Question

5. Given that the error in measuring each mass is the same (call it om), show that the propagated error in the acceleration formula in Question 4 equals Hint: It is best to use Error Propagation Rule V from Pre-Lab 01: Primer on Experimental Errors: ам ơm

Answer 1

A = (m - m_f/m + M) g Hint delta a = squareroot (partial differential a/ partial differential m (delta m))^2 + (partial differential a/partial differential m_f (delta m))^2 + (partial differential a/ partial differential M (delta m))^2 partial differential a/ partial differential m = g partial differential (m - m_f)/ partial differential m (m + M)^2 - partial differential (m + M)/ partial differential m (m - m_f)/(m + M)^2 differentiation by u/v division Rule = g((m + M) - (m - m_f))/m + M^2 = g (M + m_f)/(m + M)^2 (i) partial differential a/ partial differential m_f = g/m + M partial differential (m - m_f)/ partial differential m_f = -g/(m + M) = -g/(M + m)^2 (m + M) (ii) partial differential a/ partial differential M = (m - m_f) partial differential (1/m + M)/partial differential M = (m - m_f) g-1/(m + M)^2 = -g (m - m_f)/(m + M)^2 using (i) (ii) & (iii) delta a = squareroot (g/(m + M)^2 (M + m_f) delta m)^2 + (g/(m + M)^2 (M + m) delta m)^2 + (g (m - m_f)/(m + M)^2 delta m)^2