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Physics Laboratory: The Softball/Bowling Ball Drop Mr. Harwood Purpose: The purpose of this experiment is to determine the acceleration due to gravity for a softball and a bowling ball both analytically and graphically and then compare those experimental values to the accepted value. g acc 9.8 m 2 s Apparatus: The devices used in this lab will include: o String (pre-sized to particular lengths) o Masking Tape o Stopwatch o Bowling ball o Softball Procedure: As an overview, this lab will consist of dropping softballs and bowling balls from the side of the outside bleachers at varying heights. The time for each drop will be recorded in the table given. Each drop will require three trials. Make sure the values for the trials are fairly consistent (within 0.15s). The time values for these trials will then be averaged for the main set of calculations. Using this times and their corresponding distances, we can calculate the acceleration (due to gravity) of the respective balls. *Practice timing several drops at ground level before dropping from bleachers.* **Please also note the mandatory safety procedures found at the end of this handout.** Key Equations: The two main equations used here are the gravitational equation used to calculate distance and the percent error equation. Gravity Equation We begin with an equation from Chapter 4 (Kinematics). d vi t 12 gt 2 Since we are dropping the respective balls ( vi 0 ), the first quantity ( vi t ) drops out, leaving us with the following. d 12 gt 2 Since we will already know d and t, we need to solve the equation for g, which is shown. *This is the equation you will use.* g Percent Error You will need this equation to compare your experimental value for gravitational acceleration with an actual value for g. 2d t2 % Error Exp Acc 100 Acc % Data Collected: Fill in the tables below. Please note: you will need to present these retyped in your reports. See your instructor for assistance with tables. Softball Data d (m) t Trial 1 (s) t Trial 2 (s) t Trial 3 (s) t Average (s) g exp( sm2 ) t Trial 2 (s) t Trial 3 (s) t Average (s) g exp( sm2 ) Bowling Ball Data d (m) t Trial 1 (s) Data Derived from the Graphs (Calculating Instantaneous Velocity Using Tangent Line) d (m) Softball Data d (m) t (s) vinst ( ms ) 1 2 3 4 5 Slope of v vs t Slope Above Derived From Excel Formula Slope of v vs t BowlingBall Data 1 2 3 4 5 Slope Above Derived From Excel Formula Conclusive Data g exp avg ( sm2 ) Softball Data Bowling Ball Data g acc( sm2 ) % Error Calculations and Graphs: o Calculations Segment: Your calculations section should contain a sample calculation for each of the types of calculations that you will have needed to use in order to complete this lab report. Your equations must be type either with MathType or Microsoft Equation Editor. See your instructor for additional help with this program. o Graphing Segment: Graphs are to be neat, labeled, and understandable. All in all, you should have 4 graphs (2 d vs. t graphs and 2 v vs. t graphs). You may attach the graphs to the end of the paper or insert them in the document. Please abide by the following instructions: Use Microsoft Excel® to plot a d vs. t graph for each of the balls (2 graphs). Use the set displacements with their corresponding average times as data points. Then use the program to insert a “poly” curve to show the curved trend. (See instructor for additional help if necessary) Print a large copy of each graph. For each graph, calculate the instantaneous velocity for every integer displacement (1m, 2m, 3m, 4m, 5m, etc.) by drawing a tangent line (with a ruler) at each of the desired positions. Then make right triangles using the tangents as the hypotenuse of each respective triangle. The “rise” is the d and the “run” is the t. Don’t make the triangles too small. Overlapping triangles is not a problem. See the diagram below for sample layout. Record your findings in the data collection section (“Data Derived from Graphs”). Provide sample calculations in the calculations section. Using the data just derived for instantaneous velocity, plot a v vs. t graph for each ball using Excel®. Then use the program to insert a line with formula present. (y = mx + b format) Record the slope from the formula in the table. Conclusion: Include a summary of how the procedures and analysis found in this experiment accomplished its overall purpose. Also include a paragraph containing any pertinent sources of error for this experiment. Remember not to use “human error” as one of these sources. Then answer the following questions below. Concluding Questions: 1. What are the similarities/differences in the data recorded for the falls of the two differing balls? 2. In general, what factors may have affected the fact that your data may have varied between the softball and the bowling ball? 3. Are there any other settings/conditions in which the experiment may have worked better? If so, please explain. 4. Consider your calculations for instantaneous velocity. What is happening as time progresses? How is the velocity changing with each passing second and approximately by how much? 5. What would your estimate be of the velocity of the ball for a 6m drop? Justify your answer. 6. How does the slope of the v vs. t graph compare with your calculated acceleration due to gravity (gexp)? **Safety Notes (Please Read!)** A falling object has the potential to cause serious physical harm if participants are not following the specific safety instructions provided by the teacher. Each group will have one student whose complete job is to manage safety. This student will monitor the spot underneath the dropping point to make sure no one is present at the time that the ball is held out over the rail and/or released. It is only that particular student who will give the “ok” for each drop. This student must also be vigilant of other groups. Failure to participate in the safety procedures will result in a zero grade for the lab group. + Safety First! + Overall Lab Report Layout [Formal] *This Lab Must be Typed* o Name o Purpose o Apparatus o Theory and Equations o Data Collected (tables, etc) o Sample Calculations & Graphs o Conclusions Answers to Questions *Note: Nothing from this worksheet may be copied word for word in a report.