Power Learning Outcomes . Candidates should be able to: (a) (b) (c) (d) (e) (f) define and use work done by a force as the product of the force and displacement in the direction of the force. 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 1. give examples of energy in different forms, its conversion and conservation, and apply the principle of energy conservation. show an appreciation for the implications of energy losses in practical devices and use the concept of efficiency to solve problems. derive, from the equations for uniformly accelerated motion in a straight line, the equation EK= ~mv2. 2 1 recall and use the formula EK = -mv2. 2 (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 rela~ionship between force and potential energy in a uniform field to solve problems. 0) derive, from the definition of work done by a force, the formula EP = mgh for gravitational potential energy changes near the Earth's surface. (k) recall and use the formula Ep = mgh for potential energy changes near the Earth's surface. (I) define power as work done per unit time and derive power as the product of a force and velocity in the direction of the force. 1 Italicized part, i.e. work done by an expanding gas is not in the H1 syllabus. 1

5.1 5.1.1 Work done by a Constant Force on a System Definition Note Definition Introduction RAFFLES INSTITUTION YEAR 5-6 PHYSICS DEPARTMENT Energy is one of the most fundamental concepts in science, and is discussed in the context of Newtonian mechanics. Energy is present in various forms, w~h endless conversion from one form to another. The conservation of energy is an essential principle in Physics. The concept of work links energy and force, as work is a means of energy conversion through the application of a force. In certain situations, the concepts of work and energy can be applied to solve the dynamics of a mechanical system without directly resorting to Newton's laws. Beyond mechanics, this problem-solving approach focusing on energy can be applied to a wide range of phenomena in electromagnetism, and thermal and nuclear physics. The work-energy approach often provides a much simpler analysis than that obtained from the direct application of Newton's laws, since the former deals with scalar rather than vector quantities. In this section, we will discuss the concept of work. Work Done b a Constant Force on a S stem In scientific terms, work is done by a force on an object when the object is moved in the direction of the force. A constant force F acts on a box below at an angle B to the horizontal and displaces it horizontally to the right over a displacement s. . . s ----------.. I I I I I I • I I ----r ---·-I I The work done on a given system by a constant force F is given by I W= Fscose Work done by a constant force is the product of the force and the displacement in the direction of the force. • When the component of F (FcosB) is in the same direction as the displacement, the work done by the force is positive as cosB > 0. • When the component of F (FcosB) is in the opposite direction to the displacement, the work done by the force is negative as cosB < 0. • The component Fsin B of the force is perpendicular to the displacement, hence no work is done by this component. • Work is a scalar quantity and its S.I. unit is the joule (J). 1 J is the work done on an object by a force of 1 N when the object is displaced by 1 m in the direction of the force. 2

Example 1 5.1.2 RAFFLES INSTITUTION YEAR 5-6 PHYSICS DEPARTMENT A force F of 50 N is applied on a box of mass 4.0 kg at an angle of 35° to the horizontal for a displacements of 0.800 m horizontally. A constant frictional force f of 25 N acts on the box. Calculate the work done on the box, by the a) applied force F, F b) frictional force f, and c) normal force N from the ground. lAJ \,J ~(.o)e)) :., 10 lb)½~ ;.u-~ :. ~i.£3 C.,sf) b) w ::.[cos l~J s ) -:. <.i~ 1L--n( o,&~ -: -}u .oJ ---------------f=25 N s = 0.800 m Work Done b a Variable Force on a S stem ·---------, I I I I I I I I I I I ,_ ----4----• Work Done by a If the force F acting on the body varies with displacement s, then the work done by Variable Force on the variable force F over a displacements, to s2 is calculated by applying: a System 5.1.3 Work Done on a Spring F (Note: F and s are parallel) work s S1 S2 Note that the work done by a variable force is equal to the area under the force - displacement graph. , . •. • ;. __ • . ..;. ... a~.;: .. ~.t:":-: • .. •µ•· • ,. Work Done b an· External Force on a S rin The external force F needed to produce an extension or compression x in a spring that obeys Hooke's Law is F = kx, where k is the spring constant. This force is a variable force as its magnitude depends on the extension or compression of the spring. From the graph, work done in stretching unextended spring by x = area under force-extension graph= ~Fx 2 Since F = kx, I W=ikx' I force F ------------ x extension The above expression can also be used when the spring is being compressed. 3

Example 2 5.1.4 Work Done by a Gas at Constant Pressure Note RAFFLES INSTITUTION YEAR 5-6 PHYSICS DEPARTMENT The loading of a spring and the unloading process take different paths in a force- extension graph as shown below. force ....,... __________ ...___,. extension 0 Which area represents the work done to extend the spring? Work Done b a Gas Consider a system of gas in a cylinder with a frictionless, movable piston. Suppose the gas is gently heated such that it expands slowly at constant pressure. I 6x ' force F on piston external pressure due to constant I gas pressure p ; \ l I : : I \ cylinder \piston Fig. 2 As the gas expands, a force Fis applied on the piston by the gas molecules to move the piston against the external pressure (also constant). The work done by force Fin displacing the piston of cross-sectional area A through a small distance is the work done by the gas2, Wgas- W9as = F~ = (pA)flX I Wgas = P ll.V where AdX = V, the change in volume. •· When the gas expands, work done by the gas is positive. • If the gas contracts, work done by the gas is negative. 2 will be covered in greater detail in H2 Chap 9: First Law of Thermodynamics. 4

Example 3 5.2 5.2.1 RAFFLES INSTITUTION YEAR 5-6 PHYSICS DEPARTMENT The gas in a cylinder is expanding against an external pressure of 1.01x105 Pa . The piston sealing one side of the cylinder has a cross-sectional area of 0.050 m2• Find the work done by the gas as the piston is pushed out by 1. 0 cm when it is slowly heated. J ~) , 0 nb\ :. <.. Lui 4f fJ ( o, O) 'f-O"' H ~D,')j Ener Different Forms of Ener . Fonns of Energy Energy is the capacity to do work. It exists around us in many different forms. Some of the common forms are shown in the table below. Form of Energy Examples Chemical potential energy -a form of • fuels such as oil, wood, coal potential energy related to the structural • electric cells, food and arrangement of atoms or molecules in a substance explosives Nuclear energy -energy released from • radioactive decays atomic nuclei • nuclear reactions (fusion, fission) Electrical energy -energy possessed by • the energy associated with charge carriers moving under the current in circuits and influence of a potential difference electrical appliances • power stations • charged capacitors Electric potential energy -energy due to •