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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.
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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
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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
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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
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1 Class Lever st• 1st Class Lever: The fulcrum, or pivot, is located between the 2 forces.• E.g. lever, seesaw, teeter-totter, scissors.
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2 Class Lever nd• 2nd Class Lever: The fulcrum is located on 1 side of both forces.• E.g. wheel barrow, nutcracker
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3 Class Lever rd• 3rd Class Lever: The effort force is between the resistance force and the fulcrum.• E.g. tweezers, hockey stick
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Variations of the Lever• The pulley is a variation of the lever.• IMA = the number of supporting ropes.• IMA = ΔdE ΔdR• AMA = FR FE
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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
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The Inclined Plane• The inclined plane trades distance for force by reducing the force needed to work against gravity.• E.g. stairs, ramps, screw
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Inclined Plane Formula• IMA = length of slope = ΔdE height of slope ΔdR• AMA = FR = mg FE FE
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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Summary• Actual Mechanical Advantage, AMA, takes friction into account.• AMA = Resistance Force Effort Force
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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
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