Questions 1. (8 points) Is the reliability of your experimental value more sensitive to imprecision in length, or imprec
Posted: Sun Jul 10, 2022 11:53 am
Questions
1. (8 points) Is the reliability of your experimental value moresensitive to imprecision in length, or imprecision in time? Justifyyour answer by comparing the fractional error term for length andfractional error term for time from your calculation for Sg.
2. (10 points) Would using just one measurement of the length ofthe pendulum have resulted in a more reliable value ofgravitational acceleration? Justify your answer numerically bycalculating the error Sg’ using your first measured value forlength and the reading error of the 2-meter stick, then compare theresult to your experimental error, Sg, from the resultssection.
3. (12 points) There are many “common sense” methods of loweringthe randomness reflected in the standard deviation, Sx such asusing more precise instruments (calipers instead of a ruler, or atelescope instead of binoculars). Our pendulum experiment focuseson a particular strategy that might not be so “common sense.” Incertain situations, improving fractional error can be used toincrease your experimental precision. An error which normallyaffects a single measurement, Sx, can be distributed acrossmultiple measurements, n, effectively reducing the error to Sx/n.In the case of the pendulum, the uncertainty introduced by startingand stopping the stopwatch is limited by the experimenter’sresponse time, which cannot be easily improved. In the first partof the experiment this imprecision in timing occurs twice for everysingle measured period. In the second part of the experiment thisimprecision in timing occurs twice, but for fifty measured periods.The imprecision in timing in the second part is spread out over amuch larger measurement.
a. Assume the error in timing when starting and stopping thestopwatch is +0.2 seconds. So, if a single period is measured, theentire 0.2 second error affects this one period. Suppose thestopwatch is used to record 10 continuous periods, how much of thiserror affects a single period? How much for 50 continuousperiods?
b. Describe two changes to the experimental method that wouldincrease the precision of your experimental result for g50
1. (8 points) Is the reliability of your experimental value moresensitive to imprecision in length, or imprecision in time? Justifyyour answer by comparing the fractional error term for length andfractional error term for time from your calculation for Sg.
2. (10 points) Would using just one measurement of the length ofthe pendulum have resulted in a more reliable value ofgravitational acceleration? Justify your answer numerically bycalculating the error Sg’ using your first measured value forlength and the reading error of the 2-meter stick, then compare theresult to your experimental error, Sg, from the resultssection.
3. (12 points) There are many “common sense” methods of loweringthe randomness reflected in the standard deviation, Sx such asusing more precise instruments (calipers instead of a ruler, or atelescope instead of binoculars). Our pendulum experiment focuseson a particular strategy that might not be so “common sense.” Incertain situations, improving fractional error can be used toincrease your experimental precision. An error which normallyaffects a single measurement, Sx, can be distributed acrossmultiple measurements, n, effectively reducing the error to Sx/n.In the case of the pendulum, the uncertainty introduced by startingand stopping the stopwatch is limited by the experimenter’sresponse time, which cannot be easily improved. In the first partof the experiment this imprecision in timing occurs twice for everysingle measured period. In the second part of the experiment thisimprecision in timing occurs twice, but for fifty measured periods.The imprecision in timing in the second part is spread out over amuch larger measurement.
a. Assume the error in timing when starting and stopping thestopwatch is +0.2 seconds. So, if a single period is measured, theentire 0.2 second error affects this one period. Suppose thestopwatch is used to record 10 continuous periods, how much of thiserror affects a single period? How much for 50 continuousperiods?
b. Describe two changes to the experimental method that wouldincrease the precision of your experimental result for g50