Instruction to answer:
Use Statistics. Answer the question using the statistical principles. For example, if I ask "Are the means different?" you should know that I mean this: "Is there a statistically significant difference between the means?" If I do not state a confidence level, assume I mean 95% (=0.05).
Show your work. I need to see how you answered each question or I will not give you credit for it. The answer alone is not enough. Please give me a few lines for each problem, describing what steps you took, what program or equation you used, how you came to your conclusion. Also take screen shots of your work and insert the screenshots into a Word document.
Define uncertainties Are they SD, SEM or confidence intervals? Always state the sample size. If you want to cut and paste the results page from the program you use (or capture an image and paste that into a document) that would be fine, too. Just circle or highlight your final answer and write/type in any other information I may have asked in the question.
Significant Digits. When you express your final answer, be sure to pay attention to significant digits. Rewrite the final result with the correct significant digits and highlight it or put a box/circle around it or make it a special color so I can find the final answer easily.
Question:
The acceleration due to gravity determine the timing a pendulum swing or a drop time of a dropped object (assuming ideal behavior in a vacuum). The relationships are described with the equations below. The average value for g on earth is 9.80665 m/s2. Set up a pendulum (a heavy object on a light string) or drop a dense object from a measured height. Use the stopwatch on your smartphone to time the swing or drop time. Repeat this 20 times and record the 20 measurements.
Measurment of Gravity
Pendulum
T = period(sec)(there and back); L = Length (m)' g = 9.81 m/s2
Period (T) = 2Π√L/g
g = (2Π/T)2L
Falling object
T = time(sec); H = height(m); g = 9.81 m/s2
H = 1/2gt2
g = 2.H/t2
A) Assuming that your measurement of height is perfectly accurate and has no uncertainty, calculate the expected time in your experiment. For example t=sqrt(2H/g) for a dropped object. g=9.80665 m/s2
B) Assume that this is a new experiment that you have never done before. Plot a histogram and determine if your data are Gaussian.
C) Compare your measurements with the expected time calculated in A. Is the null hypothesis supported or not supported by your measurements?
D) What do you conclude about the accuracy of your measurement technique?