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# Topic 2.3

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### Topic 2.3

1. 1. Mechanics Topic 2.3 Work, Energy and Power
2. 2. Work A simple definition of work is the force multiplied by the distance moved However this does not take in to account of the case when the force applied is not in the direction of the motion Here we have to calculate the component of the force doing the work in the direction moved i.e. Work is equal to the magnitude of the component of the force in the direction moved multiplied by the distance moved
3. 3. Work = Fs = Fs cosθ Where  F is the force  s is the displacement  θ is the angle between the force and the direction θ F s
4. 4. The SI unit of work is the newton-metre (Nm) and it is called the joule (J) Work is a scalar quantity
5. 5. Force-displacement Graphs The area under any force-displacement graph is the work done force displacement Area = work done
6. 6. Energy and Power Kinetic Energy  This is the energy that a body possesses by virtue of its motion  If the mass of a body is m and its velocity is v then its kinetic energy, Ek = ½ m v2
7. 7. Energy and Power Gravitational Potential Energy  This is the energy that a body possesses by virtue of its position in the gravitational field  If the mass of a body is m and its height above a fixed position is h then its change in gravitational potential energy, ∆Ep = mg∆h  where g = the acceleration due to gravity
8. 8. The Principle of Conservation of Energy Energy can be transformed from one form to another, but it cannot be created nor destroyed, i.e. the total energy of a system is constant Energy is measured in joules and it is a scalar quantity
9. 9. Kinetic Gravitational Potential Elastic Heat (often refered to as internal) Light Sound Electrical Chemical Nuclear Types of Energy
10. 10. Energy and Power Elastic Potential Energy  This is the energy that a body possesses by virtue of its position from the equilibrium condition of the spring  If the mass of a body is m and its displacement from the equilibrium position is s then its elastic potential energy, ∆E elas = ½ k s2  where k = the spring constant
11. 11. In Mechanical Situations Falling objects and roller coaster rides are situations where Ep + Ek = constant if we ignore the effects of air resistance and friction. Inclined planes and falling objects can often be solved more simply using this principle rather than the kinematics equations
12. 12. In all collisions and explosions momentum is conserved, but generally there is a loss of kinetic energy, usually to internal energy (heat) and to a small extent to sound In an inelastic collision there is a loss of kinetic energy (momentum is still conserved) In an elastic collision the kinetic energy is conserved (as well as momentum)
13. 13. Power Power is the rate of working Power = work time P = ∆W ∆t The unit of power is the joule per second (Js-1 ) which is called the watt (W)
14. 14. Power and Velocity Since ∆W = Fs And power developed P = ∆W ∆t Then P = Fs ∆t But s = velocity ∆t Therefore P = Fv
15. 15. Efficiency Efficiency is defined as the ratio of the useful output to the total input This can be calculated using energy or power values as long as you are consistent Efficiency is normally expressed as a percentage