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    • Thread Starter

    Some questions I am stuck on. Hope you can answer them.

    Estimate the smallest change in amount of petrol in a car tank that a typical petrol gauge can show.

    Estimate the resolution of the skin of your hand as a temperature detecting device.

    Show that the ascii code 32 is represented by the 8-bit binary code 00100000.

    Show that
    (a) the radio of the highest to the lowest frequency of the LF to EHF bands is 10 million.
    (b) the ratio of their wavelengths is also 10 million.

    If the 1m wire was folded in half, so that it was half as long but in effect has twice the cross-sectional area, show that its resistance would be 100ohms.

    The monitor screen of a scanning electron microscope is 200mm x 200mm, and is scanned in 500 lines. If the corresponding area of a specimen is 1um x 1um, show that the linear magnification is 100000. Also show that the system can just resolve 2nm on a specimen.
    • Study Helper

    This is important:

    Reading through these questions it seems they are all about scientific 'thinking', methodology and sources of information rather than absolute answers. They are all to do with how you would go about making an estimate, where could errors creep in, limits of your measuring devices, limits of human perception etc. In all the questions, I would say it's far more important to describe your scientific thinking, method and list errors etc. than fixate on an absolute result.

    Do these for yourself, they are a valuable lesson in scientific process. If you don't think about it, you will not learn.

    q1. There is no absolute correct answer. The whole thing is an estimation so you need to show how you arrived at your estimate.
    So the petrol gauge is analogue? You need to work out the smallest change your eye can reasonably discern on that gauge - say half the width of the pointer?
    Now estimate that width as a fraction of the end-stop gauge travel. The assumption is that this is also the fraction of fuel in a full tank that can be measured assuming the measuring device is a linear and not logarithmic scale.
    You next need to determine how much fuel the average tank can hold. So you can now estimate the fraction of fuel the gauge can show. What are the sources of error? Fuel sloshing around in the tank? Parallax? Size of the gauge? As you can see, the whole estimate is based on a set of assumptions. How reliable are those assumptions?

    q2. There is no absolute correct answer. You could do an experiment with glass of water, a thermometer and a heat source. Another way is to make an assumption that the smallest division on the scale of an average thermometer is an indication of human temperature receptor sensitivity. You have to be very aware that human sensitivity to temperature is influenced by many factors. i.e. is sensitivity the same throughout the temperature scale from freezing to near boiling? Can your brain be fooled because human perception is relative? Is sensitivity the same for all humans or could you get a different answer if you used different test subjects? These are sources of error.

    q3. You need to find out what ASCII code is and how that relates to the different number bases. i.e. decimal, hex, binary.
    This is about finding the key to the ASCII code because there will not be some magic formula to convert between the different bases. The answer is arbitrary because it does not follow any laws of physics - a purely human construct. This is about finding a reliable source for your information. How do you know its reliable?

    q4. You need to find out what the terms LF and EHF mean from a radio-frequency perspective in the electromagnetic frequency spectrum.
    When you find that, it will tell you the range of frequencies covered. So then convert these to wavelengths. you will need f = 1/wavelength. You can now divide one by the other to get the ratio of both frequency and wavelength. Where did you get your information from? Is the source an international standard? How do you know it's reliable.

    q5. Not enough information is given. The resistivity for the conductor is missing and you will need the correct formula relating length and cross sectional area of the conductors to its resistance. You cannot work out the resistance unless you know what the conductor is made from, or, you make an assumption about the conductor material. i.e. Copper? Silver? Graphite? and find an appropriate source to quote a resistivity figure

    q6. The assumption here is that 1um can be displayed over the full width of the monitor screen. The rest is simple ratios and division. But where could the errors creep in?
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