2 Mechanics - Pearson Global Schools

More documents

Recommendations

Info

2<strong>Mechanics</strong>Power and velocityIf power _________ work donethen we cantimealso write P ____ Fstso P F ___( st )which is the same as P Fv wherev is the velocity.Horse powerHorse power is often used as theunit for power when talking aboutcars and boats.746 W 1 hpSo in Example 1, the power of thecar is 105 hp.to lift all 1000 kg at the same time or move each bag in 0.005 s, both of which areimpossible. Power is the quantity that distinguishes between these two tasks.Power is defined as:Power work done per unit time.Unit of power is the J/s which is the same as the watt (W).Power is a scalar quantity.Examples1. The powerful carWe often use the term power to describe cars. A powerful car is one that canaccelerate from 0 to 100 km h 1 in a very short time. When a car accelerates,energy is being converted from the chemical energy in the fuel to KE. To have a bigacceleration the car must gain KE in a short time, hence be powerful.2. Power lifterA power lifter is someone who can lift heavy weights, so shouldn’t we say they arestrong people rather than powerful? A power lifter certainly is a strong person (ifthey are good at it) but they are also powerful. This is because they can lift a bigweight in a short time.Worked exampleA car of mass 1000 kg accelerates from rest to 100 km h 1 in 5 seconds. What is theaverage power of the car?Solution100 km h 1 28 m s 1 .The gain in KE of the car 1_ 2 mv2 1_ 2 1000 282 392 kJIf the car does this in 10 s thenpower _________ work donetimeExercises ___ 392 78.4 kW547 A weightlifter lifts 200 kg 2 m above the ground in 5 s. Calculate the power of the weightlifter inwatts.48 In 25 s a trolley of mass 50 kg runs down a hill. If the difference in height between the top andthe bottom of the hill is 50 m, how much power will have been dissipated?49 A car moves along a road at a constant velocity of 20 m s 1 . If the resistance force acting againstthe car is 1000 N, what is the power developed by the engine?Efficiency and powerSince the work is going in and outat the same rate, efficiency can alsobe expressed as_________ power outpower inEfficiencyWhen a box is pulled along the floor, the person pulling has to do work. This workis converted into the KE of the box and some of it is done against friction. Sincethe result they are trying to achieve is to move the box, the energy transferred toKE could be termed ‘useful energy’ and the rest is ‘wasted’. (The waste energy inthis example turns into heat, but we will deal with that in the next chapter). Theefficiency tells us how good a system is at turning the input energy into useful work.56
Efficiency is defined as:Efficiency has no units.Efficiency is a scalar quantity.useful work out_____________energy put inIt is worth noting here that due to the law of conservation of energy, the efficiencycan never be greater than 1.Worked exampleA box of mass 10 kg is pulled along the floor for 2 m by a horizontal force of 50 N.If the frictional force is 20 N, what is the efficiency of the system?Solution50 N20 NThe work done by the pulling force force distance 50 2 100 JThe unbalanced force on the box 50 20 30 NSo the work done on the box 30 2 60 JThis work is exchanged to the box and increases its KE.Work done against friction 20 2 40 JSo work in 100 J and total work out 60 40 100 JEfficiency _____________useful work out ___ 60work in 100 0.6Expressed as a percentage, this is 60%.Exercise50 A motor is used to lift a 10 kg mass 2 m above the ground in 4 s. If the power input to the motoris 100 W, what is the efficiency of the motor?51 A motor is 70% efficient. If 60 kJ of energy is put into the engine, how much work is got out?52 The drag force that resists the motion of a car travelling at 80 km h 1 is 300 N.(a) What power is required to keep the car travelling at that speed?(b) If the efficiency of the engine is 60%, what is the power of the engine?2.10 Uniform circular motionAssessment statements2.4.1 Draw a vector diagram to illustrate that the acceleration of a particlemoving with constant speed in a circle is directed towards the centreof the circle.2.4.2 Apply the expression for centripetal acceleration.2.4.3 Identify the force producing circular motion in various situations.2.4.4 Solve problems involving circular motion.57
Page 3 and 4: Measuring velocityYou can measure v
Page 5 and 6: Equating equations (1) and(2)s_ (u
Page 7 and 8: Although a car was used in one of t
Page 9 and 10: Instantaneous velocitydisplacementW
Page 11 and 12: displacement-time graph for 4 bounc
Page 13 and 14: Horizontal componentsAt A (time 0)
Page 15 and 16: Projectile motion with air resistan
Page 17 and 18: 6. Air resistanceAir resistance is
Page 19 and 20: Exercises19 A ball of weight 10 N i
Page 21 and 22: 23 If the following two examples ar
Page 23 and 24: If the ball has mass m we can calcu
Page 25 and 26: Exercise26 The helium in a balloon
Page 27 and 28: Weight: The Earth is pulling the bo
Page 29 and 30: The law of the conservation of mome
Page 31 and 32: 2.9 Work, energy and powerAssessmen
Page 33 and 34: Solutions1 Work done force distan
Page 35 and 36: EnergyWe have seen that it is somet
Page 37 and 38: 2 This time the body loses PE and g
Page 39: ExplosionsExplosions can never be e
Page 43 and 44: 2. Car going round a bendWhen a car
Page 45 and 46: The elevator is supported by a cabl
Page 47 and 48: The balls are in contact for a time
Page 49: (a) The escalator is 30 m long and

2 Mechanics - Pearson Global Schools

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?