Need to insert conservation of energy

1. Need to insert conservation of energy

2. Work Energy and Power

3. Displacement in the direction of the force Work done = Average applied force x Work Work is done when a force moves its point of application through a distance. Q. Convert Joules into base units. Note:One Joule can be defined as the work done when a force of one Newton moves through a distance of one meter. Also note: Negative work can be done on a body. E.g. Friction always does negative work on a car moving in the positive direction. ΔW = F Δx W is measured Joules, J • 1J = 1kgm2s-2

4. Fa 30° 8000N E.g.1 A horse pulling a barge with a 800N force, through a distance of 5km. (Rope at 30° to the direction of motion) FBFD: Work done in direction of motion = FaΔx = 800 cos30 x 5000 = 3.46 x 106J canal motion barge

5. E.g.2 • The angle between the string and the tangential direction of motion at any instant is 90°. •  There is no component of the tension acting in the direction of the motion. •  Zero work is done by the tension on the ball. A ball is swung on a string in a horizontal circular motion. How much work is done on the ball by the tension in the string? Explain your answer.

6. F x Force – displacement graphs If the applied force on a body varies, the total work done can still be found: Total work done = area under a force-displacement graph.

7. F x E.g.Extending springs We know that a spring obeys Hooke’s law, i.e. its extension, x is proportional to the force applied, F: • As the spring extends the applied force must increase to a maximum value, F: • Average force applied = ½F • Work done on spring = ½Fx (This can also be seen from the area under the graph) • Energy stored in spring = ½Fx

8. Energy Energy is simply the ability of something to do work on something else. The idea of ‘types’ or ‘forms’ of energy is misleading. Most forms of energy are potential energy – if the bodies involved change their position they can do work: e.g. Stretched elastic, high masses, nuclei forced together or split apart, chemicals joined together. Things that are moving relative to other bodies have kinetic energy. Work done on something = Energy transferred to it

9. Q. In each case state what loses energy, what gains energy and what does work. a. a watch spring turning the watch hands b. petrol burning with oxygen to drive a cars engine. A. a. The spring does work on the hands. The spring loses elastic potential energy and the hands gain kinetic energy. b. The particles do work on the pistons of the engine. The particles lose chemical potential energy and the pistons gain kinetic energy.

10. h Potential Energy E.g. A skydiver falling to Earth Potential energy is the energy a system has as a result of the position of its parts and the forces acting upon them. The systemincludes two bodies: the skydiver and Earth. The potential energy they store is a result of their separation and the gravitational force between them. Thus the gravitational potential energy is a property of the ‘skydiver-Earth system’ and not of either body separately.

11. In the example above, a force equal and opposite to the skydivers weight is needed to raise him to height h: ΔW = FΔs  ΔW = mg Δh so Gravitational potential energy = mg Δh GPE = mg Δh

12. Kinetic Energy If a constant force accelerates a body of mass m through a displacement Δs to a velocity v, ΔW = FΔs but F= ma so… ΔW = ma Δs so… ΔW = m v2 2 so… ΔW = ½ m v2  Kinetic energy is the energy a body has as a result of its motion. but v2 = u2 + 2as and u=0 so as = v2 2 KE = ½ m v2

13. Power Power is measured in Watts (W) where one Watt is one Joule per second. If Work done = Force x displacement then… P = F x Δs Δt so… P = Fv Power is the rate at which work is done. Power = Work done Time taken P = ΔW Δt but v = Δs Δt

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