LAB #2- PHY 111

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College of Business & IT Batkhela, Malakand Agency *

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111

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Chemistry

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Nov 24, 2024

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Using Spark Timer Tapes to understand Kinematic Equations and Time Graphs Purpose: The purpose of this investigation is to utilize spark timer tapes to analyze positions, velocity, and acceleration of two objects. Using these tape data, the resulting data will be used to create position and velocity graphs and then formulate kinematic equations to further understand the object's movement. Material: The material used in this investigation uses paper, printer, ruler, pen or pencil, tape, and scissors. Procedure: The initial step is to print out tape one and tape two provided in the lab module. Here, the tapes then need to be cut and tape two taped together. After the set up, create a notecard that has one’s name, MEID, and section number and place it alongside the tape set up to take a picture. From this, the next step is to measure, using a ruler, the distance at each 0.1 interval indicated at the black dots to begin collecting data. The data collected, from each tape, will be then entered into data tables into Excel; these data sets will be used to calculate the velocity using the velocity formula. The data collected will be used to create a position versus time graph; in addition, the calculated velocities, from the data, will be used to create a velocity time graph for both tapes. Then, the data and graph created will be analyzed to understand the movement of the object and further understand the spark timer tapes. The graphs, tables, and all data should be properly labeled and if needed explained. Data: Tape 1: Time (s) Position (cm) Velocity (cm/s) Acceleration (cm/s/s) 0.1 0.6 0.2 2.4 19 0.3 4.4 20 0 0.4 6.4 19 10 0.5 8.2 22 10 0.6 10.8 21 -30 0.7 12.4 16 -37.5 0.8 14 13.5 0 0.9 15.1 16 25 1.0 17.2 18.5 0

1.1 18.8 16 1.2 20.4 Tape 2: Time (s) Position (cm) Velocity (cm/s) Acceleration (cm/s/s) 0.1 0.5 0.2 1 7 0.3 1.9 12.5 60 0.4 3.5 19 62.5 0.5 5.7 25 62.5 0.6 8.5 31.5 67.5 0.7 12 38.5 65 0.8 16.2 44.5 -10 0.9 20.9 36.5 10 1.0 23.5 46.5 137.5 1.1 30.2 64 1.2 36.3 Calculations: The calculations shown below are used above to find the velocity and acceleration in both tape one and tape two. A sample calculation is shown below: Formula of Velocity: ∆X/∆T, where ∆X is change in displacement and ∆T is change in time - Sample Velocity calculation from tape one: Velocity= (X3-X1)/ (T3-T1) Velocity = (4.4 cm - 0.6 cm)/(0.3 s -0.1s) = 19 cm/s Formula of Acceleration: ∆V/∆T, where ∆V is change in velocity and ∆T is change in time - Sample Acceleration calculation from tape one: Acceleration = (V4-V2)/(T4-T2) Acceleration = (19 cm/s-19 cm/s)/(0.4 s -0.2 s) = 0 cm/s/s Graphs:

Tape # 1: Tape #2:

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Results: For tape one, the position time graph shows a slope line of y= 16.1x + -0.87; here, the slope is positive indicating the object is moving forward in a constant manner. However, taking velocity versus time for the tape one, the slope shows a negative linear slope, y= -5.03x +21.4, indicating that the object is slowing down or undergoing acceleration in the negative direction. For tape two, the position time graph presents in an exponential curvature; however, to keep the data consistent, the slope or trendline was taken in a linear format. Here, the slope is y= 32.5x + -7.78 indicating a positive slope suggesting that the object is moving in a forward direction and having a positive velocity with time. Similarly, the velocity versus time graph for tape two, having a slope of y= 54.8x + -3.11, indicates that the object has a positive acceleration and is speeding up. Conclusion: The use of collecting position and time data points allowed for the calculation of both the velocity and acceleration; these values give a greater insight to the object's motion and can be later utilized via the kinematic equations to predict and understand the object's potential velocity or acceleration at various time or even the distance in certain time intervals. Calculating velocity, speed at any direction, and the acceleration, the acceleration or deceleration in a time interval, allows for the motion of the object; then, visualizing this information via graphs, the object's motion can be predicted using a linear trendline, slope, based on a few collected data points. Here, tape one, prior to qualitative measurements, is deemed to be evenly spaced out and consistent indicating that both velocity and position time graph;s would potentially be positive. However, the collected data and the graph indicate that although the object is moving in a forward motion with constant velocity; the object is actually slowing down in the velocity time graph, indicated by the negative slope. In tape two, the predicted outcomes of both positive velocity and acceleration were correct as hypotheses; the data and upward linear slopes for both time graphs indicate a positive motion, either moving forward in direction or accelerating in the forward direction.

There are a few sources of error that could have resulted in this experiment; for one, the strips of tape were not cut precisely to avoid the black outlining. So, one tape could have had remnants of this outlining adding a few extra centimeters to the quantitative measurements. In addition, the measured data points can be skewed by a few decimal points as the tape was measured using a ruler and not digital measurement of the positioning. Although these errors could have occurred, the overall trend of the graphs would remain the same as they are a few decimal places away. In order to prevent such errors, the lab should conduct multiple trials of the same experiment, another error in this experiment, to ensure that the collected data are accurate and present the actual motion of the objects for both tapes. Analysis: 1. Use your data and graphs to determine the position of both objects after 5.0 seconds of travel. Show work. a. Tape one position after five seconds is 79.63 cm y= 16.1x + -0.87 y= 16.1 (5 sec) + -0.87 y= 79.63 cm b. Tape two’s position after five seconds is 154.72 cm y= 32.5x + -7.78 y= 32.5 (5)+ -7.78 y= 154.72 cm 2. How can you use the position graph for tape-1 to determine the velocity of the object? What is the velocity of the tape-1 object? a. The position versus time graph's slope is the velocity of the object. The slope is determined by taking the rise over the run. For tape one, two points can be taken to find the slope. For example, Velocity= change in displacement/ change in time; therefore, velocity= (2.4 cm- 0.6 cm) / (0.2s -0.1 s) = 18 cm/s 3. How can you use the velocity graph for tape-2 to determine the acceleration of the object? What is the acceleration of the tape-2 object? a. The velocity versus time graph slope shows the acceleration of the object. The object's acceleration can be also calculated using the rise over run method. The acceleration’s formula is change in velocity over change in time. Acceleration= (38.5-25)/(0.7-0.5) = 67.5 cm/s/s

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