Work, Energy & Power PDF

Work, Energy & Power The Concept of Work When a man moves from one point to another carrying a load, the man has performed work, but when a boy carries a load for 2 hours without moving from one point to another, no work has been done. Therefore, for work to be done, force must be applied to a bod...

Work, Energy & Power The Concept of Work When a man moves from one point to another carrying a load, the man has performed work, but when a boy carries a load for 2 hours without moving from one point to another, no work has been done. Therefore, for work to be done, force must be applied to a body through a particular distance. Therefore, work is said to be done whenever a force moves a body through a distance in the direction of the force. Or Work is defined as the product of the force and its perpendicular distance moved in the direction of the force. Work done = force x distance in the direction of the force = force x displacement = Newton x metre = Nm Also, Remember that Force = mass x acceleration Therefore, Work done can also be written as mass x acceleration x displacement The S.I unit of work is joule (J) or Newton metre (Nm) Example i. A man applied a force of 20N to a cart which moved through a distance of 15m. Calculate the work done by the man. Solution: F = 20N, distance = 15m Work done W = Force F x dsitance d = 20N x 15M = 300Joules. ii. If the work done by a force on an object is 30J and the distance moved by the object is 1.45m, calculate the amount of force that was applied on the object. Solution: Work done = 30J, distance = 1.45m Work done W = Force F x dsitance d Force = 20.67N iii. Calculate the amount of work that is done when a force of 35N moves a 12kg mass through a distance of 1.25 m. Solution: mass = 12kg, force = 35N distance = 1.125 Formula for work done = Force x distance = 35 x 1.25 = 43.75 J When a force F is applied at an inclined angle θ to a body at an angle θ Work done = F x dθ = Fdcosθ When a body is lifted to a height, h, work is done against gravity, hence the work done, w = weight of the body x height w = mg x h w = mgh Where, m = mass of the body g = acceleration due to gravity h = height to which the body is raised Example: 1. A boy of mass 80kg runs up a staircase of 30 steps each of 15cm. Calculate the work done by the boy. (g = 10ms-2). Solution Work done = Force x distance F = mg = 80 x 10 = 800N Distance = 0.15 x 30 = 4.5m Work done = mg x h = 800 x 4.5 = 3600 Joules. 2. A force of 50N is inclined at an angle of 30° makes a wheelbarrow to move through a distance of 40m. Calculate the work done. Solution Work done = Force x distance distance = dcosθ = 40cos30° = 40 x 0.8660 Work done = Force x distance = 50 x 40 x 0.8660 = 1732 J Energy Energy is the ability to do work. It is a scalar quantity and is always measured in Joules. There are different forms of energy and these include: Chemical Energy: Energy stored in the chemicals which is used as food or as chemicals in giving light energy. It is also easily converted to heat. Mechanical Energy: Energy due to motion or rest. Position of a body. Nuclear Energy: Energy stored in the nucleus of atoms which can be used to generate heat. Sound Energy: Energy produced by the vibration of air particles Hydro Energy: Energy produced from water at a particular height. Solar Energy: Energy produced from the sun. Potential & Kinetic Energy Mechanical energy is divided into potential and kinetic energy. Potential Energy: Potential Energy is the energy possessed by a body by virtue of its position at rest. The object is usually stationary or at rest. Such energy is used to do work when the body is free to move. For example, when a metal flask is placed on top of a table, it has potential energy. When allowed to fall on a flat glass mirror on the floor, it will shatter the mirror. Potential energy is expended in shattering the mirror. When a body of mass (m) is lifted, vertically upwards to a height ‘h’, the work done, w, against the gravity by the weight of the body, the body is said to possess gravitational potential energy. Gravitational potential energy, P.E = weight x height = mg x h P.E = mgh Examples: i. A boy lifts a load of mass 30kg to a height of 5m. Calculate the potential energy of the body. (g = 10ms-2). Potential Energy = mgh m = 30kg, h = 5m, g = 10ms-2 Potential Energy P.E = mgh = 30 x 10 x 5 = 1500 Joules. ii. Calculate the potential energy of an apple at the top of an apple tree 14.2m high, if the mass of the mango is 0.55 kg. (g = 10 m/s² ) P.E = mgh m = 0.55kg, h = 14.2m, g = 10ms-2 Potential Energy P.E = mgh = 0.55 x 10 x 14.2 = 78.1 Joules. iii. An object of mass 15kg has 55 Joules of energy at a particular height. Calculate the height. (g = 10 m/s² ) Mass = 15 kg, P.E = 55J, g = 10 m/s², h = ? P.E = mgh make h the subject of the formula h = 0.366m Kinetic Energy: Kinetic energy is the energy possessed by a body by virtue of its motion. It is a scalar quantity and is also measured in Joules. If a body of mass, m, moves with a velocity, v, the kinetic energy of the body is m = mass of the body in kilogram (kg) v = Velocity of the body in ms-2 Examples: i. A car of mass 25kg is moving with a speed of 15ms-1. Calculate its kinetic energy. = 2812.5 Joules. ii. The Kinetic Energy of a car is 550J. If the mass of the car is 3.75 kg, calculate the velocity of the car. K.e = 550 J, m = 3.75kg, v = ? v = 17.3 m/s