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1 of 15 © Boardworks Ltd 2010 What is energy? Energy is the measure of the ability of an object or a system to perform work. There are many types of energy: kinetic energy – energy of an object due to its speed gravitational potential energy – energy of an object due to position in a gravitational field elastic energy – energy stored when an object is stretched or compressed chemical energy – energy stored in chemical bonds nuclear energy – energy stored in nuclei. 2 of 15 © Boardworks Ltd 2009 Energy transfer When work is done, energy is transferred. That energy might be: gravitational potential energy – e.g. when an object changes height within a gravitational field kinetic energy – e.g. when an object changes speed light energy – e.g. when a light bulb is switched on heat and sound – e.g. when a car brakes sharply. 3 of 15 © Boardworks Ltd 2009 Conservation of energy The law of conservation of energy states that: Energy cannot be created or destroyed; it can only be changed into another form. In other words, the total energy of a system is constant. A bungee jumper’s gravitational potential energy is changed into kinetic energy as they jump, and then stored as elastic potential energy as the bungee rope stretches. 4 of 15 © Boardworks Ltd 2009 What is gravitational potential energy? Gravitational potential energy (GPE, Ep or Egrav) is the energy of an object due to its position in a gravitational field. The Ep gained by a mass is proportional to the force used to lift it, and the distance it is lifted: gravitational = mass × gravitational × height potential energy field strength Ep = mgh It is often talked about in terms of a change in an object’s Ep due to a change in its height: 5 of 15 ΔEp = mgΔh © Boardworks Ltd 2009 Ep: example question 1 A supermarket employee lifts a can of baked beans, weighing 250 g, from the floor, to a shelf 2 m high. How much gravitational potential energy does it gain? (g = 9.81 N kg-1) ΔEp = mgΔh = 0.250 × 9.81 × 2 = 4.9 J 6 of 15 © Boardworks Ltd 2009 Ep: example question 2 A pole vaulter of mass 80 kg jumps a height of 5 m. What is his gravitational potential energy at the highest point of his jump? (g = 9.81 N kg-1) Ep = mgh = 80 × 9.81 × 5 = 3924 J 7 of 15 © Boardworks Ltd 2009 Work done using slopes 8 of 15 © Boardworks Ltd 2009 What is kinetic energy? Kinetic energy (KE or Ek) is the energy of an object due to its speed. kinetic energy = ½ × mass × speed2 Ek = ½mv2 Where: kinetic energy is measured in joules (J) mass is measured in kilograms (kg) speed is measured in meters per second (ms-1). 9 of 15 © Boardworks Ltd 2009 Deriving Ek = ½mv2 Consider a force F acting on an object of mass m, initially at rest, moving it a distance s in time t. From ‘suvat’ equations: s = ½ (u + v)t a = (v – u) / t Because u = 0 ms-1: s = ½vt a=v/t Newton’s 2nd law: F = ma Substituting a = v / t: F = mv / t Work done by force: W = Fs W = (mv / t) × ½vt W = ½mv2 Work done = energy transferred: 10 of 15 Ek = ½mv2 © Boardworks Ltd 2009 Ek and Ep If resistive forces, such as friction and air resistance, are ignored, Ek and Ep are related as follows: loss of Ek = gain in Ep lose of Ep = gain in Ek For example, if an object of mass m is released above the ground at height h, it will gain speed, v, as it falls. Due to the conservation of energy, and assuming air resistance is negligible, after falling a height of Δh: ½mv2 = mgΔh 11 of 15 © Boardworks Ltd 2009 Conservation of energy: example question A ball of mass 400 g is thrown upwards at a speed of 5 ms-1. (g = 9.81 N kg-1). What is the ball’s Ek as it is released? Ek = ½mv2 = ½ × 0.4 × 52 = 5J What is the ball’s maximum gain of Ep? ΔEp = Ek = 5J What is the ball’s maximum height? Ep = mgh h = Ep / mg = 5 / (0.4 × 9.81) = 1.27 m 12 of 15 © Boardworks Ltd 2009 Resistive forces Resistive forces are forces that act on a moving body in the opposite direction to the direction of movement. The main resistive force is friction, which includes drag or air resistance. When an object such as a rollercoaster moves vertically without a driving force, any difference between a change in ΔEp and ΔEk corresponds to a loss of energy to resistive forces, or work done against resistive forces: W = ΔEp + ΔEk Where ΔEk is positive if ΔEp is negative, and vice versa. 13 of 15 © Boardworks Ltd 2009 Investigating Ek and Ep 14 of 15 © Boardworks Ltd 2009 Energy calculations 15 of 15 © Boardworks Ltd 2010