Question 3 (10 points) If Galileo measured an object\'s path to be 4.2 cm long,

Question

Question 3 (10 points) If Galileo measured an object's path to be 4.2 cm long, and the time taken crossing this path to be 3.0 seconds, what would be the range of acceptable values for the object's speed implied by the Galileo's use of significant figures? First: Compute this by finding the largest and smallest values for both distance and time implied by Galileo's use of significant figures. Use these values to compute the smallest and largest values of the velocity for this object. Find the difference of these values from the mid-point value of the speed (average value). Now compute the percent error utilizing these values. Second: Find the percent error by using the formula given in the formula sheet, (or given below). Pick the right one for this computation AL Compare your values.

Explanation / Answer

L = 4.2cm = 4.2 +/- 0.1 cm

t = 3.0s = 3.0 +/- 0.1 s ..... because last digit is always the uncertain. Hence an error equivalent to that order is possible.

first:

V = 4.2 / 3 = 1.4 cm/s
Vmax = 4.3/2.9 = 1.483 cm/s
Vmin = 4.1/3.1 = 1.323 cm/s

% error = difference in value/ average value x 100

Percentage error using max = 0.083/1.4 x 100 = 5.93%
% error using min = 0.077/1.4 x 100 = 5.5%

second:

using the given formula...

(v/V)^2 = (0.1/4.2)^2 + (0.1/3)^2 = 1.68 x 10^-3

v/V = 0.041 = 4.1%

The second formula shows lesser error that the original formula.

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