ASSIGNMENT: ERROR ESTIMATION

1.	Two forces have magnitudes (50  3) N and (25  2) N. Calculate the absolute and percentage maximum uncertainty in
(a)	the sum of the forces,
(b)	the difference of the forces.			[(a) 5 N, 7%     (b) 5 N, 20%]

2.	The force exerted by a gas on a piston of radius (8.0  0.4) mm is measured to be (30  2) N. Calculate
(a)	the uncertainty in the area of the piston, and
(b)	the maximum percentage uncertainty in the calculated value of the gas pressure in the cylinder.					[(a) 20 mm2     (b) 17%]

3.	If the maximum error in measuring the period of a simple pendulum is 0.05% and in measuring the length is 0.6%, what is the maximum percentage error in the calculated value of the gravitational acceleration?		[0.7%]

4.	Calculate the maximum percentage uncertainty in the following example: X = a - 2b where a = 50  1 m and b = 24  0.5 m. (The answer illustrates the need for careful measurement when dealing with the difference between two almost equal quantities.) 
							[100%]

5.	A rectangular block has a mass of (1.5  0.1) kg, and a volume that can be calculated from the following dimensions: (80  2) mm, (50  1) mm and (30  1) mm. Assuming that all the errors are independent, calculate the maximum uncertainty in the measured values of 
(a)	the volume of the block
(b)	the density of the block.
					[(a) 9.4  10-6 m3     (b) 1.8  103 kg m-3]

6.	Standard deviation. This gives a measure of the spread or scatter of a number of observations. It is defined as the r.m.s. value of the deviations from the mean. The following readings are for a particular time interval t:
t/s = 190, 186, 181, 195, 191, 189, 196 and 184.
Calculate
(a)	the mean of the observations
(b)	the deviations from the mean
(c)	the sum of the squares of the deviations from the mean
(d)	the mean square deviation 
(e)	the standard deviation.			[(a) 189 s      (e) 4.8 s]