SS Dec 2001Example experiment report for PHYS 342LThe following report is written to help students in compiling their own reports for PHYS 342L class. Note that this report does not represent a real experiment and thus should be used only as an example of style and form. The actual experiment reports will usually be longer as there is more material to cover.Boris YolkinData analysis, results and uncertainties.The data obtained by using automated data acquisition setup was analyzed in two ways.DiscussionConclusionAcknowledgementsReferencesSS Dec 2001Example experiment report for PHYS 342LThe following report is written to help students in compiling their own reports for PHYS342L class. Note that this report does not represent a real experiment and thus should beused only as an example of style and form. The actual experiment reports will usually belonger as there is more material to cover.Disclaimer : The attached report has no scientific value, any resemblance of the theory,referred names or experiments presented in it with known theories, names or experimentsis absolutely coincidental. It is expected, however, that students will describe real theory,use real names and present data from real experiment in their reports.1Measuring the magnitude of the gavitational field of Earth g.Boris YolkinDepartment of Physics, Purdue University, W.Lafayette, IN 47907Abstract. In this work we determined the magnitude of Earth’s gravitational field g by measuringfree fall times for various objects released at different heights and using the Newton’s 2ndlaw. We found that g=9.810.08 N/kg, which is in good agreement with the commonlyaccepted value of 9.8 N/kg. 2Introduction.The empirical fact that all material objects fall towards Earth if not supported has beenknown to humankind for as long as it has existed. Moreover, all live creatures on Earthconsciously or unconsciously use this phenomenon in everyday life. However, it haslong been believed that heavier objects fall faster than lighter ones, and there was noexact theory to describe the motion of an object. Only in the 17th century, when IsaacNewton stated his famous motion laws and gave an exact relationship between force,mass, and acceleration, the quantitative description of motion became possible. In thefollowing paper, we have used the laws of motion to measure the magnitude of thegravitational field of Earth.Theory.Newton’s 2nd law states that any object would accelerate at a constant rate a if subjectedto a constant force F [1]:a=F/m (1)where m, the proportionality coefficient, is called mass of an object. The mass of anobject should not be confused with its weight, as it is an intrinsic property of an object toresist acceleration (inertia), while weight refers to a force which attracts one object toEarth or some other usually larger object. While mass is constant1, weight may bedifferent on different planets, or even in different places on the same planet.We can rewrite Eq. 1 in a more conventional form:F=ma (2) Surface of Earth F=mg h Fig. 1. Any object is a subject to force F=mg toward Earth1 We consider only nonrelativistic case.3The force at which an object is attracted to Earth, or its weight, is also proportional to its mass (Fig. 1) [2]:Fweight=mg (3)where g is proportionality coefficient. By comparing Eq. 2 and Eq. 3, one can see that g has the same units as a. Moreover, if an object is subjected to gravitational force we can combine Eqs. 2 and 3:ma=mg (4) ora=g (5)The last equation states that an object in free fall will accelerate toward earth withconstant acceleration equal to g. The units of g are therefore m/s2, the same as foracceleration. Sometimes, however, units of N/kg are used to reflect the nature of g.defined by Eq. 3. Since acceleration is a second derivative of object’s coordinate, we can rewrite Eq. 5 in the following form:gdthd22(6)where h is a height of an object from the surface of Earth. Integrating Eq. 6 we get:gtgdtdtdht0 (7)tgtgtdth022(8)22thg (9)The last equation shows that g can be easily determined if one measures free fall times tas a function of height h. In fact, a single pair of (h,t) is sufficient to uniquely determinethe value of g. In this work, however, we will measure fall times for various heights totest the validity of Eq. 9 as well.Experimental apparatus and proceduresIn the first part of the experiment a 0.5 kg solid aluminum ball was dropped down fromdifferent floors of a 10-story building and fall times were measured by a stop watch. Theheights to different floors were measured by a conventional ruler.4T S B PE Computer Figure 2. Experimental setup for measuring fall times as a function of height. T –translation stage, S – automated shutter, PE – piezo-electric detector, B – metal ball.In the second experiment fall times from heights up to 2 meters were measured by anautomated setup (Fig. 2). Here, a container filled with small metal balls B and equippedwith computer controlled shutter S is attached to a caret of a vertical translation stage T.Computer program slowly moves the caret T and releases metal balls at specified heights,one at a time. Simultaneously, the computer timer is started. The ball falls onto piezo-electric detector PE and that sends a stop signal to the computer timer. The precision ofthe timer is 1 ms, and the height is determined to 5 mm. The experimental apparatus isdescribed in more details in [3].Data analysis, results and uncertainties. Part 1. The results of the first experiment are shown in Fig. 3. Here, the error in fall timemeasurement was estimated to be 0.2 s and is mostly determined by the reaction time ofthe experimentalist. The height was measured by a ruler to ±2 cm precision. Error barsfor height are not shown in Fig. 3 since they are smaller than the size of the dots whichrepresent the measured points. The general shape of this graph is well described with the quadratic dependence defined by Eq. 8, the solid line in Fig. 3 represents the expected dependence with the value g=9.8 m/s2. To analyze these data further, we used Eq. 9 to calculate the value of g for each datapoint, and the result of this calculation is shown in Fig. 4.500.511.522.533 6 9 12 15 18 21 24 27 30Height, mTime, sFigure 3. Dependence of fall time on height. The solid line is theoretical simulation usingEq. 8 and g=9.8 m/s2. Error