physics A2 , further mechanics Watch

shk79
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A do-it-yourself company is advertising a wind turbine that they state can deliver a power of 1 kW. Their specification provides the following data: • area swept out by the blades in one revolution = 2.4 m2 • power output = 1 kW at a wind speed of 12.5 m s–1 • typical operating speed of blades = 600 revolutions per minute (a) (i) Show that the length of each blade is approximately 0.9 m.
(ii) Show that the angular velocity of the blades at the typical operating speed is approximately 63 rad s–1.
(iii) Calculate the speed at which the tips of the blades will then be travelling.
(b) The theoretical power available from a wind turbine is given by p = ½ ρAv3 where ρ = density of air = 1.3 kg m–3 A = area swept out by blades per revolution v = wind speed (i) Show that when the wind speed is 12.5 m s–1, the theoretical power from the advertised turbine is about 3 kW.
(ii) Suggest two reasons why the actual power is less than the theoretical power.
(c) The manufacturer has to ensure that when the turbine is attached to a chimney stack, the force exerted on the chimney does not cause it to collapse. The turbine is designed to cut out at a wind speed of 14 m s–1. (i) Calculate the mass of air hitting the blades each second when the wind speed is 14 m s–1.
(ii) Hence calculate the maximum force that the wind could exert on the blades
answer:
(a) (i) Use of A = πr 2 leading to 0.87 (m)
(ii) Correct use of ω = 2π/t leading to 62.8 (rad s–1)
(iii) Correct use of v = rω = 55 m s–1 [allow use of show that value]
( b) (i) Substitution into p = ½ ρAv3 (1) 3047 (W)
(ii) Air is hitting at an angle/all air not stopped by blades ,Energy changes to heat and sound
(c) (i) Attempts to find volume per second (A × v) (1) 44 kg s–1
(ii) Use of F = ∆mv/∆t (1) F = 610 N (1)

my problem is part (C)
c)i) my answer is V=Axv= 2.4x14=33.6
c)ii) F=∆mv/∆t = 33.6x14=470.4 N
as I think the density of air is 1 therefore m=V(volume)
my answeres for this part are very different from the mark scheme !
I need help wih this.
thanks
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uberteknik
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The density of air stated in the question is 1.3 kg m-3 must be used in both answers.

The volume of air must be multiplied by the density to get the mass of the air passing through the blade area.
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shk79
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Oh yes of course . Thank you so much for that. so part c) i) is now sorted. Do you know what is the problem with part C)ii)? where I am making a mistake?i can't get 44, i get 33.6 instead !
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uberteknik
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(Original post by shk79)
Oh yes of course . Thank you so much for that. so part c) i) is now sorted. Do you know what is the problem with part C)ii)? where I am making a mistake?i can't get 44, i get 33.6 instead !
You again used 33.6 kg s-1 instead of using 43.68kg s-1


F=∆mv/∆t = {(1.3 x 2.4 x 14) x 14} / 1 = 43.68x14= 611.52 N
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shk79
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(Original post by uberteknik)
You again used 33.6 kg s-1 instead of using 43.68kg s-1


F=∆mv/∆t = {(1.3 x 2.4 x 14) x 14} / 1 = 43.68x14= 611.52 N

Thank you so much uberteknik, my problem was basically the density of the air which I thought it's one.
Thank you so much again. that was a great help.
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shk79
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The last part of this question is as below . I need help with this part as well. :confused::confused::confused:

(d) The average wind speed in the UK is 5.8 m s–1, which results in an actual average power output of 100W. Discuss whether it would be better for the environment to replace some filament light bulbs with low energy bulbs than to use this turbine. Assume each filament light bulb is rated at 100W and each low energy bulb is rated at 11 W.
answer of mark scheme :
(d) Recognise that 100 W is produced over 24 hours (1)
Estimates if this would fulfil lighting needs for a day(1)
Estimates energy used by low energy bulbs in day(1)
Conclusion (2) :confused:
Example: The 100 W is an average over the whole day. Most households would use light bulbs for 6 hours a day in no more than 4 rooms, so this would mean no other energy was needed for lighting. 4 low energy bulbs would be 44 W for 6 each hours so would require energy from the National grid. [Accept an argument based on more light bulbs/longer hours that leads to the opposite conclusion]
I don't understand this answer properly, especially because I don't know what the conclusion is in the end.
so I basically need a clear conclusion. It may sound silly but I don't even know what the National grid is !!!!!!
Thanks in
advance
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uberteknik
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(Original post by shk79)
The last part of this question is as below . I need help with this part as well. :confused::confused::confused:

(d) The average wind speed in the UK is 5.8 m s–1, which results in an actual average power output of 100W. Discuss whether it would be better for the environment to replace some filament light bulbs with low energy bulbs than to use this turbine. Assume each filament light bulb is rated at 100W and each low energy bulb is rated at 11 W.
answer of mark scheme :
(d) Recognise that 100 W is produced over 24 hours (1)
Estimates if this would fulfil lighting needs for a day(1)
Estimates energy used by low energy bulbs in day(1)
Conclusion (2) :confused:
Example: The 100 W is an average over the whole day. Most households would use light bulbs for 6 hours a day in no more than 4 rooms, so this would mean no other energy was needed for lighting. 4 low energy bulbs would be 44 W for 6 each hours so would require energy from the National grid. [Accept an argument based on more light bulbs/longer hours that leads to the opposite conclusion]
I don't understand this answer properly, especially because I don't know what the conclusion is in the end.
so I basically need a clear conclusion. It may sound silly but I don't even know what the National grid is !!!!!!
Thanks in
advance

The National Grid is the high voltage electricity distribution network across the country, which interconnects electric power generation sources to the end users (domestic, industrial and civil/municipal).





Power comes from a mix of fossil based electric power sources (gas, oil, coal), nuclear power stations and renewable sources (solar, wind, tidal, geothermal, biomass).

You need to understand that some renewable sources (solar, wind, tidal) are not continuous throughout the day. e.g. solar can only be generated during the day and power output varies with seasons and weather conditions etc. Similarly wind is completely weather dependent and tidal sources depend on twice daily tidal movements.

This means that renewable sources can only be used as a supplement to continuously available sources like coal, oil and nuclear.

Low energy more efficient devices and appliances, mean that less power is needed per household.

Aggregated across the millions of households throughout the country, this equates to fewer continuous power stations needed using non-renewable fossil fuels. Fewer fossil fuel use results in less greenhouse gas emissions responsible for climate change and less pollution from airborne particulates.

Conclusion: more efficient and lower energy use devices are better for the environment.
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shk79
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(Original post by uberteknik)
The National Grid is the high voltage electricity distribution network across the country, which interconnects electric power generation sources to the end users (domestic, industrial and civil/municipal).





Power comes from a mix of fossil based electric power sources (gas, oil, coal), nuclear power stations and renewable sources (solar, wind, tidal, geothermal, biomass).

You need to understand that some renewable sources (solar, wind, tidal) are not continuous throughout the day. e.g. solar can only be generated during the day and power output varies with seasons and weather conditions etc. Similarly wind is completely weather dependent and tidal sources depend on twice daily tidal movements.

This means that renewable sources can only be used as a supplement to continuously available sources like coal, oil and nuclear.

Low energy more efficient devices and appliances, mean that less power is needed per household.

Aggregated across the millions of households throughout the country, this equates to fewer continuous power stations needed using non-renewable fossil fuels. Fewer fossil fuel use results in less greenhouse gas emissions responsible for climate change and less pollution from airborne particulates.

Conclusion: more efficient and lower energy use devices are better for the environment.
wow
Thank you so much Uberteknik.
Your explanation is great and I learnt so much. It's just the question is involved with some numbers. How can I explain that 100W ? I think a numerical answer is also needed here as this was 5 marks and the Mark scheme has answered it with some sort of calculation which I don't understand.
I have already put the answer in previous message but I now copy it here for you again.

answer of mark scheme :
(d) Recognise that 100 W is produced over 24 hours (1)
Estimates if this would fulfil lighting needs for a day(1)
Estimates energy used by low energy bulbs in day(1)
Conclusion (2)
Example: The 100 W is an average over the whole day. Most households would use light bulbs for 6 hours a day in no more than 4 rooms, so this would mean no other energy was needed for lighting. 4 low energy bulbs would be 44 W for 6 each hours so would require energy from the National grid. [Accept an argument based on more light bulbs/longer hours that leads to the opposite conclusion]
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uberteknik
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(Original post by shk79)
wow
Thank you so much Uberteknik.
Your explanation is great and I learnt so much. It's just the question is involved with some numbers. How can I explain that 100W ? I think a numerical answer is also needed here as this was 5 marks and the Mark scheme has answered it with some sort of calculation which I don't understand.
I have already put the answer in previous message but I now copy it here for you again.

answer of mark scheme :
(d) Recognise that 100 W is produced over 24 hours (1)
Estimates if this would fulfil lighting needs for a day(1)
Estimates energy used by low energy bulbs in day(1)
Conclusion (2)
Example: The 100 W is an average over the whole day. Most households would use light bulbs for 6 hours a day in no more than 4 rooms, so this would mean no other energy was needed for lighting. 4 low energy bulbs would be 44 W for 6 each hours so would require energy from the National grid. [Accept an argument based on more light bulbs/longer hours that leads to the opposite conclusion]
There is no strict answer unlike the other numerical questions.

All they want to know is that you recognise and understand the difference between various methods of generating power: the difference between continuous averaged and intermittent power output of different power generation sources: their advantages and limitations.

You can illustrate this by comparing the energy requirements of different appliances based on their average power consumption estimated through a typical daily cycle.

i.e. a 100W lamp uses more energy per hour than an 11W lamp of the same light output.

Your own experience can be used to estimate an average domestic use of lamps, there is no right or wrong answer, but it does need to be realistic.

A possible estimate shown was 6 lamps used for 6 hours a day on average throughout the whole year.
The 100W lamps will use on average 100 x 6 x 6 x 365 = 1,314 kW hours of energy per year.
The 11W lamps will use on average 11 x 6 x 6 = 145 kW hours of energy per year.

It's an average because usage will change between seasons, winter and summer, day and night.

Having estimated the total energy needed, you then need to compare the various energy sources as previously described with respect to their advantages and limitations when applied to when that estimated power will be required and whether the wind turbine source is suitable for use in isolation or needs to be used in conjunction with a different type of generator.

Finally make a conclusion as based on your assessment.

As I said, they are not looking for absolutes but you do need to provide enough content so that the examiner can decide whether you do indeed understand the issues related to power generation, energy consumption and protection of the environment.
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shk79
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Thank you so much Uberteknik. Very clear as always.

(Original post by uberteknik)
There is no strict answer unlike the other numerical questions.

All they want to know is that you recognise and understand the difference between various methods of generating power: the difference between continuous averaged and intermittent power output of different power generation sources: their advantages and limitations.

You can illustrate this by comparing the energy requirements of different appliances based on their average power consumption estimated through a typical daily cycle.

i.e. a 100W lamp uses more energy per hour than an 11W lamp of the same light output.

Your own experience can be used to estimate an average domestic use of lamps, there is no right or wrong answer, but it does need to be realistic.

A possible estimate shown was 6 lamps used for 6 hours a day on average throughout the whole year.
The 100W lamps will use on average 100 x 6 x 6 x 365 = 1,314 kW hours of energy per year.
The 11W lamps will use on average 11 x 6 x 6 = 145 kW hours of energy per year.

It's an average because usage will change between seasons, winter and summer, day and night.

Having estimated the total energy needed, you then need to compare the various energy sources as previously described with respect to their advantages and limitations when applied to when that estimated power will be required and whether the wind turbine source is suitable for use in isolation or needs to be used in conjunction with a different type of generator.

Finally make a conclusion as based on your assessment.

As I said, they are not looking for absolutes but you do need to provide enough content so that the examiner can decide whether you do indeed understand the issues related to power generation, energy consumption and protection of the environment.
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