2. What is work? Physics Definition of WorkPhysics Definition of Work with practice problems Explanation Videos:

3. Based on the video of work, Which people are doing work and why? Holding a large stack of books at rest Lifting a light cardboard box Walking with drinks at a constant speed Mowing the lawn Lifting Weights F F F F F Pushing a crate at a constant speed across the floor F 1. 2.3. 4. 5. 6. 7. A satellite orbiting Earth

4. Work? 1No, no displacement 2Yes, work against gravity (W=F g d) 3No, force and displacement are not in the same direction (they are perpendicular) 4Yes. (W=Fdcosθ) 5Yes (W=F f d) 6Yes (W=F g d) 7No, the force and displacement are not in the same direction (they are perpendicular)

5. What is the physical definition of work and how do we calculate it? Work occurs when a force applied to an object causes that object moves through a displacement. – The direction of the displacement must be in the same direction as the force (or component of the force) doing the work! – Formula: W=Fd (work = force x displacement) Work is a scalar quantity (has NO direction, ie North or South) But work can be positive or negative (Lost or gained) Force and displacement are both vectors (you can only multiply numbers that are in the EXACT SAME DIRECTION!) – Units: J=Nm (Joule = Newton x meter)

6. W=Fd Work done against gravity The man lifts a 5Kg box initially on the ground at a constant speed to a height 1.4m above the ground. – Draw a free body diagram of the forces acting on the box. (make sure the length of the arrows represent the relative strengths of the forces) – How much force is the man putting on the box? – How much work is done by the man while lifting the box? W=F g d=mgd= 68.6J

7. W=Fd Work done against gravity The women does 300J of work while lifting the weights 0.75m in the air. – How much does the barbell weigh? – What is the mass of the barbell? The weights are then lowered back to their original height, how much total work is done by the women? W=F g d 300J = F g (.75m) F g =400N F g =mg 400N = m (9.81m/s 2 ) m= 40.8kg Zero joules of work because the total displacement is zero

8. Positive vs. Negative Work When doing work against gravity, – lifting things into the air is considered positive work by the person doing the lifting. Negative work by gravity – lowering things back to the ground considered negative work by the person positive work by gravity The force is in the same direction as the displacement and the energy of the object increases. The force is in the opposite direction of the displacement The force is in the opposite direction of the displacement and the energy of the object decreases The force is in the same direction as the displacement

9. Work done against friction horizontal force W=F f d The man pushes a 50Kg wooden crate box at a constant speed across a wooden floor covering a distance of 12m (coefficient of friction is 0.3) – How much force is the man applying on the box to keep it moving at constant speed? – How much work is done by the man while pushing the box?

10. Work done on an angle angled force W=Fdcosθ The child applies a 45N force at an angle of 50 o to push a 3.5kg mower 20m across the lawn at a constant speed. – How much force is the child putting on the mower in the direction the mower is moving? – How much work is done by the child while pushing the mower?

11. examples 1.A 9kg box is lifted at a constant speed to a height of 4m by a fork lift. How much work does the fork lift do? 2.A weight lifter does 400J of work when lifting his weight a distance of 1.2 meters above the ground. What is the mass of the weight he is lifting? 3.A mother applies a constant 67N horizontal force while pushing a shopping cart at a constant speed down a 13m long aisle in the market. How much work does the mother do? 4.If 320J of work are done while pushing a 55Kg sofa 2.3m across the floor at a constant speed, what is the coefficient of kinetic friction between the sofa and the floor?

12. Do Work Mastering Physics Now

13. Power Power “the rate at which work is done” Power Explanation video

14. Aim: What is mechanical power and how do we calculate it? Mechanical Power is defined as the amount of work done per time. Formula: P is the symbol for power in an equation The unit of power is the Watt (W) A Watt is equal to a Joule/second (J/s)

15. Examples 1.A man brings a 7Kg box up the stairs to the second floor of his house that is 10m above the ground. If it takes him 20 seconds to get up the stairs, a.How much work does he do? b.What is the power he develops?

16. Examples 2.A fork lift generates 3000W of power when lifting a car 3m in the air in 10 seconds. a.How much work does the fork lift do? b.What is the mass of the car? 3.A body builder generates 2000Watts of power when lifting 150kg mass 0.9m in the air. a.How much work does the body builder do? b.How much time does it take the body builder take the lift the masses up?

17. Power On an angle angled force 4.The child applies a 60N force at an angle of 55 o to push a 3.5kg mower 20m across the lawn at a constant speed in 30 seconds. – How much force is the child putting on the mower in the direction the mower is moving? – How much work is done by the child while pushing the mower? – What is the power generated by the child?

18. A second way to calculate Power

19. Examples 5.An engine provides a 3000N force to keep a car moving at a constant speed of 25m/s. What is the power of the engine? 6.A remote controlled car has an engine that can provide 18W of power to cause a car to move at 3m/s. What is the force provided by the car’s engine? 7.An elevator motor provides 10KW of power while lifting a 450Kg elevator at a constant speed. What is the speed of the elevator?

20. Work Graphically F(N) d(m) F(N) d(m) 10 6 15 10 To calculate the work done, find the area under the curve

21. Do Power Mastering Physics Now

22. Potential Energy Due to Gravity Potential Energy Due to Gravity Think about it: Describe what you would feel if you were the guy in the picture to the left. DO NOW: What does it mean to say “you have a lot of potential” to someone?

23. Aim: What is potential energy? The word potential in general means the ability to do something. – Athletic Potential: you have the ability to perform well at athletics – Academic Potential: you have the ability to do well academically. Gravitational Potential Energy: An object has the ability to do work based on its position above the ‘ground’

24. Gravitational Potential Energy An object has the ability to do work because of its gravitational position The gravitational potential energy PE g of an object depends on – Its mass m measured in Kilograms – Its height above the chosen reference point h measured in meters – The gravitational acceleration on the planet g (9.81m/s 2 on Earth).

25. Calculate the gravitational potential energy of the following objects Reference Point 0.0m 20Kg 3m 10Kg 8m 15Kg 2m 8Kg 1.5m

26. Kinetic Energy Do Now: A horizontal force of 800N is applied to a bobsled over a distance of 4.5m. How much work is done on the bobsled?

27. Kinetic Energy Defined Kinetic energy is the energy a moving object has. The kinetic energy KE of an object depends on – The mass m of the object in Kilograms – The velocity v of the object in m/s Formula Units: Kinetic energy can never be a negative value – Mass is always positive – Velocity can be negative, but when squared, it becomes positive

28. 1.A 1200Kg car is moving down the road at 14m/s. What is the kinetic energy of the car? 2.A 30g bullet has a kinetic energy of 30,000J. What is the speed of the bullet? 3.An object has 500J of Kinetic energy when moving at 6m/s. What is the mass of the object?

29. Do Conservation of Energy Mastering Physics Now Potential Energy due to Gravity

30. Elastic Force and Hooke’s Law

31. The Elastic Force The elastic force is a “restoring force” because it always pulls back towards its original starting position. – Think of a spring for example. Every spring has a natural rest length – If stretched to the right, the spring will pull to the left. – If compressed to the left, the spring will push back towards the right. The spring is always trying to restore its original length F applied F spring F applied

32. Hooke’s Law F s = kx There is a linear relationship between the force applied to a spring (F s ) and the resulting change in length of that spring (x) if the elastic limit has not been reached k is known as the spring constant and describes how easily a spring can be stretched. k has the units of N/m FsFs F app x

33. Objects that Follow Hooke’s Law FsFs x Stiffer spring (higher slope =higher k) Looser Spring (Lower slope = lower k) Object that follow Hooke’s Law have linear graphs when the force applied to them is graphed versus the change in length of that object. The slope of the graph is the spring constant

34. Things to watch out for! Make sure the force (F) is in Newtons and the change in length (x) is in meters! Make sure you are using a change in length of the spring, not the actual length of the spring! On a graph, the slope of a F vs. x graph will be k The slope of a x vs. F graph will be 1/k

35. Practice Questions 1.A spring can be stretch 0.3m from its original length by applying a force of 10N. What is the spring constant for that spring? 2.The same spring is now compressed 0.15m. What force would it take to achieve this compression? 3.A spring has a spring constant of 90N/m. If this spring is originally 10cm long and is compressed to 5cm, what force was applied to the spring? 4.A spring has a constant of 100N/m. What is the change in length of that spring when a 55N force is applied?

36. Elastic Potential Energy What is PE s ? How do we calculate PE s ? How do we used PE s in our lives?

37. Elastic Potential Energy Elastic potential energy is the energy stored in a stretched or compressed elastic object. – It depends on the… k (the spring constant in N/m) x (the amount that object has been compressed or stretched) – Formula PE s =1/2 kx 2 units: Joules FsFs x

38. Example Questions F s =kx PE s =1/2kx 2 1.A spring with a spring constant of 135N/m is compressed 0.2m a.What is the force that caused this compression? b.What is the energy stored in the spring? 2.A 240N force causes a spring to compress 0.25m. a.What is the spring constant of that spring? b.How much energy is stored in that spring?

39. Do Energy Mastering Physics Now

40. Work Energy Theorem Watch the above video for good practice problems and examples of the work energy theorem.

41. Work as a change in PEg

42. Work done by Friction / Internal Energy Internal energy (symbol U) is the equal to the work done by friction in a system. It is also called heat. Is can be calculated by – finding the difference between the actual work done (W=Fd) and the resulting energy of the object (kinetic if moving, potential if above the ground) – Calculating the energy lost during motion U = E final - E initial

43. Example 1: For a 1.2kg cart dragged to a height of 0.9m up a distance of 1.7m by a force of 15N. -What is the gravitational potential of the cart at the top? -What is the work done on the cart? -What is the work done against friction?

44. Example 2: A women does 300J of work lifting a 2kg block 10m in the air using a rusty pulley system. How much work was done against friction?

45. Work as a change in Kinetic energy When pushing an object, the work you do is equal to the object’s change in kinetic energy (when friction is NOT present) W=ΔKE A horizontal force of 800N is applied to a 250Kg bobsled over a distance of 4.5m. – How much work is done on the bobsled? – How fast is the bobsled going after the they are done pushing?

46. 1.In a drag race, a 120Kg car reaches a speed of 30m/s over a distance of 20m. (neglecting friction) -What is the car’s change in kinetic energy? -How much work is one by the car’s engine? -What force does the engine put on the car? 2.A 60kg runner runs a 5k in 25 minutes -What is the average velocity of the runner? -What is the kinetic energy of the runner? 3.A women pushes her 20Kg son on a swing. She applies a 50N force over a distance of 0.75m - What is the velocity of the kid after being pushed assuming there is no friction?

47. Work as a change in Kinetic energy (with Friction) When pushing an object, the work you do is equal to the object’s change in kinetic energy PLUS the work done against friction W=ΔKE+W f A horizontal force of 300N applied for a distance of 20m causes a 20Kg crate to reach a speed of 23m/s. How much work was done against friction?

48. Conservation of Mechanical Energy WITHOUT friction, the total mechanical energy of a system is conserved – Remember, total mechanical energy (E T ) is the sum of PE g =mgh KE=1/2mv 2 PE s =1/2kx 2 – When solving conservation of energy questions, you need to ask yourself if the object possess each type of energy at the point of interest. – To find the total mechanical energy (E T ) at a point, add up the energies it has. – This total will NEVER CHANGE!

49. Do Conservation of Energy Mastering Physics Now Review of gravitational potential energy and kinetic energy

50. Type of energy it has Energy Transfers Type of energy it has Energy Transfers At rest at the top Starting to fall Bungee starts to stretch Bungee at max length Bungee is back to rest length On the way back up Back to original position

51. Type of energy it has Energy Transfers Type of energy it has Energy Transfers At rest at the top Starting to fall Bungee starts to stretch Bungee at max length Bungee is back to rest length On the way back up Back to original position All PE g PE g is decreasing and transferring to KE PE g + KE PE g and KE are decreasing and transferring to PE s PE g + max KE PE g and KE are zero and transferred all to PE s PE s max PE s transferring back into max KE and PE g PE g + max KE KE is transferring to PE g All PE g

52. Victoria Falls: 111m high 40m bungee 55kg person 1.What is her total energy in situation 1? 2.What is her potential energy in situation 3? 3.What is her kinetic energy in situation 3? 4.How fast is she moving in situation 3? 5.What type of energy does she have in situation 4? 6.How far did the bungee stretch while in situation 4? 7.What is the spring constant of the bungee cord?