Work done, Energy and Power JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS WORK, ENERGY AND POWER 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 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 Ek = ½ mv2 (f) recall and use the equation Ek = ½ mv2 (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 defini tion 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

2 Introduction This topic involves the core ideas of Conservation Laws as well as Systems and Interactions. The concept of energy is one of the most important concepts in Science. Energy is present in various forms. The transformation of energy from one form to another and its conservation are essential in the study of physics. The concept of work links energy and force. Work is a means of transferring energy through application of a force. The concepts of work and energy can be applied to the dynamics of a mechanical system without resorting to Newton’s laws. Beyond mechanics, this approach can be applied in a wide range of phenomena in electromagnetism, thermal and nuclear physics. In addition, the energy approach often provides a simpler analysis than direct application of Newton’s laws because (1) energy is a scalar whereas force is a vector, and (2) only the initial and final states of a situation need to be considered without involving the intermediate processes. 1 Work (a) define and use work done by a force as the product of the force and displacement in the direction of the force 1.1 Definition of Work 1.2 Work done by a constant force If the force acting on the object is constant in magnitude and direction throughout the motion of the object, then the work done W by a force F in moving an object through a displacement s is where W is the work done on the object by the constant force F (unit: J) F is the magnitude of the constant force acting on the object (unit: N) s is the displacement of the object (unit: m)  is the angle between F and s Fig.1 to Fig. 4 show different scenarios which the equation above can be applied. The work done by a force on a n object is defined as the product of the force and the displacement of the object in the direction of the force. F  s Fig. 1: Constant force at an angle  to the displacement displacementdisplacement F  initial position final position s  F W = Fs cos W = Fs cos

3 NOTE:  The SI unit of work done is the joule (J). One joule (1 J) is defined as the work done by a force of one newton (1 N) when its point of application moves through a displacement of one metre (1 m) in the direction of the force. Work done = (1 N) (1 m) (cos 0°) = 1 J  Work done is a scalar quantity. F s Fig. 3: Constant force 90° to the displacement displacementdisplacement F initial position final position 90° s F W = Fs cos(90°) = 0 90° 90° F s Fig. 4: Constant force opposite to the displacement displacementdisplacement F initial position final position W = Fs cos = Fs cos(180°) = −Fs s F 180° F s Fig. 2: Constant force in the same direction as the displacement displacementdisplacement F initial position final position s F W = Fs cos = Fs cos(0°) = Fs

4 Example 1 The figure below shows a man pulling a box of mass 20 kg with a constant force of 50 N at an angle  of 35° to the ground. The box moves through a horizontal distance of 10 m and the frictional force between the box and the ground is 11 N. Determine the work done by the following forces on the box: (a) The force applied by the man. (b) The frictional force on the box. (c) The normal contact force on the box by the ground. (d) The gravitational pull by Earth. (e) The resultant force on the box. Solution (a) Work done by the force applied by the man = (50) (10) (cos 35°) = 410 J (b) Work done by the frictional force = (11) (10) (cos 180°) = −110 J (c) Work done by normal contact force = (N) (10) (cos 90°) = 0 J (d) Work done by gravitational pull = (W) (10) (cos 90°) = 0 J (e) Work done by resultant force = (FR) (s) (cos  ) = (Fcos − f) (10) (cos 0°) = (50 cos 35° − 11) (10) = 300 J Alternatively, Part (a) to (d) constitute all the forces acting on the box. Hence the sum of all the work done by each of the force is also the work done by the resultant force on the box. Work done by resultant force = (a) + (b) + (c) + (d) = 410 + (−110) + 0 + 0 = 300 J

5 NOTE:  If a force F is in the same direction as the object’s displacement, or has a component in the same direction as the object’s displacement, the work done by force F on the object is positive.  If a force F is in the opposite direction to the object’s displacement, or has a component in the opposite direction to the object’s displacement, the work done by force F on the object is negative.  Work is a process of transferring energy through the application of a force. If the work done on an object is positive, it means energy is transferred to the object. If the work done is negative, it means energy is transferred out from the object. In Example 1, the 50 N forc e exerted by the man on the box results in the man transferring energy to the box. This could be in the form of kinetic energy if the man is pulling a box which is initially at rest, until the box reaches a certain final velocity. On the other hand, the 11 N frictional force exerted on the box results in energy being removed from the box. This is in the form of heat loss to the surroundings. Hence the box cannot reach a higher speed than it could have if the frictional force was absent.  Work done on an object by a force A statement like ‘Determine the work done on the box’ is not clear as there are many forces acting on the box. A statement like ‘Determine the work done on the box by the man when pulling the box’ should be interpreted as ‘Determine the work done on the box by the force exerted by the man when pulling the box’. A statement like ‘Determine the work done on the box by Earth should be interpreted as ‘Determi