Energy & electricity

Name: ……………………………………………………………………………………………….

Physics in

Physical Sciences 3C

Theory & Exam ples Book 2 Criterion 7

! I V W ork, Energy & Pow er ! V Electricity

Rosny College

2013

Physical Sciences 3C Energy Physics Theory

Rosny College 2 2013

Contents BOOK 1 Motion [Criterion 5] Page Part A Introduction Measurement and Units Vectors 3 Scale Drawing Addition of Vectors Components of Vectors Part B Kinematics 6 Graphs of Motion Displacement~time graphs 8 Velocity~time graphs 10 Acceleration~time graphs 13 Linear Motion – Equations of Motion 15 Vertical Motion 18 Motion on an Inclined Plane 19 Projectile Motion 20 Part C Forces and Newton’s Laws Forces 22 1st Law 27 2nd Law 29 3rd Law 33 Lifts and Parachutes General Problems Part D Momentum Momentum and Impulse 40 Conservation of Momentum 44 BOOK 2 – Energy [Criterion 7] Part E Work, Energy and Power 3 Part F Electricity 15 Electricity Questions 29 Answers 33 BOOK 3 Nuclear Structure and Radioactivity [Cr 6,7] Atomic and Nuclear Structure Radioactive Half-Life Nuclear Equations Alpha, Beta and Gamma decay Fission and Fusion Ionising Radiation and Radio-isotopes This teaching booklet is a work in progress. The editor welcomes any corrections, comments or suggestions.



Part E:Work, Energy and Power

Work Work (W) is done when a force F causes an object to undergo displacement s Work done is the product of Force and displacement

W = F.s Work is a scalar quantity (even though both force and displacement are vectors). The units for work are N m (newton metre) which is given the name joule (J). Note that if there is no displacement, then no useful work is done! You can push against a wall all day, but if the wall does not move you have not done any mechanical work. It is only the component of the force in the direction of the displacement which actually does work. So if the force is at an angle to the displacement

W = FCos θ.s ie W = FsCos θ

Examples 1 How much work is done by:

a) A force of 35 N (east) that moves an object 12.0 m (east)?

b) A force of 50.0 N (N30oE) that moves an object 20 m (north)?

c) A motor which lifts a 100 kg load through 15 m at a steady speed?

F

s

θ



Work can be calculated from an 'F' ~’s’ graph. The work done is given by the AREA under the graph! Area = F.s = Work done

This is also true for varying (non-constant) forces.

Example 2 How much work is done by the force shown in the graph above?

0

1

2

3

0 10 20 30 40 50 60

F (N)

s (cm)



ENERGY The ENERGY of a body determines its ability to do WORK. Since energy is measured in terms of the work a body can do, energy has the same units as work; ie. joules (J). Like work, energy is a scalar quantity. The energy of a body is determined by its MASS and either its: (i) POSITION (called potential energy EP) or (ii) VELOCITY (called kinetic energy EK)

POTENTIAL ENERGY (EP) This is the energy of an object due to its position or elevation (gravitational EP) above some arbitrary zero or base level. The amount of energy the object possesses is equal to the work done in lifting the object to that level. An object of mass 'm' lifted a vertical height 'h' has the work done in overcoming the force which is the body's weight 'm.g' i.e. Work done = FW x s = m x g x h Thus the object's potential energy is given as:

EP = mgh

KINETIC ENERGY (EK) Consider an object of mass m at rest; ie. u = 0 Having no motion, it has zero kinetic energy ie. EK = 0 Let the object be acted on by a force F and thus undergoes a displacement s and gaining velocity 'v'. Work done

= F x s

= m x a x s

= m x

v2 = u2 + 2.a.s and u = 0

= m.

thus

a.s =

Now that the object is moving, we say that it possesses the kinetic energy (EK) equal to the work done on it.

EK =

or EK =

Note there are other forms of energy: electrical, elastic, chemical etc. Heat is a very important form of energy. When there is friction, kinetic energy is being converted into heat energy.



Examples 3 Find the change in potential energy (EP) when a 15 kg mass is lifted through a

height of 1.5 m.

4 What is the kinetic energy of a) A 100 kg cyclist travelling at 22 m s -1 eastwards.

b) An electron of mass 9.1x10-31 kg moving at 2.0x107 m s-1 ?



Work and Energy Work is a transfer of energy. When work is being done on an object, its energy level changes. If an object has a change in energy, then work must have been done on it.

Work done = change in energy W = ΔE

The energy is transferred from the body doing the work to the object having work done on it. If a body changes speed as a result of a force applied, then Work done = change in kinetic energy W = final EK – initial EK = EKf – EKi Or EKf = EKi + W

Examples

5 A 200 kg cart is moved from rest to be moving southwards at 5.0 m s-1. a) What was its final kinetic energy?

b) What was its change in kinetic energy?

c) How much work was required to bring the cart to that speed?

d) If the accelerating force was 500 N (south), how far did the cart move while the force was acting on it?



6 A 40.0 kg trolley is travelling northwards at 1.0 m s-1. It then has a resultant force acting on it as shown.

a) Calculate the initial kinetic energy of the trolley.

b) What was the work done on the trolley by the force?

c) Find the final kinetic energy of the trolley.

d) Calculate the final speed of the trolley.

0 2 4 6 8

10 12

0 2 4 6 8 10 12

F (N) North

s (m)



CONSERVATION OF ENERGY: In any interaction or change, the total energy before and after is the same. However, this energy is often converted into forms which we cannot easily use e.g. heat and sound. In a car collision for example, considerable energy is used to deform the cars and this generates a lot of heat and sound. Mechanical Energy is kinetic and potential energy. A collision which loses mechanical energy as heat or sound is said to be inelastic. A collision where no energy is lost in this way is called elastic. Objects in elastic collisions always “spring back” to their original shape. All collisions (except on a sub-atomic scale) lose some mechanical energy, but we can approximate an elastic collision with little energy loss (eg Newton’s cradle, billiard balls. A roller coaster approximates an elastic interaction between cart and the earth). If we can ignore friction Conservation of Mechanical Energy ie. {EP + EK}INITIAL = {EP + EK}FINAL Thus in the closed system with no friction the mechanical energy is conserved.



Examples 7 A 30 kg child is at the top of a 3.0 m high slide (assumed frictionless)

a) What is her potential energy at the top of the slide?

b) What is her EP at the bottom of the slide?

c) Find her increase in kinetic energy.

d) If the girl was at rest at the top of the slide, what would her speed be when she reached the bottom?

e) Her 85 kg father then rode the slide. What would his speed be at the bottom?

8 A 2.0 kg cart is travelling at 3.0 m s-1 along a smooth horizontal surface when it reaches a plane inclined at 150 to the horizontal. Calculate: a) The initial kinetic energy of the cart

b) The final potential energy of the cart

c) The maximum vertical height reached by the cart

d) The distance along the inclined plane the cart travels before it comes to rest.



9 A 120 kg kart is travelling northwards at 16 m s-1. It then comes to rest in a distance of 18.0 m. a) How much heat is generated by the brakes in

bringing the Kart to rest?

b) Calculate the average force exerted by the brakes.

10 A 1000 kg roller-coaster car, at point A 30m above the ground is travelling at 2.0 m s-1. A short while later, it is at point C 5.0 m above the ground. Ignore friction. a) What is its speed at C?

b) Between A and C, the car went through a loop-the-loop. At point B at top of the loop, the car is 10m above the ground. Calculate the car’s speed at B.

A B

C



Power This is defined as the rate of doing work.

Power = W = work in joules (J) t = time in seconds

P =

P = power in watts (W) [Watt = Joule per sec (J s-1)]

Since work equals the change in energy of an object, this equation can also be written

P =

∆E is change in energy

Another useful equation is easily obtained

P =

= and since

P =

- only use this formula for constant velocity.

Examples 11 Calculate the power required to:

a) Do 2.4 kJ of work in 2.0 minutes

b) Lift a 65 kg mass 6.0 m in 9.2 seconds

c) Accelerate a 500 kg car from rest to 72 km/hr in 6.0 sec.



12 The engine of a 600 kg car has a useful power output of 20 kW.

How long will it take the car to accelerate from rest to 100 km/hr?

13 A 1.5 kW electric motor is driving a pump which is delivering water to a tank 8.0 metres above the ground. If the motor & pump are 65% efficient; in 45 minutes, a) how much work is done on the water?

b) How much water is delivered to the tank?



14 A 45 kW lift motor raises a 3.5 tonne elevator through a

height of 25 metres in 35 seconds. Calculate: a) The energy output from the motor.

b) The useful work done on the lift in raising it 25 m.

c) The heat energy dissipated.

d) The efficiency of the lift system



Part F: CURRENT ELECTRICITY Current electricity is the flow of free electric charges through a conductor. We use electricity for two main purposes: • To carry energy: from hydro stations to our homes and industries for heating etc or

from a car battery to the starter motor for example. • To transfer information: copper telephone lines and computers run on electrical

signals. CHARGE and CURRENT ELECTRIC CHARGE: (Q) This is measured in units of coulombs (C). It is a derived quantity ELECTRONIC CHARGE: (e-) The electrical charge on a single electron is: 1.00 C of charge is equivalent to 6.242 x 1018 electrons!!! Also, the number of electrons associated with a charge of Q coulombs is:

Example 1 A plastic ruler has a charge of -1.5 nC. How many excess electrons are on the ruler?

ELECTRIC CURRENT: (I) Current is the rate of flow of electrical charge. It is measured in amperes (A). It is a base quantity. A current of 1 amp is a flow of 1 coulomb of charge per second. i.e. I = current (in amperes)

Q = charge (in coulombs) t = time (in seconds)

and



A I

Measuring Current Current is measured using an Ammeter. An ammeter measures the current passing through a point in an electrical circuit. Example 2 A current of 1.6 amps flowed through a meter for 2½ minutes.

a) What charge has passed through the meter?

b) How many electrons flowed through the meter?

Continuity in an Electrical Circuit • An electrical circuit needs to be continuous – no breaks. • The circuit must form a complete loop, so the charge can flow from the battery to the

load and then be returned to the battery. • The current leaving the battery is the same size as the current returning to the battery. • The electric charge is NOT used up as it goes around the circuit – the electrons do not

disappear. Energy is used up however.

Direction of Current (I). I is taken as the direction of motion of positive charges. We know that in many conductors, metals especially, it is the negative charges (eg electrons) which are actually moving. The current (I) would therefore be in the opposite direction to the motion of the electrons.



ENERGY and VOLTAGE Energy in an Electric Circuit The energy is carried by the electric charge as it moves around the circuit. The energy is supplied to the charge by a cell, battery or generator. This energy is then dissipated as heat and motion etc by the electrical components.

E.m.f. (electromotive force) [E ]

This is what we usually refer to as the “voltage” of a battery or the mains. The e.m.f. tells us how much energy is given to each coulomb of charge delivered by the battery etc. A 12V car battery gives 12 joules to every coulomb of charge delivered. The 240V mains supply gives 240 joules to every coulomb of charge. i.e. a coulomb of charge delivered by the mains has 20x as much energy as a coulomb from a car battery.

A battery is usually indicated by: The longer line is the positive terminal: the (positive) current flows out from positive and in towards negative.



POTENTIAL DIFFERENCE: (p.d.) (V) Electric current flows from a region of high energy to one of low energy. [Similar to the way water flows from high to low.] This difference in energy is indicated by potential difference. p.d. is measured in units of joules per coulomb (J C-1) which is commonly known as the volt (V). Thus a potential difference of 6.0 volts between two points indicates that each coulomb of charge will lose or dissipate 6.0 joules of energy as it moves between the points. This becomes heat energy or similar. i.e.

V = p.d. [= “voltage”] (in volts = joules/coulomb) = change in energy (in joules) Q = charge (in coulombs)

and

Note: V is used for both the variable (p.d.) and the unit (volts)!! Be careful. Remember: See “volt”, think “joules per coulomb”.



Current flows from high potential (high energy) to low potential (low energy).



Measuring Potential Difference (pd). Potential difference (“voltage”) is measured using a voltmeter. The voltmeter is measuring the difference in electrical energy between two points in the circuit (usually before and after a resistor or other component). As the charge moves through the component, it is losing energy - often as heat. The voltmeter shows this energy loss. Examples 3 2.0 C of charge flowed through a potential difference of 12 volts.

How much energy was dissipated by the charge?

4 If 0.15 C of charge loses 3.0 J of energy, through what potential difference has it

moved?

5 An electric heater is connected to the (240V) mains.

a) What is the p.d. across the heating element?

b) If 2.0 amp flows for 30 minutes, how much charge has passed through the heater?



c) How many joules of heat energy have been released in that time?



ELECTRIC CIRCUITS and METERS Series and Parallel Connections

Series Parallel

In a series connection, all the current passes through both components

In a parallel connection, the current is split between the two branches. The amount in each branch depends on the resistances.

Connection of Ammeters and Voltmeters

Ammeters are connected in series with the component being measured.

Voltmeters are connected in parallel with the component being measured.

Properties of Ammeters and Voltmeters. Ammeters are designed to let current flow without interruption. They therefore have a very low resistance. Thus, ammeters are quite easily damaged if they are connected incorrectly – it is easy for too much current to pass through the ammeter and burn it out. Take particular care when connecting and using ammeters. If using a variable power supply, be sure to turn it right down before connecting the ammeter. Then turn the voltage up slowly while keeping an eye on the meter needle; if the needle moves hard to the right, turn off the power supply immediately! Voltmeters are designed so that very little current passes through them – all the current should pass through the component. Voltmeters therefore have a very high resistance. This means that voltmeters are more robust than ammeters and are less likely to experience burn-out. This is a simple circuit to measure both the current through the resistor and the potential difference across it. (To test Ohm’s Law for example.) The emf source is a variable supply.

Note: The positive terminals (+) are usually red. The other (-ve) terminal is usually black).



RESISTANCE and OHM’S LAW RESISTANCE: (R) If current passes easily through an object, the object has low resistance. If the current does not pass easily, the object has high resistance. Resistance depends on what the object is made of and its shape and size. Resistance is measured in ohms (Ω). [The letter R is occasionally used in place of the Ω symbol, especially in Electronics.] There is a simple relationship between resistance, p.d. and current. i.e.

R= resistance (in ohms (Ω)) V = p.d. [= “voltage”] (in volts = joules/coulomb) I = current (in amps)

and

This relationship is often referred to as “Ohm’s Law”

A component made specifically for its resistance is called a resistor. The resistor has two symbols: (new style) and (old). An insulator is a non-conductor – it has high resistance.

V

I R



Examples 6 A 0.60 A current flows through an electrical component which has a 12V potential

difference across it. What is the resistance of the component?

7 A 100R resistor has a p.d. of 12V across it. What current will flow through the resistor?

8 If 15 mA flows through a 10kΩ resistor, find the potential difference across the resistor.



ELECTRICAL POWER: (P) Power is the rate of dissipation of energy.

P = power (in watts (W) = joules/second) E = energy change (in joules) t = time (in seconds)

P = V x I

P = I2 x R

Examples 9 A car light globe has 12V across it and 2.5A passing through it.

At what rate is the globe dissipating energy?

10 A light globe rated at 60W is connected to the mains. a) What current will flow through the globe?

b) What is the resistance of this globe?



ELECTRICAL ENERGY and POWER

Since , then

i.e. Energy dissipated = Power x time

Example 11 A 1.0kW mains heater runs for 1.0 hour.

a) How much heat energy (in joules) does the heater emit in this time?

b) How much electrical energy was used?

c) If the whole generation and distribution process in hydro-generation is 65% efficient, how much potential energy due to the water was used?

d) If the dam in question has a head of 35m, how many of litres of water ran through the turbines to generate the required energy?



Household Electrical Energy In the electrical supply industry, electrical energy is usually sold, not in joules, but in electrical “units” or kilowatt-hours (kWh). E is in kilowatt-hours when P is in kilowatts and t is in hours. Remember: When you buy electricity, you are paying for ENERGY not POWER!! Examples 12 How many joules in 1 kWh?

13 An off-peak heater draws 6.0 kW of electrical power for 720 hours over the winter. a) How many kWh has it used?

b) What is the cost of running this heater if the electricity costs 6.5c per unit?

c) How many joules of energy were used?



DOMESTIC ELECTRICITY & ELECTRICAL SAFETY Active and Neutral Wires Electricity supply requires two wires: one to the consumer/appliance and another to return to the energy source. The return wire is usually connected to the earth (i.e. there is no p.d. between this wire and the earth). This helps stabilise the electricity supply and the earth is also a fairly good conductor. The wire connected to the earth is called the neutral wire; the other wire is the active wire. The active wire will of course be at a potential difference of 240V from the earth.

Hazardous Currents Contrary to popular belief, high voltages in themselves are not necessarily dangerous. When you remove clothing from a drier or comb your hair, the crackling indicates that you are dealing with many thousands of volts. However the current flow is extremely small and there is no danger. It is the current flow through the body, the heart in particular, which is hazardous and the electrical mains can potentially deliver a very large current. The lethal effects are a combination of the size of the current and its duration. Current in mA Effect 1 Maximum safe current. 2 – 5 Causes a reaction in most people. 10 Muscular spasms – unable to let go, could become fatal 100 Probably fatal if through the heart. As indicated by Ohm’s Law, the size of the current depends on the voltage across the body and the total resistance. The resistance can vary enormously depending on factors such as whether the person is wet or dry or is in direct contact with the ground. ELECTRIC SHOCK is the reaction we get from this current. ELECTROCUTION describes a fatal shock; i.e. the person is killed. Grounding. If an appliance is faulty, the active wire might touch the case. If this is metal, the appliance is then “live” i.e. the case is at 240V relative to the ground. If a person who is in contact with the ground then touches the case, they provide a pathway to the ground. A current can then pass through that person to ground with potentially fatal consequences.



Three Pin Plugs and Fuses. To reduce this problem a third wire is used in houses – this is the earth wire. This explains the “three-pin plugs” we use. The earth wire is connected directly to earth near the house and is connected to the metal frame of any appliance. This ensures that the appliance case is always at ground potential, reducing the electrical hazard. If the active wire touches the case, the case still remains at close to ground potential. It will usually result also in a large current straight to ground which will “blow” the fuse; this isolates the appliance from the mains. If a fuse blows, check for faulty appliances before replacing the fuse. Circuit breakers are similar in operation to fuses but are more convenient as they can be reset. Fuses and circuit breakers also “blow” if too many appliances are connected to a circuit whose current capacity is exceeded. The Earth (third) wire is a safety feature; it plays no part in normal electrical operation. In some (less safe) parts of the world there is no third wire or pin. Double Insulation. Some appliance have “double insulation”. They have two layers of insulation between the live wires inside and the case. This makes the appliance safe and they generally only have two wires (i.e. use a 2-pin plug). Residual Current Device (RCD). These are in addition to fuses. In normal operation, the current in the Active and Neutral lines should be the same. However, if a person touches the active wire, some of the current is diverted to ground and the currents are no longer in balance. The RCD detects this imbalance and turns off the circuit. These devices offer great personal safety as they trigger very quickly and they respond to current leakages which are quite small.



Earth Leakage Circuit Breaker (e.l.c.b.) works in a similar fashion to RCDs. Some questions to ponder • Why don’t birds get an electric shock (or get

electrocuted) when they perch on a power line?

• Can a bird get electrocuted from power lines? • Sometimes electrical workers work on

power lines when the line is “live”, even high voltage ones (22kV or higher). How are they able to do this?

• Why is it particularly hazardous to touch an electrical appliance when you are in the bath?

• Why do electricians use fibreglass ladders not aluminium ones which are lighter?

• If you get a tingle when touching a toaster, what does this indicate? What should you do?



ELECTRICITY PROBLEMS Electrical Charge and Current 1 If an electrical charge of 25.0 coulombs passes a point in an electrical circuit in 210

seconds, find: a) the current flowing. b) the number of electrons that passed.

2 During the starting of a car, 220 coulombs passes through the starter motor in 5.5

seconds. Find: a) the electric current through the motor. b) the number of electrons passing in the 5.5 s.

3 A current of 5.00 A is required to operate a portable refrigerator. If 60.0 C of charge

passes, find: a) the time the fridge was operating. b) the number of electrons passing in this time.

4 In a computer monitor the current in the electron beam forming the picture on the

screen is 2.5 mA. In 32 seconds, a) what charge reaches the screen? b) how many electrons reach the screen?

5 A car battery supplies an electric current of 4.0 A for 3.0 minutes. Find:

a) the total charge flowing and b) the number of electrons leaving the battery.

6 A service station charges a car battery using a current of 5.50 A for 6.00 hours. Find:

a) the charge which flowed and b) the number of electrons passing in this time.

7 What is the current flowing through a cell membrane in the body if 1000 sodium ions

cross the cell membrane in 1.0 microsecond? The charge on each sodium ion is 1.60 x 10-19 coulombs.

Potential Difference (pd) and emf

8 An electric cell supplies 115 J of energy to every 23.0 C of charge that passes

through it. Find the EMF of the cell.

9 A power pack with an EMF of 12.0 volts is delivering a current of 2.50 A. How much electrical energy does it supply per minute?

10 15 C of charge “falls” through a p.d. of 240 V. How much energy is released?

11 Calculate the work done by the electrical forces in maintaining a current of 1.50 A for 50.0 seconds in an electrical motor which operates with a 12.0 V battery.

12 How much work is done when an electric charge of 5.00 coulombs is moved through an electric kettle by a P.D. of 240 V?



13 In a computer disc-drive circuit, an electron carrying a charge of 1.60 x 10-19 C used 8.00 x 10-19 J of energy to move between two points. What is the P.D. between these two points?

14 An electron gun in a colour T.V. set has a P.D. of 15.0 kV. How much energy would an electron have when it left the gun?

Resistance and Ohm's Law 15 A resistance of 30 Ω is placed across a 90 V battery.

What current flows in this circuit?

16 A potential difference (P.D.) of 75 V is placed across a 15 Ω resistor. What current flows through the resistor?

17 What is the resistance of a light filament if the current flowing in it is 0.523 A when the P.D. across it is 240 volts?

18 What is the current flowing in a 50.0 Ω resistor if the P.D. across it is 250 V?

19 What is the voltage drop across a 45.0 Ω resistor when the current flowing through the resistor is 255 mA?

20 A current of 0.50 A flows through a lamp when it is connected to a 120 V source. What is the resistance of the lamp's filament?

21 A motor with an operating resistance of 30 Ω is connected to a power source. If the current in the circuit is 4.0 A, what is the P.D. across the motor?

22 A radio draws a current of 0.20 A when it is connected to a 3.0 V battery. What is the resistance of the radio's circuit?

23 A resistance of 60 Ω allows a current of 0.40 A to flow when it is connected to the terminals of a battery. What is the P.D. across the resistor?

24 Draw a diagram to show a circuit having a 90 V battery, an ammeter and a resistance of 60 Ω. What does the ammeter read?

25 Draw a diagram to show a circuit having a 60.0 V battery, an ammeter, a voltmeter to read the P.D. across the resistor and a resistance of 12.5 Ω. What does the ammeter read?

26 Draw a circuit diagram to include a 16.0 Ω resistor, a battery, an ammeter that reads 1.75 A and a voltmeter to read the P.D. across the resistor. What would the voltmeter read?

27 What would be the size of the power source (in volts) required to drive a current of 20.0 mA through a resistor of 4.7 MΩ?

28 What current would a 9.0 V transistor radio battery drive through a 4.7 MΩ resistance?



Electrical Power and Energy 29 An immersion heater has a resistance of 20 Ω and is used with 240 V mains supply.

a) What current flows through it? b) What is its power output?

30 The element of an electric oven is designed to produce 3.00 kW of heating power

when connected to a 240 V mains supply. Find: a) the current flowing. b) the resistance of the element.

31 A 6.0 W light bulb is connected to a 12 V supply. Find:

a) the current flowing. b) the resistance of the bulb's filament.

32 A transistor radio with a 9.0 V battery draws a maximum current of 400 mA. Find:

a) the resistance. b) the power output of the radio.

33 An electric jug is rated at 2.4 kW. How much heat energy does it dissipate in 1½

minutes?

34 a) What is the current through the filament of a 100 W light globe powered by a

120 V supply? b) How many 100 W light globes can be operated in parallel with a 120 V supply

without melting a 10.0 A fuse?

35 What is the cost of using a 60.0 W electric light for 12.0 hours if the tariff is given as 9.30 cents per kW.h?

36 A particular electric kettle is power rated at 2.50 kW. The kettle is to be used with a 240 V electrical supply. Find the: a) current the kettle draws. b) resistance of the kettle's element. c) cost of using the kettle for 15 minutes

(given: each kW.h of energy costs 9.30 cents)

37 A household has a three-month electricity bill of $425. If the average unit cost of electricity is 8.5c, find: a) The number of kWh used and b) The average power consumption of the household over the period.



38 a) A swimming pool electric heater is rated at 4.50 kW. If to initially warm the

water in the pool requires continual heating for the first two days, find the energy used in the two days in units of: i) joules. ii) megajoules. iii) kW.hours.

b) Once the pool is warmed to the required temperature, a thermostatic control

turns the heater on for an average of six minutes per hour to maintain the temperature. i) For how many minutes per week is the heater on? ii) How many kW.h of energy is consumed each week? iii) What is the cost per week of maintaining the pool at the desired temperature

assuming the "off-peak" tariff rate is 6.56 cents per kW.h?

39 The specific heat capacity of water is 4.17 kJ kg-1 K-1. [i.e. it requires 4.17 kJ to raise the temperature of 1 kg (1 L) of water by 1 degree.] a) How much energy is required to raise the temperature of 2.0 L of water from 15O

C to 95 O C? b) How much electrical energy would be required? c) How long would it take a 2.4 kW heating element to do this?

40 Estimate how much water would need to flow through the turbines at the power

station at the Gordon Dam to heat the electric jug in the previous question. Indicate any assumptions.



Answers

1 a 0.119 A 31 a 0.5 A b 1.56 x 1020 b 24 Ω 2 a 40 A 32 a 22.5 Ω b 1.38 x 1021 b 3.6 W 3 a 12.0 s 33 216 kJ b 3.75 x 1020 34 a 0.833 A 4 a 0.080 C b 12 globes b 5.0 x 1017 35 6.70 c 5 a 720 C 36 a 10.4 A b 4.5 x 1021 b 23.04 Ω 6 a 1.19 x 105 C c 5.81 c b 7.42 x 23 37 a 5 000 kW h 7 1.6 x 10-10 A b 2.26 kW 38 a 7.78 x 108 J (778 MJ) 8 5.0 V 7.78 x 108 J 9 1 800 J 216 kW h

10 a 3 600 J b 1 008 minutes 11 900 J 75.6 kWh 12 1 200 J $4.96 per week 13 5.0 V 39 a 667.2 kJ 14 2.4 x 10-15 J b 667.2 kJ 15 3.0 A c 278 sec (4 min 38 s) 16 5.0 A 40 ~ 2 000 L 17 459 Ω ( 2 tonnes!!) 18 5.0 A 19 11.5 V 20 240 Ω 21 120 V 22 15 Ω 23 24 V 24 1.5 A 25 4.8 A 26 28 V 27 94 kV 28 1.9 µA 29 a 12 A

b 2 880 W 30 a 12.5 A

b 19.2 Ω

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