If Galileo measured an object’s path to be 4.2 cm long, and the time taken cross
ID: 1879412 • Letter: I
Question
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.
(V/V)^2=(L/L)^2+(t/t)^2
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 .... calculating for 2 significant figures
Vmax = 4.3/2.9 = 1.5 cm/s.... calculating for 2 significant figures
Vmin = 4.1/3.1 = 1.3 cm/s.... calculating for 2 significant figures
% error = difference in value/ average value x 100
Percentage error using max = 0.1/1.4 x 100 = 7.1%
% error using min = 0.1/1.4 x 100 = 7.1%
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%