This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
✅ Correct. The calculations and the application of the uncertainty propagation formula are correct. Step 1: Calculate S_s. S_s = (4 × 0.004)/(6 × 3.90) = (0.016)/(23.4) ≈ 0.00068376 m/s^2 Rounding to one significant figure, S_s ≈ 0.0007 m/s^2. This matches the student's calculation. Step 2: Use the uncertainty propagation formula. The formula for propagating relative uncertainty is given as: (S_g)/(g) = (S_s)/(S) Rearranging to solve for S_g: S_g = (S_s × g)/(S) Given: S_s = 0.0007 m/s^2 (uncertainty in slope) g = 9.8 m/s^2 (assumed value of acceleration due to gravity for calculation of uncertainty) S = 0.25 m/s^2 (nominal value of the slope) Step 3: Substitute the values and calculate S_g. S_g = 0.0007 m/s^2 × 9.8 m/s^20.25 m/s^2 S_g = (0.00686)/(0.25) m/s^2 S_g = 0.02744 m/s^2 Rounding to two significant figures (consistent with the precision of 9.8 and 0.25, and a common practice for uncertainties), S_g ≈ 0.03 m/s^2. This matches the student's calculation. Step 4: State the final result. The final result for g is given as 9.86 ± 0.03 m/s^2. The calculated uncertainty 0.03 m/s^2 is correctly applied to the experimental value of g (assumed to be 9.86 m/s^2). The number of decimal places for the uncertainty and the central value are consistent.