Work, Energy and Power

In everyday language, work means any effort, but in physics work is done only when a force produces a displacement. This chapter begins with the scalar product of two vectors and uses it to define work, W = F.d = Fd cos(theta). You will study kinetic energy, (1/2)mv^2, and the work-energy theorem, which states that the work done by the net force on a body equals the change in its kinetic energy. The chapter shows how to find the work done by a variable force as the area under a force-displacement graph, and introduces potential energy as the energy of position or configuration, mgh near the Earth's surface. You will learn the difference between conservative and non-conservative forces, and the conservation of mechanical energy when only conservative forces act. The potential energy of a spring, (1/2)kx^2, is derived. The chapter defines power as the rate of doing work, P = F.v, with units of watt and horsepower. Finally, it studies elastic and inelastic collisions in one dimension and introduces collisions in two dimensions.

Detailed Worksheet: Work, Energy and Power Section A - Definitions (10 marks) 1. Define work and write its SI unit. (2 marks) 2. Find the work done by a force F = (3i + 4j) N that displaces a body by d = 5i m. (2 marks) 3. State the work-energy theorem. (2 marks) 4. When is the work done by a force zero? Give an example. (2 marks) 5. Define power and write its SI unit. (2 marks) Section B - Calculations and Applications (15 marks) 6. A 0.5 kg ball speeds up from 10 m/s to 20 m/s. Find the work done on it. (3 marks) 7. A body is dropped from a height of 20 m. Find its speed just before it hits the ground, using the conservation of energy. Take g = 9.8 m/s^2. (3 marks) 8. A spring of spring constant 200 N/m is compressed by 0.1 m. Find the potential energy stored in it. (3 marks) 9. A pump lifts 1000 kg of water to a height of 10 m in 20 s. Find its power. Take g = 9.8 m/s^2. (3 marks) 10. A 2 kg ball moving at 6 m/s hits a 4 kg ball at rest, and they stick together. Find their common velocity and the loss of kinetic energy. (3 marks) Section C - Diagrams (10 marks) 11. Draw a force-displacement graph for a variable force and show how the work done is found from it. (4 marks) 12. Draw a graph of the potential energy of a spring against its extension x. (3 marks) 13. Draw diagrams showing two balls before and after a one-dimensional elastic collision. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. State and prove the work-energy theorem for a constant force. (5 marks) 15. Derive the final velocities of two bodies after an elastic collision in one dimension. Show that when equal masses collide with one at rest, the velocities are exchanged. (5 marks) 16. A car of mass 1000 kg moving at 18 km/h on a smooth road hits a horizontal spring of spring constant 6.25 x 10^3 N/m. Find the maximum compression of the spring. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Take g = 9.8 m/s^2 unless stated otherwise. Use i, j and k for unit vectors.