v*",+o,,"\,4 4* *\h *.o, ob: tt m] 4nu>\;* Yr t{ I o L L ) z l h ,L J I J L+ o b I 4.o Va.*,,' tt>-l 4t tr'/c o>r r> a1 h r) ? 7 ! a-h ) ,Ll !k b 2 )( rr>4 -) ,.0. r 2 s. ,IU [. t2 Ow Ot4^ ) r1 dn'^ . )o1 (-) & r..rn, t ot^ q I t L A )o ( az \Irru + r,^a)F-h- sl, Vt - ,\ 4/- Lab 5: Ballistic Pendulum due at the beginning of Iab two weeks after data collection will strike the floor. Objective Use consen,ation of er.rergy and momentum to predict the location that a ball Equipment Ball + launcher, balance, ruler, I - and 2-meter sticks, triangle, tape, paper, carbon paper, laptop. Procedure I Detach the arm from the ballistic pendulum. Measure its mass. Measure the mass of the ball (the projectiie). 2 ball in the arm. Find the location of the center of mass of the arm + ball by locating its balance point. Mark this point with a small piece of tape, if necessary. (Later, we will leam that we can calculate tire change in gravitational potential energy ofthe anl + ball by considering the total mass of the arm + ball to be at the location of the center of mass.) Reattach the arm. Place the 3 Obtain an expression for the initial velocity ofthe projectile that is fired into the ballistic pendulum in terms of the change in height of the center of mass and other measured quantities. Do this using conservation of momentum and energy. (Hints: Is momentum conserued during the collision? Is energy conserved? ls momentum conserved during the swing of the pendulum? Is energy consen/ed?) Present a derivation ofyour results. 4 Fire the ball into the arm eight times and measure the change in height of the center of mass of the ann assembly each tirne. Calculate the initial velocity of the ball for each trial, and find the average, maxirnurn and minimum of these velocities. 5 Measure the initial height of the ball above the floor. Calculate the time the ball will be in the air. Using the average, maximum, and minimurn velocity and the initial height of the ball above the floor, calculate the horizontal distance the ball will travel when fired horizontally from the top of the lab table to the floor. The maximum and minimum velocities will yield maximum and minimum distances traveled. The average velocity will yield a typical distance traveled. 6 Make a paper-carbon paper-paper "sandwich" to measure the actual distance ffaveled by the ball. Place the sandwich on the floor where you expect the ball to land. On the top sheet, draw and label lines for the average, maximum and minimum distances. Fire the ball at the paper eight times. Measure all eight distances and find the average, maximum and minimum horizontal distances that the ball moves. Comment on any discrepancies between your predictions and your observations. Sample Data Tables These are sample data tables for your final report. Do not take your data on this sheet. 0bserved mu.-:1,fr. fo (hcu)i mhell: I I . \.!,,v1 Calculated (hcrrl)r 2t.Zta ) ,i.1.n t.bcn Ahcu Vball Vavel Observed heieht: Calculated time: drve! d-*! dmin! A full uncertainty analysis is required for this lab write-up. Be sure to think about this while vou are taking data. distance duve! dmax! Vmu! Vmin! Observed dmin! Diablo Valley College IMPORTRNT Physics 130 Rodriguez Fall2018 Guidelines for Lab Reports (How to Get Full Credit on Lab Reports and Make Everybody Happy) Summary Keep it simple, but keep it complete. A short repofi that is well organized and contains all of the necessary a higher score than one that is much longer that contains essentially the same information. Make it easy to read-don't make the reader work harder than necessary to understand the results of your lab information will get Lab Write-Up Guidelines Your lab reports should be short and to the point, and should address the most important aspects of the lab. You must type your reports. Every lab report should have the following sections, in order: l. Lab partners' names in top right-hand comer. 6. 7. 8. 9. 2. Title 3. Objective 4. Results Summary (include uncertainties) 5. Data Tables and Graphs Discussion/Error Analysis Conclusion (if not redundant) Formulas and Sample Calculations Original data sheets (pen only) Section 4 should address only the content of Section 3. For example, in the first lab of Physics 130 you might be measuring the acceleration due to gravity. Your results should be presented as in the following table. g (m/s2) fractional uncertainty (69/9) t 0.09 9.3 0.8 Your goal is to measure a quantity as accurately as possible. However, the true value of the measured quantity should lie within your error. These two constraints work in opposite directions, and keep lab interesting. Note that here I have reporled value for g. A common error is to report several values, each based on a different set ofdata. ry Section 5 should have all data presented neatly in tables. For Tables: include units and uncertainties; include lines; don't break tables across pages. For Graphs: label axes; include error bars, equations oftrendlines, and R3 values; do not connect dots. Be sure that I know what I am looking at when I read your report-if you need to be there to explain your report to me, your report can be improved. Section 6 should concentrate on major sources ofuncertainties (usually instrument and use), and should explain how you arrived at the estimates of uncertainties presented in the Results Summary. We will use a simple method for propagating uncertainties. Usually, in the labs that you will do, differences between careful (e.g., quadrature) and simple (e.g., MinAvlax) propagation of uncertainties will be overwhelmed by instrument/use uncertainties. Also, uncertainties can arise in two somewhat different ways: (l) uncertainfy in measurement and (2) combining the results of several trials. Be sure to distinguish between these two in your report, if relevant. Section 8 should contain the derivation of each non-trivial formula you used, as well as a numerical example of using every formula you used. This allows me to, among other things, give partial credit for incorrectly calculated uncertainties. Section 9 must contain your original data sheets (ifapplicable). These must be taken clearly and legibly by hand, in pen, and must be initialed by the professor in lab on the date the data was taken. Uncertainties Rules 1. Experimental uncertainties must have one significant figure. 2. the last significant figure in a measured quantity must be of the same order of magnitude (in the same decimal position) as the uncertainty in that quantity. The Three Most Common Reasons for Lost Points . Defective Results Summary o . BreakingUncertainties Rules No units Diablo Valley College IMPORTONT Physics 130 Rodriguez Fall2018 Uncertainty measured value of x : xr.rt * fractional uncertainty 6x : 6ry'xu",t "How Do I Calculate 5x?" Often one of the most important and most difficult things to do is to calculate 6x, the uncertainty in x, where x is a directly measured quantity. Here are two methods-the "Official" method and the "Fudge" method-that are acceptable in this class. In your lab reports, always be sure to indicate which you're using. Utlicial Method In the Official Method, we say that 5x: dxr + 6xu, where 6x is the "Total uncertainty," 5x1 is the "Instrument uncertainty," and 6xu is the "Use uncertainty." You usually should address these while you are taking data. : 6x Total uncerlainty 6xr Instrument uncertainty 6xu Use uncertaintv 6xr + 6xu Usually, half of the smallest division (or one-third, depending on your taste). For a ruler, for example, this is often 0.5 mm. Due to the User. Examples: Parallax in reading a ruler, not putting the ruler exactly at the end of the object being measured, not holding the ruler parallel to the object, uneven-ness ofend ofobject being measured, etc. etc. etc. Determining 6x_is the step that often gives students the most trouble. Fudge Method In the Fudge Method, there must be several independent measurements of the same value. We choose the minimum 5x such that some large percentage (say, 80%) of the data points lie within 6x of xu,".ur.. This is easiest to understand by looking at some examples, such as those below. 7 7 4 6 6 Data 3 2 5 5 3 5 2 6 I 2 4 9 I I 1 3 2 3 4 8 10 8 7 3 3 4 5 4 1 5 5 9 2 5 6 4 I 3 3 Average Fudge 5x 2 2 Propagating Uncertainties or "How Do I Get 6Q from 6x, 6y, ...?" How do you calculate the uncertainty in an indirectly measured quantity? You "propagate" the uncertainties in the directly measured quantities. Three ways to propagate error are 1. Fudge (described above),2. Min/Max (described below), 3. Quadrature (possibly described in earlier classes). You are welcome to use any of these three methods. In your write-up, clearly indicate which method you use. Max/Min Method: Imagine that we are trying to indirectly measure a quantity Q, which is related to two directly measured quantities x and y. Data is taken in sets: (x + 6x, y 5y). We estimate the uncertainty 5Q (Q* - Q-)/2, where Q* is the maximum value of Q and Q- is the minimum value of Q. t : For example, if x'tan(y)lz3,then Q: x/y, then Q*: (x + 6x)/(y- 6y) and Q-: (x - 6x)/(y + 6y). Another example: if Q: Qr: (x + Ex)tan(y + 6y)l(z- 6z)3 and Q- - (x - 6x)tan(y - 6y)/(z + 6z)3 Note that this simply gives the uncertainty in Qfor each data sel. If several values of Q are averaged together to produce one reported value, then there are (at least) two uncertainties in Q: the individual 5Q for each set, and the spread of the Q values, often modeled by taking the standard deviation, o. If the number of data sets is small (less than 4 or so), you should use the above method to estimate the final reported value of 6Q. If the number of data sets is larger, you can use the standard deviation or a graphing/fifting method. In the latter cases, however, be sure to report the individual 6Q in your lab report.
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