iSucceed Quick Study Notes, Work and Energy.pdf
The document "Work and Energy.pdf" serves as an introductory resource to core principles in physics. It meticulously defines work as the energy transferred when a force acts on an object and causes its displacement, emphasizing the component of force along the direction of motion. The document likely differentiates between positive work (force aids displacement), negative work (force opposes displacement), and zero work (force perpendicular to displacement or no displacement occurs). Energy, the capacity to do work, is then explored in its various manifestations, including kinetic energy (associated with motion, quantified as 1/2 * mass * velocity squared) and potential energy (stored energy due to an object's position or configuration, such as gravitational potential energy, mgh). The crucial work-energy theorem, linking the net work done on an object to its change in kinetic energy, is likely discussed. Furthermore, the principle of conservation of energy, a cornerstone of physics stating that energy cannot be created or destroyed within an isolated system but can only be transformed from one form to another, is likely elaborated upon with illustrative examples of energy conversions. Finally, power, defined as the rate at which work is done or energy is transferred (work/time or energy/time), is introduced as a measure of how quickly energy is used or produced. In essence, "Work and Energy.pdf" provides a foundational overview of these interconnected concepts, crucial for understanding mechanics and other branches of physics
iSucceed Quick Study Notes, Work and Energy.pdf
- 1. Quick Study Notes Work and Energy 1 Work Work is said to be done, if an applying a force on an object, it is displaced from its position in the direction of force. Its Sl unit is newton-metre which is also called joule. Scientific Conception of Work From the point of view of science, following two conditions need to be satisfied for work to be done. i. A force should act on an object. ii. The object must be displaced. If any one of the above conditions does not exist, work is not done. e.g., A girl pulls a trolley and the trolley moves through a distance. In this way, she has exerted a force on the trolley and it is displaced. Hence, work is done. Work Done by a Constant Force Work done by a force on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of force. Work done = Force × Displacement in the direction of force or W = Fs Positive, Negative and Zero Work When the force F and displacement s are in the same direction (angle between direction of force and displacement is 0°), work done will be positive, i.e., work is done by the force. e.g., A boy pulls an object towards himself. W = + F × s When the force F and displacement s are in opposite direction (angle between direction of force and displacement is 180° ) work done will be negative, i.e., work is done against the force. e.g., Frictional force acts in the direction opposite to the direction of displacement, so work done by friction will be negative. W = - F × s When the force and displacement are in perpendicular direction (angle between direction of force and displacement is 90° ) work done is zero. e.g., A coolie carrying load on his head. In this case, gravitational force is acting vertically downward (Weight of load) and displacement is along horizontal direction, i.e., force and displacement are perpendicular to each other. Thus, work done by gravitational force is zero. W = 0 Energy It is the ability to do work. It is always essential for performing any mechanical work. The energy of an object is measured in terms of its capacity of doing work. The SI unit of energy is Joule (J). Forms of Energy Energy exists in various forms like mechanical energy (the sum of kinetic + potential), heat energy, chemical energy, electrical energy, light energy, etc. Kinetic Energy The energy which is possessed by an object due to its motion is called kinetic energy. Its St unit is Joule (J). Calculation of Kinetic Energy The kinetic energy of an object moving with a certain velocity is equal to the work done on it to make it acquire that velocity. Consider an object of mass m moving with a uniform velocity u. A force F is applied on it which displaces in through a distance s and it attains a velocity v. Then, work is done to increase its velocity from u to v. W = Fs ………………………………………………………..(i) According to the third equation of motion, v2 – u2 = 2as s = – ……………………………………….………..(ii) where, a is uniform acceleration, u is initial velocity and v is final velocity. Also, from, F = ma ………………………………………….(iii) Substituting the values of F and s from Eqs. (ii) and (iii) in Eq. (i), we have,
- 2. Quick Study Notes Work and Energy 2 𝑊 = 𝑚𝑎 . or 𝑊 = 𝑚 (𝑣 − 𝑢 ) This is known as work-energy theorem (i.e., total work is equal to change in kinetic energy). If initial velocity, u = 0 Then, W = 1/2 × m × v2 This work done is equal to the kinetic energy of the object. KE = 1/2 × m × v2 Potential Energy • The energy possessed by a body due to its change in position or shape is called potential energy. • Its Sl unit is Joule (J). Potential Energy of an Object at a Height When a work is done is raising the height of an object, energy transferred as a gain in the gravitational potential energy of the object. The gravitational potential energy of an object of mass m at a height is given by the relationship Ep = mgh Law of Conservation of Energy • The principle of conservation of mechanical energy states that if only the conservative forces are doing work on a body, then its total mechanical energy remains constant. • Although, the kinetic energy and potential energy may change individually from one state of the system to another, but their sum of the total mechanical energy of the system remains constant under the conservative force. • When on object is dropped from some height, its potential energy continuously converts into kinetic energy. When an object is thrown upwards, its kinetic energy continuously converts into potential energy Transformation of Energy One form of energy can be converted into other form of energy and this phenomenon is called transformation of energy. Some energy transformations are as follows: S.No. Device Transformation 1 Electric Motor Electrical energy into Mechanical energy 2 Electric Generator Mechanical energy into Electrical energy 3 Steam Engine Heat energy into Kinetic energy 4 Electric Bulb Electrical energy into Light energy 5 Dry Cell Chemical energy into Electrical energy 6 Solar Cell Light energy into Electrical energy Rate of Doing Work: Power The rate of doing work or the rate at which energy is transferred or used or transformed to other formed is called power. If work W is done in time, t then, 𝑃𝑜𝑤𝑒𝑟 (𝑃) = 𝑊𝑜𝑟𝑘 (𝑊) 𝑇𝑖𝑚𝑒 (𝑇) Its Sl unit is Watt (W). Average Power • It is defined as the ratio of total work done by the total time taken, • An agent may perform work at different rates at different intervals of time. In such situation, average power is considered by dividing the total energy consumed by the total time taken. 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑜𝑤𝑒𝑟 = 𝑇𝑜𝑡𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛