Lesson 3 Work, Power & Energy PDF
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Uploaded by OptimalMelodica8110
Singapore Polytechnic
2023
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This document is a set of examples for work, power and energy in mechanics. It includes different examples of problems and solutions for energy conservation principle.
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Lesson 3 – Work, Power & Energy 2-13 Lesson 3 Topic 2 - Work, Power & Energy Objectives: At the end of this lesson, students should be able to: a) Understand the relation...
Lesson 3 – Work, Power & Energy 2-13 Lesson 3 Topic 2 - Work, Power & Energy Objectives: At the end of this lesson, students should be able to: a) Understand the relation between Work, Energy & Power State the Principle of Conservation of Energy. Solve problems involving the different forms of mechanical energy using the Principle of Conservation of Energy. Mechanics II (ME2101) DL/GKS Version 4.1 (April 2023) 2-14 Lesson 3 – Work, Power & Energy 2.9 Principle of Conservation of Energy The Principle of Conservation of Energy states that: energy cannot be created or destroyed. The form of energy may change, but the total quantity of energy in a system remains constant. For example, when a body falls through a height above the ground, it loses potential energy but gains kinetic energy. After striking the ground, the kinetic energy does not disappear but is converted to other forms of energy such as heat and sound energy, or is used to do a certain amount of work. The Principle of Conservation of Energy may be expressed in the following form: (PE0 + KE0 + SE0) + W.D. = (PE1 + KE1 + SE1) where PE0 + KE0 + SE0 = initial energy of body PE1 + KE1 + SE1 = final energy of body W.D. = net work done on the body The net work is the sum of positive work done on the body by forces acting in the direction of motion and the negative work done by the body against resisting forces, e.g. friction, braking forces, etc. Note: W.D. excludes work done by weight (gravity) on the body as this will be accounted for by the change in P.E. DL/GKS Mechanics II (ME2101) Version 4.1 (April 2023) Lesson 3 – Work, Power & Energy 2-15 Example 2.6 A 4-wheeled car of mass 900 kg is accelerated from 54 km/h to 90 km/h after travelling a horizontal distance of 100 m. Determine the tractive effort required if the resistance to motion is 200 N and each of its axles together with its two wheels has a moment of inertia of 15 kgm2 and the wheel diameter is 0.8 m. v0 v1 Wheel data v Mechanics II (ME2101) DL/GKS Version 4.1 (April 2023) 2-16 Lesson 3 – Work, Power & Energy Example 2.7 A 4-wheeled vehicle of total mass 1500 kg is accelerated from rest to a speed of 72 km/h after travelling a distance of 400 m up an incline of 1 in 10. It has two axles, each of which together with the wheels has a mass of 150 kg and radius of gyration of 400 mm about its axis of rotation. The wheel diameter is 1.0 m. The resistance to motion is 500 N. Calculate the tractive effort required. Solution: v1 v0 DL/GKS Mechanics II (ME2101) Version 4.1 (April 2023) Lesson 3 – Work, Power & Energy 2-17 Example 2.8 A lift cage of mass 250 kg descends from rest under the action of its own weight through a height of 10 m in a time of 4 s as shown in the figure below. Determine the frictional torque in the flywheel bearings. Flywheel I = 5 kgm2 axle 120 mm m 10 m Mechanics II (ME2101) DL/GKS Version 4.1 (April 2023) 2-18 Lesson 3 – Work, Power & Energy Lesson 3 Tutorial Topic 2 - Work, Power & Energy Q2.7) A trolley with four wheels has a total mass of 200 kg. Each wheel has a moment of inertia of 1.5 kgm² and a diameter of 0.5 m. The trolley moves with a speed of 5 m/s down a 30 incline against a constant resistance of 58 N acting up the plane. Find the velocity of the trolley after it has moved 6 m down the incline. (7.9 m/s) Q2.8) A vehicle has a total mass of 1500 kg and moves up an inclined track making an angle of 10 to the horizontal. It starts from rest with a tractive effort of 3.8 kN up the plane for the first 500 m. After that, no more tractive effort is applied. The vehicle has two axles, each with its two wheels has a mass of 110 kg and radius of gyration of 320 mm about its axis of rotation. The diameter of each wheel is 800 mm. If the tractive resistance is 300N, find the: a) velocity of the vehicle at the end of 500 m. b) furthest distance it could move up the incline after the tractive effort is removed. (24 m/s; 165.5 m) Q2.9) A four-wheeled car of mass 1000 kg descends a slope of 1 in 6. Each axle of the car with its two wheels has a radius of gyration of 400 mm and a mass of 120 kg. If the diameter of the wheel is 900 mm, and the tractive resistance is 200 N, determine the: a) moment of inertia of two wheels and its axle about its rotation axis. b) total kinetic energy of the car if it is moving with a speed of 48 km/h. c) braking force required to bring the car to rest in 18 m from an initial velocity of 48 km/h. (19.2 kgm2; 105.7 kJ; 7306.6 N) DL/GKS Mechanics II (ME2101) Version 4.1 (April 2023) Lesson 3 – Work, Power & Energy 2-19 Q2.10) A vehicle is accelerated from rest to a velocity of 14 m/s in a distance of 110 m up an incline of 1 in 8. The total mass of the vehicle (inclusive of wheels and axles) is 1500 kg and it has two axles, each of which together with the wheels has a mass of 120 kg, radius of gyration of 350 mm and a tread diameter of 800 mm. The resistance to motion is 200 N/tonne. Calculate, for the speed of 14 m/s, a) the kinetic energy of translation of the vehicle. b) the kinetic energy of rotation of the wheels and axles. c) the total kinetic energy of the vehicle. d) the tractive effort required by using the energy principle. e) the power required. (147 kJ; 18.01 kJ; 165.01 kJ; 3639 N; 50.9 kW) Q2.11) A 4-wheeled vehicle of total mass 1500 kg is accelerated from rest to a speed of 72 km/h on travelling a distance of 400 m up an incline of 1 in 10. It has two axles, each of which together with the wheels has a mass of 150 kg and radius of gyration of 400 mm about its axis of rotation. The wheel diameter is 1 m. The resistance to motion is 500 N. Calculate, for the speed of 72 km/h, a) the kinetic energy of translation of the vehicle. b) the kinetic energy of rotation of the wheels and axles. c) the total kinetic energy of the vehicle. d) the tractive effort required by using the energy principle. e) the power required. (300 kJ; 38.4 kJ; 338.4 kJ; 2817.5 N; 56.35 kW) Q2.12) A wheel and axle having a total mass of 90 kg and radius of gyration of 250 mm about its axis is mounted in horizontal frictionless bearings (i.e. no work is done against frictional torque). The diameter of the axle is 76 mm. Around the axle is wrapped a light cord from which is hung a mass of 16 kg. When the wheel has turned through 8 revolutions from rest, the cord becomes detached from the axle. Calculate the: a) kinetic energy stored in the wheel and axle when the cord becomes detached; b) subsequent number of revolutions made by the wheel before coming to rest if a retarding torque of 3 Nm is then applied to the axle. (298.58 J; 15.84 revs) ******************** Mechanics II (ME2101) DL/GKS Version 4.1 (April 2023)