Question

1. Assume an experiment is performed with an N-number of trials. Each trial measures the same thing with exactly the same procedure and measuring tools. The thing which we measured is the "time" of a process, the trial number N is 3, the time is: "5.0s, 6.0s, 5.5s".

a.Then the "best" value (arithmetic average) of this measurement of time is s (keep 2 significant figures);

b. the standard deviation is s (keep 1 significant figures);

c. the random uncertainty associated with this "best" value is s (keep 2 significant figures).

d. If the true value is 5.0s, then what's the "t" value of this result?

2. a. An object falls from a height of 50.0m; the initial velocity is 0m/s, the acceleration is the acceleration of gravity 9.81m/s². What's the velocity of this object at t=2s?

b. How long will it take to reach the ground?

3. we assume that for a free-fall motion, the displacement "D" is 4.91m, the time "T" is 1.00s, the uncertainty of time "$LaTeX: \delta T$ δ T " is 0.10s. What is the uncertainty of gravitational acceleration "$LaTeX: \delta g$ δ g "?

Answer 1

Given N = 3, The time rightarrow 5.0 sec, 6.0 sec, 5.5 sec The best value (arithmetic average), x^bar = 5 + 6 + 5.5/3 x^bar = 16.5/3 = 5.5 sec The standard deviation S = squareroot sigma (x_1 - x^bar)^2/N - 1 S = squareroot (5 - 5.5)^2 + (6 - 5.5)^2 + (5.5 - 5.5)^2/(3 - 1) S = squareroot 0.25 + 0.25 + 0/2 = 0.5 sec The random uncertainty = maximum value - minimum value/no. of readings = 6 - 5/3 = 0.333 sec given, True value mu = 5 sec We know, x^bar = 5.5 sec, s = 0.5 sec, n = 3 t - value = x^bar - mu/(s/squareroot n) = 5.5 - 5/(0.5/squareroot 3) = 0.5/0.289 t - value = 1.730