1. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Mechanics 7 Work, Energy and Power IFP Friday 13 th November 2015

2. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Work What do you already know? Some key stuff to note down…

3. Work Work is done by a force when the force moves its point of application in the direction of the force. e.g. by lifting a weight, one does work Work produced by a force on an object is proportional to the strength of the force and proportional to the distance travelled by the object in the direction of the force. (more simply: W = Fd) Unit of work is the joule (J): this is the work done when a force of 1 N moves its point of application through 1 metre in the direction of the force.

4. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words F and S at an angle? W = Fs cosθ Work done = force x distance travelled in the direction of the force Although a scalar, work has a sign!

5. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words What about a variable force? Work done is just the area under the graph. You could just count the squares, or use integration to calculate it. You won’t be asked to in this course!

6. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Energy What is it? What can it do? What forms are there? Put them on the board

7. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Energy What is it? the capacity to do work. What can it do? moves things, heat things up, cool them down, make light, make noise, break things, power our electronics etc… Examples of Energy Transfers

8. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Kinetic energy Energy of motion: E k = ½ m v 2 1 J = 1 joule = 1 kg (ms -1 ) 2 =1 kg m 2 s -2 Simple example a mass of 1 kg moves at 2 ms -1. E k = ½ (1 kg) (2 ms -1 ) 2 =2 J

9. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Potential energy Potential energy is “stored” energy resulting from any force which depends only on position e.g. gravity, force in a spring, electrostatic attraction/repulsion Gravitational potential energy is only one form of potential energy: It arises from height in a gravitational field

10. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Potential Energy E p = m g h h: height above the origin level. The origin (h=0) can be freely chosen. Potential energy is always relative to some reference level or position e.g. a 1 kg mass is held 20m above the ground. What is its gravitational potential energy relative to the ground? U = 1kg 9.8 ms -2 20m= 196 J

11. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words

12. Conservation of energy It’s a Very important principle Has nothing to do with the answer: :“the law of conservation of energy is a law passed by the government to tell us to save energy” (student in a test) In an isolated system the total energy is conserved. Isolated system: one where there is no energy transfer into or out of the system. Energy can only be transformed from one form to the other. Energy cannot be created or destroyed. Examples of energy transfers?

13. Power

14. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Power We can relate power, force and speed: P = dW/dt = d (F s cosθ)/dt for fixed F (both magnitude and angle) P = F ds/dt cosθ = F v cos θ or P = F v

15. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Efficiency In many cases (machines) energy is transformed from one form to the other but in the process there is a waste of energy. E.g. friction in a machine or resistance in wires of electric motors waste energy. Notion of efficiency of a machine: Efficiency = useful power delivered /total power supplied (often a %)

16. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Examples Example 1 A 500 kg rock slides from rest down a hill 500m long and 300m high. The coefficient of kinetic friction between the rock and the hill is μ=0.25. If the gravitational potential energy is set to 0 at the bottom of the hill, (a) What is the rock’s potential energy just before the slide? (b) How much work is done by the frictional force during the slide? (c) What is the kinetic energy and the speed of the rock when it reaches the bottom of the hill?

17. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Problem 1 Solution – on handout! Tricky problem. Principles… 1.E p = mgh. This is easy, =1.47 MJ 2.Work done = force * distance moved 3.Force = reaction force * friction coeff 4.Reaction force = component of weight acting perpendicular to slope 5.Work that out first! Then 6.E p – work done against friction = energy left over 7.Use ½ mv 2 to find v

18. Solution 1 (a) U = m g h = 500 kg 9.8 m/s 300m = 1,47 MJ (b) W= - Ff s = -μ m g cosθ s sinθ=h/s cosθ = (s 2 -h 2 ) 1/2 /s W= - μ m g (s2-h2)1/2 = -0.49 MJ (c) K = ½ m v 2 =U + W = 0.98 MJ v = 62.6 m/s (note – this is a “clever” way to use cos and sin. Might be better just to use pythagoras to get horizonal distance of 400m )

19. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Example 2 A car of mass m=1000 kg travelling at speed v i =30m/s has its speed reduced to v f =10 m/s by a constant breaking force over a distance of 80m. Find: (a) the car’s initial kinetic energy (b) the final kinetic energy (c) the breaking force

20. Objectives Describe and define Work Energy Power Efficiency Discuss conservation of energy and conservative forces Carry out calculations to demonstrate understanding. Key Words Problem 2 solution (a) E i = ½ m v i 2 = 450000 J (b) E f = ½ m v f 2 = 50000 J (c) ΔE=E f - E i = (50000 – 450000) J = -400000 J W = F s = ΔE= -400000 kJ F = ΔE/s = -400,000/80 N = 5000 N (the minus sign indicates direction is opposite to direction of motion)

21. Example 3 Mass m 1 with initial velocity v 1i collides with mass m 2 which is initially at rest. The collision is elastic (energy and momentum are conserved). What are the velocities of the two masses after the collision?

22. Elastic collision, important information: 1. total momentum before = total momentum after m 1 v 1i = m 1 v 1f + m 2 v 2f (1) 2. total energy before = total energy after ½m 1 v 1i 2 = ½ m 1 v 1f 2 + ½ m 2 v 2f 2 (2) Strategy: solve for v 2f Eq (1) and substitute this into (2) then solve the resultant equation for v 1f.

23. v 1f = v 1i (m 1 -m 2 )/(m 1 +m 2 ) Then substitute back v 1f into equation for v 2f and get: v 2f = v 1i 2 m 1 /(m 1 + m 2 ) If m 1 =m 2 then the two masses exchange velocities! -If m 2 is enormous compared to m 1 then m 1 reverses its velocity and m 2 almost at rest. -What if m1 is enormous compare to m2? Note – the algebra is tricky. You will NOT be asked to do this!