Determine the calculated value using the given values and given equations. Using the error propagation method, calculate the percent error in the calculated value. g=2h/t^2
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To determine the calculated value using the equation \( g = \frac{2h}{t^2} \) and to calculate the percent error using error propagation, we will follow these steps: Show more…
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Rule (4) Suppose t = 3.40 ± 0.10 s, g = 9.81 ± 0.05 m/s^2, and h = (1/2) gt^2 h = (1/2) gt^2 = (1/2) • (9.81) • (3.40)^2 = 56.7 m The fractional error in g is Δg/g = (0.05/9.81) = 0.005 The fractional error in t^2 is Δt^2/t^2 = 2(Δt/t) = 2(0.10/3.40) = 0.059 The numerical factor (1/2) has no error. Therefore, Δh/h = [0.005^2 + (0.059)^2]^{1/2} = 0.0592 = 0.059 (rounding off). Then, Δh = h (Δh/h) = (56.7 m) • (0.059) = 3.3 m And finally h ± Δh = 57 ± 3 m Note: In this example, the fractional error in g may be neglected since it is ~ 10 times smaller than that in t^2. Therefore, the fractional error in h is equal to the fractional error in t^2.
Sri K.
A ball is dropped (with zero initial velocity) from a height from the floor; the time (t) it takes for the ball to hit the floor can be calculated by the equation, "t^2 = 2H/g" or equivalently (2H/g)^(1/2) where g is the Earth's gravitational acceleration. If the height is measured to be H = 1.410 m with a probable error of 0.010 m, and the gravitational acceleration is known to be g = 9.82 m/s^2 with a probable error of 0.23 m/s^2, what is the relative error in the determination of the time t? HINT: Keep your final numerical answers to at least 3 significant figures regardless of how many figures the input numbers have.
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The theoretical value of G is 6.674 x 10^-11 Nm^2/kg^2. Use the equation below to calculate your percent error. % error = |theoretical value - experimental value| / theoretical value x 100% Hint: Use the value you found from question 3 in the previous section. Watch your significant figures. Explain why you have a non zero value for the percent error. Hint: Students will think that since this is a simulation that the error should be 0, but it won't be. Think about what can affect your results and human error is not a permitted answer. This kind of answer doesn't provide any specific information that would allow a future researcher to improve upon the experiment.
Suzanne W.
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