Work and Energy

This chapter gives the scientific meaning of work, energy and power. In science, work is done only when a force acts on an object and the object is displaced in the direction of the force, so W = F x s, measured in joules. You will see that work can be positive, negative, as when friction opposes motion, or zero, as when a person holds a heavy load without moving. Energy is the capacity to do work, and you will study its forms, especially mechanical energy: kinetic energy, the energy of motion, given by (1/2)mv^2, and potential energy, the energy due to position or shape, given by mgh for an object raised to a height h. You will learn the law of conservation of energy, that energy can only be converted from one form to another, and see that the total mechanical energy of a freely falling body stays constant. Finally, you will study power, the rate of doing work, measured in watts, and the commercial unit of energy, the kilowatt hour.

Detailed Worksheet: Work and Energy Section A - Definitions (10 marks) 1. Define work in the scientific sense. When is the work done on an object zero? (2 marks) 2. Define one joule. When is work negative? Give an example. (2 marks) 3. Define kinetic energy and potential energy and write their formulae. (2 marks) 4. State the law of conservation of energy. (2 marks) 5. Define power and one watt. What is a kilowatt hour? (2 marks) Section B - Calculations and Applications (15 marks) 6. A force of 7 N acts on an object, which is displaced by 8 m in the direction of the force. Find the work done. If the force acted opposite to the motion, what would the work be? (3 marks) 7. An object of mass 15 kg is moving with a uniform velocity of 4 m/s. What is its kinetic energy? What will its kinetic energy be if its velocity is doubled? (3 marks) 8. An object of mass 10 kg is raised to a height of 6 m. Find its potential energy. If it is allowed to fall, find its kinetic energy when it is halfway down. (Take g = 9.8 m/s^2.) (3 marks) 9. A girl of mass 40 kg climbs 8 m on a rope in 20 s. Find the work done and her power. (Take g = 10 m/s^2.) (3 marks) 10. A household uses a 1 kW electric heater for 2 hours a day, and four 60 W bulbs for 6 hours a day. Find the energy consumed in a 30-day month in kWh. If each unit costs Rs 7, find the bill. (3 marks) Section C - Diagrams (10 marks) 11. Draw a diagram showing a ball falling from a height h, and mark its potential energy and kinetic energy at the top, at the midpoint and just before touching the ground. Show that total energy remains constant. (4 marks) 12. Draw a diagram showing a force acting at an angle of 90 degrees to the direction of motion, as in a satellite moving in a circular orbit. Explain why no work is done. (3 marks) 13. Draw a flowchart showing energy changes in a hydroelectric power station, from water stored in a dam to electrical energy in our homes. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A car of mass 1500 kg is moving at 60 km/h. How much work must be done to stop it? Explain where this energy goes when the brakes are applied. (5 marks) 15. Explain whether work is done in each case: (i) a man pushing a wall (ii) a coolie carrying a load on his head walking on a level road (iii) a girl climbing stairs (iv) a ball moving on a smooth floor at constant speed (v) a bullock pulling a cart. (5 marks) 16. A pendulum swings from one side to the other. Explain the energy changes during one swing. Why does it eventually stop? Does this violate the law of conservation of energy? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Write the formula, convert all units to SI and give the unit with every answer.