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MEASUREMENTS
     
1. A body is observed to move a distance s=15m in a time t=6s.
The distance was measured using a ruler marked in cm and the time was measured using a watch giving readings to 0.1s.
  a) Express these results correctly.
  b) Use the measurements to calculate the speed of the body, including the uncertainty in the value of the speed.
2.   The dimensions of a piece of paper are measured using a ruler marked in mm.
    The results were x=50mm and y=40mm.
  a) Rewrite the results of these measurements correctly (that is, giving the right number of significant figures and the appropriate indeterminacy).
  b) Calculate the maximum and minimum values of the area of the sheet of paper which these measurements give.
  c) Express the result of the calculation of area of the sheet of paper in the form: area = A δA.
     
3.   The diameter of a cylindrical piece of metal is measured to a precision of 0.01mm.
    The diameter is measured at five different points along the length of the cylinder.
    The results are shown below; units are mm.
   
  i) 6
  ii) 6.4
  iii) 5.7
iv) 6
  v) 6.4
  a) Rewrite the list of results correctly (that is, giving the right number of significant figures and the appropriate indeterminacy).
  b) Calculate the average value of the diameter.
  c) State the average value of the diameter in a way which gives an indication of the precision of the manufacturing process used to make the cylinder.
  d) Calculate the average value of the area of cross section of the cylinder.
    State the result as area=Amm2 x%
     
4.   The diameter of a metal ball is measured to be 30.0mm 0.1mm.
    The mass of the ball is measured to be 110g 1g.
    Use these results to find a value for the density, ρ of the metal of which the ball is made.
    Density is defined as mass per unit volume so to calculate the density of a substance we use the equation:
   
    Calculate the indeterminacy in this result and state your final answer in the form: density=ρx%.
     
5. A body which is initially at rest, starts to move with acceleration a.
It moves a distance s=10.00 0.01m in a time t=4.0 0.1s.
    Calculate the acceleration.
    Now find first the percentage uncertainty in the value of the acceleration then the absolute uncertainty.
     
6.   A person uses a simple balance to find the mass of a sheet of paper.
    The balance has a box of known masses of which the smallest is 1g.
    It is found that when 50 identical sheets of paper are on the balance, 15g is not quite enough for balance but 16g is just too much.
   
    Assuming that the balance itself is perfect and ignoring the indeterminacy in the manufacture of the masses, state the mass of one sheet of paper including first an absolute uncertainty and then a percentage uncertainty.
 
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