Purpose: To observe and calculate the acceleration of gravity by measuring displacements and times.Hypothesis: The rate of acceleration will be slightly less than 9.8m/s2 due to friction from the ticker timer and the pulley.Materials:* Recording Timer* Timer Tape* Carbon-paper Disks* C-clamp* Masking Tape* 250g mass* Centimeter Ruler* StopwatchProcedure:1. Arrange the recording timer on a convenient table top and clamp it to the edge of the table using the c-clamp.2. Calibrate the timer using a stopwatch and a piece of tape. Divide the total dots by the total time to find the dots per second. Do this three times and average the results for an accurate calibration.3. Attach a pulley on the opposite edge of the table.4. Measure out a 3 lengths of string that reach from the ticker timer to the outer edge of the pulley.5. Prepare three strips of timer tape by taping each to a length of string measured above.6. Tie the 250g weight to the opposite edge of the string and place on the pulley. Then feed the length of timer tape through the timer.7. Turn on the timer and simultaneously drop the weight, allowing the tape to feed through the ticker timer.8. Record the data and calculate the rate of acceleration.Data:Calibrating Ticker TapeTrial1234Dots94948992Time (s)1.691.661.531.65Period (dot/s)55.656.658.255.8Average Period56.6 dots/sec.CalculationsPeriods94/1.69 = 55.694/1.66 = 56.689/1.53 = 58.292/1.65 = 55.8Average Periods55.6 + 56.6 + 58.2 + 55.8 = 56.84Acceleration of GravityTrial12345Dots2825262525D (cm)89.671.781.871.074.4Acceleration7.317.357.757.287.63CalculationsAccelerations “d=vit + 1/2 at2”.896 = 0 + 1/2 a(28/56.6)2 = 7.31.717 = 0 + 1/2 a(25/56.6)2 = 7.35.818 = 0 + 1/2 a(26/56.6)2 = 7.75.710 = 0 + 1/2 a(25/56.6)2 = 7.28.763 = 0 + 1/2 a(28/56.6)2 = 7.63Average Acceleration7.31 + 7.35 + 7.75 + 7.28 + 7.63 = 7.465TicksTotal Displacement (cm) vs. Time (ticks)Average Velocity (cm/tick) vs. Time (ticks)0000000000010.8 ï¿½.160.3 ï¿½.060.3 ï¿½.060.45 ï¿½.090.25 ï¿½.050.80.30.30.450.2521.6 ï¿½.320.85 ï¿½.170.9 ï¿½.181.4 ï¿½.280.85 ï¿½.170.80.430.450.70.4332.3 ï¿½.462.35 ï¿½.471.9 ï¿½.382.8 ï¿½.561.45 ï¿½.290.770.780.630.930.4843.2 ï¿½.643.4 ï¿½.682.7 ï¿½.543.9 ï¿½.782.15 ï¿½.430.80.850.6750.960.5454.2 ï¿½.844.65 ï¿½.933.7 ï¿½.744.95 ï¿½.993.05 ï¿½.610.840.930.740.990.6165.6 ï¿½1.126.15 ï¿½ 1.234.8 ï¿½.966.65 ï¿½ 1.334.2 ï¿½.840.931.020.81.110.777.35 ï¿½ 1.477.85 ï¿½ 1.576.2 ï¿½1.248.5 ï¿½1.75.7 ï¿½1.141.051.120.891.210.8189.25 ï¿½ 1.859.7 ï¿½ 1.948 ï¿½1.610.5 ï¿½2.17.65 ï¿½ 1.531.161.2111.310.96911.5 ï¿½2.312.1 ï¿½ 2.4210 ï¿½212.9 ï¿½ 2.589.7 ï¿½1.941.281.341.11.431.081013.9 ï¿½ 2.7814.8 ï¿½ 2.9612.3 ï¿½ 2.4615.65 ï¿½ 3.1311.85 ï¿½ 2.371.391.481.231.561.191116.4 ï¿½ 3.2817.4 ï¿½ 3.4814.9 ï¿½ 2.9818.55 ï¿½ 3.7114.15 ï¿½ 2.831.491.581.351.691.291219.25 ï¿½ 3.8520.3 ï¿½ 4.0617.7 ï¿½ 3.5421.6 ï¿½ 4.3217.25 ï¿½ 3.451.61.691.481.81.441322.75 ï¿½ 4.5523.6 ï¿½ 4.7220.5 ï¿½4.124.9 ï¿½ 4.9820.5 ï¿½4.11.751.821.581.921.581425.95 ï¿½ 5.1927.3 ï¿½ 5.4623.75 ï¿½ 4.728.15 ï¿½ 5.6323.5 ï¿½4.71.851.951.72.011.681529.65 ï¿½ 5.9330.8 ï¿½ 6.1627.55 ï¿½ 5.5131.75 ï¿½ 6.3527 ï¿½5.41.972.051.842.121.81633.4 ï¿½ 6.6834.9 ï¿½ 6.9831.1 ï¿½ 6.2235.1 ï¿½ 7.0230.65 ï¿½ 6.132.092.181.942.191.921737.4 ï¿½ 7.4838.8 ï¿½ 7.7634.75 ï¿½ 6.9539.55 ï¿½ 7.9134.4 ï¿½ 6.882.22.282.042.332.021841.55 ï¿½ 8.3141.7 ï¿½ 8.3439.05 ï¿½ 7.8144.8 ï¿½ 8.9638.6 ï¿½ 7.722.312.322.172.492.141946.35 ï¿½ 9.2745.95 ï¿½ 9.1943.8 ï¿½ 8.7649.2 ï¿½ 9.8443.15 ï¿½ 8.632.442.422.32.592.272051.35 ï¿½ 10.2750.2 ï¿½ 10.0448.2 ï¿½ 9.6454.3 ï¿½ 10.8647.36 ï¿½ 9.472.572.512.412.722.372156.15 ï¿½ 11.2355.65 ï¿½ 11.1353.1 ï¿½ 10.6259.0 ï¿½ 11.852.05 ï¿½ 10.412.672.652.532.812.482260.95 ï¿½ 12.1960.75 ï¿½ 12.1558.1 ï¿½ 11.6264.4 ï¿½ 12.8857.25 ï¿½ 11.452.772.762.642.932.6Data Analysis:Analysis Questions:1. The increase of velocity in a uniformly accelerated motion increases at a constant rate; therefore the slope is linear in a velocity vs. time graph.2. This graph indicates that the acceleration of the falling body increases as time passes.3. In a displacement-time graph, the slope represents the velocity of a falling body. The slope in this case is not linear, indicating acceleration.4.Average of First Seven Displacement ValuesTicksTrial 1Trial 2Trial 3Trial 4Trial 5Average10.80.30.30.450.25.4221.60.8184.108.40.2061.1232.32.3220.127.116.112.1618.104.22.168.92.153.0754.24.653.74.953.054.122.214.171.124.654.25.4877.357.8126.96.36.199.25. The curve on the displacement vs. time-squared graph is probably a root curve. It illustrates a gradual increase in velocity (acceleration of the weight. Had the weight fallen from a much greater height and been allowed to reach terminal velocity, the graph would have eventually tapered off to a constant velocity.6.Accelerations “d=vit + 1/2 at2”.896 = 0 + 1/2 a(28/56.6)2 = 7.31.717 = 0 + 1/2 a(25/56.6)2 = 7.35.818 = 0 + 1/2 a(26/56.6)2 = 7.75.710 = 0 + 1/2 a(25/56.6)2 = 7.28.763 = 0 + 1/2 a(28/56.6)2 = 7.63Average Acceleration7.31 + 7.35 + 7.75 + 7.28 + 7.63 = 7.4657.46 m/s2, the value calculated for the acceleration of gravity, is substantially lower than that of the reference value, 9.8 m/s2. This decrease is acceleration is the result of systematic error-namely friction- which hindered the 250 g weight from reaching the theoretical or given value.Conclusion:Hypothesis:The hypothesis of the lab proved true. The calculated results for the acceleration of gravity proved to be significantly less than the given value of 9.8 m/s2.Evaluating the Results:The calculated results for the acceleration of gravity proved to be significantly less than the given 9.8 m/s2. Although the 7.46 m/s2 is substantially lower than the given value, the experiment is still valid in demonstrating the acceleration of gravity. While human error surely affected the results, the primary influences on the value obtained were systematic errors. Friction predominantly affected the acceleration of the 250 g weight.Many aspects of the ticker tape machine caused considerable friction: the metal guide substantially slowed the tape that it held under the needle, which also constantly halted the progress of the strip as it relentlessly struck the paper. The pulley, which the string ran off of, also contributed significant friction and slowed the progress of the weight. Although miniscule, air resistance must not be excluded from the reasons for the results. All these factors combined were able to notably decelerate the rate of acceleration of gravity.Evaluating the Procedure:The procedure had some obvious flaws that hindered the ability of obtaining accurate calculations. Built-in defects such as the reliance of a short time to calibrate the timer, coupled with the error margin for human reaction time inevitably resulted in inaccuracy. From the start, students calibrated their timers with huge margins of error, resulting in permanently skewed data.The mere fact the timer was place horizontally on the table, demanding the need of a pulley to change vertical motion into horizontal motion, resulted in the primary cause of such an off-scale answer. The paper dragged through the ticker timer’s guide rails considerably slowed the acceleration, and the need for a pulley also was a factor in hindering the calculations from accurate results.Modifications:Modifications to this lab could greatly improve the accuracy of the results and ease the process of obtaining those results. Clearer instructions could have been given, especially on the data requested. Many students had trouble understanding the poor dittos, and ended up calculating data tables more than once due to misunderstandings. The procedure could have been improved, especially by the vertical attachment of the ticker timer to a wall or post.Without the need to change vector directions or the need for pulleys, the friction could be greatly reduced. If a larger displacement had been available, more accurate results could have been obtained simply from the diminishing percentage of error as the range increased. In addition, more accurate calibrations could be taken by increasing the length of time per calibration, lowering the percent error for reaction times.