JPJC 2026 Energy and Fields Lecture Notes Student

2026/JPJC/PHYSICS/9478 1 JURONG PIONEER JUNIOR COLLEGE 9478 H2 PHYSICS ENERGY AND FIELDS Content  Energy stores and transfers  Work done by a force  Kinetic energy  Concept of a field  Potential energy  Power and efficiency Learning Outcomes Candidates should be able to: (a) show an understanding that physical systems can store energy, and that energy can be transferred from one store to another (b) give examples of different energy stores and energy transfers, and apply the principle of conservation of energy to solve problems (c) show an understanding that work is a mechanical transfer of energy, and define and use work done by a force as the product of the force and displacement in the direction of the force (d) derive, from the definition of work done by a force and the equations for uniformly accelerated motion in a straight line, the equation 212kE mv (e) recall and use the equation 212kE mv to solve problems (f) show an understanding of the concept of a field as a region of space in which bodies may experience a force associated with the field (g) define gravitational field strength at a point as the gravitational force per unit mass on a mass placed at that point, and define electric field strength at a point as the electric force per unit charge on a positive charge placed at that point (h) represent gravitational fields and electric fields by means of field lines (e.g. for uniform and radial field patterns), and show an understanding of the relationship between equipotential surfaces and field lines (i) show an understanding that the force on a mass in a gravitational field (or force on a charge in an electric field) acts along the field lines, and the work done by the field in moving the mass (or charge) is equal to the negative of the change in potential energy (j) distinguish between gravitational potential energy, electric potential energy and elastic potential energy (k) recall that the elastic potential energy stored in a deformed material is given by the area under its force-extension graph and use this to solve problems

2026/JPJC/PHYSICS/9478 2 (l) derive, from the definition of work done by a force, the equation pE mg h   for gravitational potential energy changes in a uniform gravitational field (e.g. near the Earth’s surface)* (m) recall and use the equation pE mg h   to solve problems** (n) define power as the rate of energy transfer (o) show an understanding that mechanical power is the product of a force and velocity in the direction of the force (p) show an appreciation for the implications of energy losses in practical devices and solve problems using the concept of efficiency of an energy transfer as the ratio of useful energy output to total energy input. * Learning outcome (c) of topic Projectile Motion ** Learning outcome (d) of topic Projectile Motion

2026/JPJC/PHYSICS/9478 3 Introduction This topic explores the fundamental principles of Conservation Laws and Systems and Interactions, with a focus on energy stores, transfers, and the role of fields. Energy is stored in various ways, including kinetic, potential (gravitational, chemical, elastic), nuclear, and internal energy stores. Energy can be transferred from one store to another through different mechanisms such as mechanical work, electrical work, heating, and radiation. The concept of work is central to energy transfers, describing how energy moves between stores through the application of a force. In particular, fields—such as gravitational, electric, and magnetic fields—play a crucial role in energy transfers. Objects within a field experience forces that can cause energy to be stored or transferred. For example, an object in a gravitational field gains energy in its gravitational potential store when lifted, while charges in an electric field transfer energy as electrical work. Analysing energy stores and transfers allows us to describe physical systems without relying solely on Newton’s laws. This approach extends beyond mechanics to electromagnetism, thermal physics, and nuclear processes. Because energy is a scalar quantity, calculations are often more straightforward than those involving forces, which are vectors. Additionally, considering only the initial and final energy stores simplifies analysis by removing the need to track intermediate processes. By focusing on energy stores, transfers, and the role of fields, we gain a deeper understanding of a wide range of physical phenomena, making energy a unifying concept in science. 1 Work (c) show an understanding that work is a mechanical transfer of energy, and 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 an object is defined as the product of the force and the displacement of the object in the direction of the force. W = Fs cos

2026/JPJC/PHYSICS/9478 4 NOTE:  The S I 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. 1: Constant force at an angle  to the displacement displacementdisplacement F  initial position final position s  F W = Fs cos F s Fig. 3: Constant force 90° to the displacement 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

2026/JPJC/PHYSICS/9478 5 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 force