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# Physics 504 Chapter 15 Simple Machines

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### Physics 504 Chapter 15 Simple Machines

1. 1. Energy and its Transformations Simple Machines, Work & Power Chapter 15
2. 2. Examples
3. 3. Simple Machines and Work• A simple machine is a device used to make work easier.• It is used to multiply forces or change the direction of the force.• No machine is 100% efficient.• Energy is always lost to friction.• The person must do more work, but easier work, i.e. less force.• A lesser force is applied over a greater distance.
4. 4. Definitions & Equation• Effort Force, FE: Force used by person, N• Effort Distance, ΔdE: Distance person’s force is applied over, m.• Resistance Force, FR: Force that comes from machine, or weight of object, N• Resistance Distance, ΔdR: Distance object is moved, m.• FE x ΔdE = FR x ΔdR
5. 5. Mechanical Advantage• Mechanical Advantage is a measure of how much easier the task has become.• Ideal Mechanical Advantage – no friction:• IMA = ΔdE = Effort arm length ΔdR Resistance arm length• Actual Mechanical Advantage – with friction.• AMA = FR FE
6. 6. Levers• The fulcrum is a pivot that can act to change the direction and magnitude of the force.• Depending on force direction and position of fulcrum: – 1st class – 2nd class – 3rd class
7. 7. 1 Class Lever st• 1st Class Lever: The fulcrum, or pivot, is located between the 2 forces.• E.g. lever, seesaw, teeter-totter, scissors.
8. 8. 2 Class Lever nd• 2nd Class Lever: The fulcrum is located on 1 side of both forces.• E.g. wheel barrow, nutcracker
9. 9. 3 Class Lever rd• 3rd Class Lever: The effort force is between the resistance force and the fulcrum.• E.g. tweezers, hockey stick
10. 10. Variations of the Lever• The pulley is a variation of the lever.• IMA = the number of supporting ropes.• IMA = ΔdE ΔdR• AMA = FR FE
11. 11. Wheel and Axle• The wheel and axle acts like a 2nd class lever. E.g. doorknob, taps, steering wheel• IMA = radiusE AMA = FR radiusR FE
12. 12. The Inclined Plane• The inclined plane trades distance for force by reducing the force needed to work against gravity.• E.g. stairs, ramps, screw
13. 13. Inclined Plane Formula• IMA = length of slope = ΔdE height of slope ΔdR• AMA = FR = mg FE FE
14. 14. Activity• A 1st class lever has a AMA of 4. How much force is needed to lift 5 kg?• AMA = FR = mg FE FE• 4 = 5kg x 9.81 m/s2 FE• FE = 12.25 N
15. 15. Exam QuestionA workman uses a pulley to lift a 50 kg sack of potatoes by pulling downwards on a ropewith a force of 550 N. xWhat is the acceleration of the sack? A) 1.0 m/s2 B) 2.1 m/s2 C) 4.5 m/s2 D) 11 m/s2
16. 16. Measuring Work• Work is defined as the energy that comes from applying a force over a certain distance.• W = F Δd = mad (horizontal)• = magd (against gravity)• Work is in Joules, J• Force is in Newtons, N• Distance is in metres, m
17. 17. Activity• E.g How much work is done by a boy pushing a car with a force of 800 N over a distance of 200m?• W=Fd• = 800 N x 200 m• = 160 000 J = 160 kJ• Do page 330, Q. 1-4
18. 18. Exam QuestionA 200 g brick falls from a wall 4.0 metres above the ground. It hits the ground with avelocity of 8.5 m/s. 4.0 mHow much work did gravity do on the brick? A) 8.0 J B) 7.2 J C) 3.4 J D) 1.7 J
19. 19. Exam QuestionA sled has a mass of 10 kg.A child pulls the sled a distance of 20 metres with a force of 10.0 N at an angle of 35° withrespect to the horizontal. During this motion, a force of friction of 4.0 N acts in the oppositedirection of the motion.How much work is done on the sled by the child over the distance of 20 metres? A) 1.6 × 102 J B) 1.1 × 102 J C) 8.4 × 101 J D) 3.5 × 101 J
20. 20. Efficiency• The IMA is always greater than the AMA.• The MA must be greater than 1.• % Efficiency = Work output x 100 = AMA Work input IMA• The maximum efficiency is 100%.• It is a measure of what energy is lost to friction, vibration, and other factors.
21. 21. Power• Power is defined as the rate at which work is being done.• P=W• Δt• Work is in Joules,• Time is in seconds• Power is in Watts
22. 22. Activity• What is the power of a bulldozer that does 55000J of work in 1.1s?• P = W = 55000J = 50000 Watts Δt 1.1s• If 100000 J of energy was expended by the bulldozer, what is its efficiency?• Do page 334, Q 1-5
23. 23. Exam QuestionA horse is hitched up to a buggy with a mass of 500 kg including the people inside.Disregard the effects of friction.Starting from rest, the horse exerts a horizontal force of 300 newtons on the buggy over adistance of 30 metres.What is the average power that the horse develops over the first 30 metres? A) 9.0 × 102 W B) 9.0 × 103 W C) 4.5 × 105 W D) 4.5 × 106 W
24. 24. Summary• Work done on object equals the applied force times the displacement of the object in the direction of the force.• W = FΔd• The units are Joules, J, or Nm.• Power is the rate at which work is done per unit of time.• P = W/Δt• The units are Watts, W, or J/s
25. 25. Summary• The Efficiency of a machine is given by the formula, Efficiency = Work output x 100 Work input• A machine is supposed to reduce the force required by a person to do a physical task.• Ideal Mechanical Advantage does not take into account friction.• IMA = effort distance
26. 26. Summary• Actual Mechanical Advantage, AMA, takes friction into account.• AMA = Resistance Force Effort Force
27. 27. Exam QuestionA car with a mass of 1000 kg and moving at a speed of 30 m/s comes to rest over adistance of 100 metres.What is the force of friction (acting on the wheels of the car) which causes the car tostop? A) 3 000 N B) 3 500 N C) 4 000 N D) 4 500 N
28. 28. Activity• Do Page 338, Q. 1-6