EJC Physics H205 WEP 2023 1. Notes (FULL)

Content • Work • Energy conversion and conservation • Efficiency • Potential energy and kinetic energy • Power Learning Outcomes Candidates should be able to: (a) define and use work done by a force as the product of the 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 = pΔV (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 Ek = ½mv2 (f) recall and use the equation Ek = ½mv2 (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 Ep = mgh for gravitational potential energy changes near the Earth’s surface (k) recall and use the equation Ep = 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 a force and velocity in the direction of the force * Not required for 8867 H1 Physics, will be revised in greater details in H2 Topic 9: First Law of Thermodynamics ^ Will be dealt with in H2 Topic 13: Electric Fields Richard Feynman in 1961 said, “there is a fact, or if you wish, a law, governing all natural phenomena that are known to date . There is no known exception to this law —it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.”

Sometimes, trying to analyse Physics scenarios using forces can be very complicated – there may be many forces or there are many interactions between various forces. Using the relationships between work, energy and power can be an alternative to deciphering the Physics. In Physics, work has a very specific meaning: As both force F and displacement s are vector quantities, the angle θ helps to manage the information concerning direction. Mathematically, the operation is known as the dot product or scalar product of 2 vectors: W F.s= We can interpret the above either of two ways: the product of • the displacement and • the component of force cos//FF = along the same direction as the displacement the product of • the force and • the component of displacement cos//ss = along the same direction as the force The S.I. unit for work done is joule (J). 1 J is defined as the work done when a force of 1 N moves its point of application through a distance of 1 m in the direction of the force.  force exerted  force exerted  force exerted  weights displaced by force  wall not displaced by force  wall displaced by force  work is done by force of man on weight  no work done by force of man on wall  work is done by force of man on wall s F θ s F θ Work done by a force is the product of the force and the displacement in the direction of the force. by force cosW Fs =

Example 1 Calculate the work done by force F below where the body moves 2.0 m to the right: Notes: Work is a process that causes energy transfer to or from a body. Positive work done on a body result in mechanical energy being transferred to the body, and hence the body gains energy. Negative work done in (d) and (e) show mechanical energy being transferred away from the body. So, if the body was already moving to the right with constant speed (there fore constant kinetic energy) and then a leftward braking force is applied across 2.0 m of displacement - the body will lose kinetic energy. Solution force is same direction with displacement force is perpendicular to displacement no work done (a) F = 10 N 2.0 m F = 10 N (b) F = 10 N 2.0 m 60 o F = 10 N 60 o (c) F = 10 N 2.0 m F = 10 N (d) F = 10 N 2.0 m 60 o F = 10 N 60 o (e) F = 10 N 2.0 m F = 10 N

In general: If a force is constant, then • area under the F-s graph is a simple rectangle • the area can be found by “length  height” • which reduces to the equation given in 5.1. We regard each small rectangular strip as having width s over which a force F acts: Consider a gas enclosed in a cylinder of cross -sectional area A fitted with a light, frictionless piston. When the gas expands against an external pressure, it does work against external pressure. We imagine the gas “exerting” a force against external pressure as the piston is displaced “outwards” ( )( ) ( )( ) ( )( ) by cos x pA x p A x V W Fs F p   = = = =  = The equation above assumes that the external pressure remains constant. In the event that pressure is not constant, we can apply the same principle as Section 5.1.1, and the work done by the expanding gas is given by the area under the pressure-volume graph. s s s s s s work done The area under a force-displacement graph is the work done by the force. external pressure (enclosed gas) expand Work done by gas, ( )  =− =by final initialp V V VpW x p s V s s work done p : external pressure (Pa) Vinitial : initial volume (m-3) Vfinal : final volume (m-3)

When dealing with problems involving the motion of a body, we typically consider the mechanical energy, which includes kinetic energy and potential energy. For H2 Physics, we concentrate on translational motion and the associated kinetic energy. H2 Physics does not equip us with sufficient tools to analyse rotational motion, such as the rotational kinetic energy associated with a cylinder rolling down a slope. Students who are interested can read up about moment of inertia, angular momentum, and the Newton’s 2 nd Law equivalent for rotation . You may also wish to consider offering H3 Physics. Derivation Consider a mass m that is displaced by a displacement s by a constant net force F on a smooth, horizontal surface. It has an initial velocity u and final velocity v: Since work done by force F results in the object’s kinetic energy (only, not potential energy) thus K K, final K, initial EEWE −== If mass is initially at rest (u = 0) then 0K,initialE= and kinetic energy of the object, 2 K 1 2E mv= smooth surface Mass experiences constant acceleration due to constant force Work done on mass by force F is m m s F F u v Kinetic energy is the energy possessed by a mass due to its speed/motion. 2 K 1 2E mv= EK : kinetic energy (J) m : mass (kg) v : velocity (m s-1)

The above equation PE mgh= does not provide an absolute value for the gravitational potential energy. The zero reference for height h can be chosen and is often taken to be at Earth’s surface. Derivation Consider a mass inside a uniform gravitational field of field stren