What is energy?

2. 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.

3. 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.

4. Conservation of energy Energy cannot be created or destroyed; it can only be changed into another form. The law of conservation of energy states that: 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.

5. What is gravitational potential energy? gravitational potential energy gravitational field strength = mass × × height Ep = mgh ΔEp = mgΔh 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: It is often talked about in terms of a change in an object’s Ep due to a change in its height:

6. Ep: example question 1 A supermarket employee lifts a can of baked beans, weighing 250g, from the floor, to a shelf 2m high. How much gravitational potential energy does it gain? (g = 9.81Nkg-1) ΔEp = mgΔh = 0.250 × 9.81 × 2 = 4.9J

7. Ep: example question 2 A pole vaulter of mass 80kg jumps a height of 5m. What is his gravitational potential energy at the highest point of his jump? (g = 9.81Nkg-1) Ep = mgh = 80 × 9.81 × 5 = 3924J

8. Work done using slopes

9. What is kinetic energy? kinetic energy = ½ × mass × speed2 Ek = ½mv2 Kinetic energy (KE or Ek) is the energy of an object due to its speed. Where: • kinetic energy is measured in joules (J) • mass is measured in kilograms (kg) • speed is measured in meters per second (ms-1).

10. 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 = 0ms-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: Ek = ½mv2

11. Ek and Ep ½mv2 = mgΔh loss of Ek = gain in Ep lose of Ep = gain in Ek If resistive forces, such as friction and air resistance, are ignored, Ek and Ep are related as follows: 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:

12. Conservation of energy: example question A ball of mass 400g is thrown upwards at a speed of 5ms-1. (g = 9.81Nkg-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) = 1.27m

13. Resistive forces W = ΔEp + ΔEk 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 ΔEkcorresponds to a loss of energy to resistive forces, or work done against resistive forces: Where ΔEk is positive if ΔEp is negative, and vice versa.

14. Investigating Ek and Ep

15. Energy calculations