Posted by Joy on Monday, November 11, 2013 at 10:51am.
d1 = 2.53 cm +/ .05 cm
d2 = 1.753 m +/ .001 m
0 = 23.5 degrees +/ .5 degrees
v1 = 1.55 m/s +/ .15 m/s
Using the measured quantities above, calculate the following. Express the uncertainty calculated value.
1. d3 = 4 (d1 + d2)

Physics  Count Iblis, Monday, November 11, 2013 at 11:12am
If f(x1,x2) is a function of x1 and x2 which have independent uncertainties sigma1 and sigma2, then the uncertainty in f(x1,x2) is:
sigmaf = sqrt[sigmaf1^2 +sigmaf2^2]
where sigmaf1 and sigmaf2 are the contributions to the uncertainty in f coming from x1 and x2:
sigmaf1 = f(x1+sigma1,x2)  f(x1,x2)
sigmaf2 = f(x1,x2+sigma2)  f(x1,x2)
Clearly, the uncertainty in d1 makes a contribution to the uncertainty in d3 of:
4*0.05 cm = 0.2 cm
while the uncertainty in d2 makes a contribution to the uncertainty in d3 of:
4*0.1 cm = 0.4 cm
The uncertainty in d3 is then:
sqrt[(0.2 cm)^2 + (0.4 cm)^2] =
0.45 cm