In an experiment to determine the acceleration of free fall g, the time t taken for a ball to fallthrough distance s is measured. The percentage uncertainty in the measurement of s is 2%. Thepercentage uncertainty in the measurement of t is 3%.The value of g is determined using the equation shown.22tsg What is the percentage uncertainty in the calculated value of g?A 1% B 5% C 8% D 11%
Question
In an experiment to determine the acceleration of free fall g, the time t taken for a ball to fallthrough distance s is measured. The percentage uncertainty in the measurement of s is 2%. Thepercentage uncertainty in the measurement of t is 3%.The value of g is determined using the equation shown.22tsg What is the percentage uncertainty in the calculated value of g?A 1% B 5% C 8% D 11%
Solution
The percentage uncertainty in a calculated quantity is the sum of the percentage uncertainties of the measurements used to calculate it.
In this case, the equation for g is g = 2s/t^2.
The percentage uncertainty in s is 2%.
The percentage uncertainty in t is 3%. However, because t is squared in the equation, we need to double its percentage uncertainty, making it 6%.
Therefore, the total percentage uncertainty in g is 2% (from s) + 6% (from t^2), which equals 8%.
So, the answer is C, 8%.
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