PHYSICS MINI-LAB2.4: Culminating Example for Unit 2: Mathematical Toolkit
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1 PHYSICS MINI-LAB2.4: Culminating Example for Unit 2: Mathematical Toolkit Name: Date: PURPOSE: The purpose of this activity is to use various mathematical techniques to analyze data collected for an object sliding down a frictionless incline plane and illustrate the level of agreement between the data and the theoretical equations. APPARATUS: The air track will be placed on an incline as shown below, with one end propped up by 20.0 cm, along with the data collection hardware and the computer: Photogate 1 Photogate sec 0.20 m/s sec EXPERIMENTAL DATA: The PASCO sensors and data collection software is used to record the following data as the cart, which begins at rest, moves between the two photogates solely under the influence of gravity. A row of data will be collected for each of the distances indicated in the table: Travel Time (t) Time required to cover the distance between the Photogates. Distance (l) Distance between the Photogates. Speed (v) Speed of the cart when it passes Photogate 2. Time Interval (w) Time interval over which the Photogate 2 light beam is blocked by the cart as the cart passes the photogate. Travel Time (t) (sec) Distance (l) (m) Speed (v) (m/sec) Time Interval (w) (sec)
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3 DISTANCE VERSUS TRAVEL TIME: Data/Graph: Copy the travel time and distance data from the original data table into the table below. Then graph the data using good graphing techniques and identify the parent function that best describes the relationship between the variables. Travel Time (t) (sec) Distance (l) (m) Analysis/Predictions: 1. Selecting the Appropriate Physics Equation: One of the following is the equation that describes relationship between the distance (l) and travel time (t): Note: g = 9.81m/sec 2 and a = m 2 l 0.102gt l 0.204gt l gt l a t a. Based ONLY on the graph of the data, hypothesize which of these equations is correct b. Use unit analysis to demonstrate that the equation you selected in part a. is dimensionally consistent:
4 2. Graphing the Appropriate Physics Equation: Complete the table below using the physics equation you selected and then graph the data on the same graph as the observational data. Be certain to show ALL OF the work that supports your graph and include a key that distinguishes between the graph for the data and the graph for the equation. t (sec) l (m) 3. Using the Graph to Interpolate the Data: Predict the distance traveled by the object at 0.50 sec Predict the travel time for the object to move a distance of 9.00 inches 4. Using the Equation to Extrapolate the Data: Isolate the variable for travel time (t) in the physics equation you selected Predict the travel time for the object to move 2.49 x 10-3 miles
5 VELOCITY VERSUS TRAVEL TIME: Data/Graph: Copy the travel time and velocity data from the original data table into the table below. Then graph the data using good graphing techniques and identify the parent function that best describes the relationship between the variables. Travel Time (t) (sec) Velocity (v) (m/sec) Analysis/Predictions: 1. Selecting the Appropriate Physics Equation: One of the following is the equation that describes relationship between the velocity (v) and travel time (t): Note: g = 9.81m/sec 2 and a = m 2 v 0.102gt v 0.204gt v gt v a t Based ONLY on the graph of the data, hypothesize which of these equations is correct Use unit analysis to demonstrate that the equation you selected in part a. is dimensionally consistent:
6 2. Graphing the Appropriate Physics Equation: Complete the table below using the physics equation you selected and then graph the data on the same graph as the observational data. Be certain to show ALL OF the work that supports your graph and include a key that distinguishes between the graph for the data and the graph for the equation. t (sec) v (m/sec) 3. Using the Graph to Interpolate the Data: Predict the velocity of the object at 0.50 sec Predict the travel time at which the velocity reaches x 10 7 cm/day 4. Using the Equation to Extrapolate the Data: Isolate the variable for travel time (t) in the physics equation you selected Predict the travel time at which the velocity reaches 5.0 x 10-3 km/sec
7 VELOCITY VERSUS DISTANCE: Data/Graph: Copy the distance and velocity data from the original data table into the table below. Then graph the data using good graphing techniques and identify the parent function that best describes the relationship between the variables. Distance (l) (m) Velocity (v) (m/sec) Analysis/Predictions: 1. Selecting the Appropriate Physics Equation: One of the following is the equation that describes relationship between the velocity (v) and distance (l): Note: g = 9.81m/sec 2 and a = m 2 a v 0.102gl v 0.204gl v gl v l Based ONLY on the graph of the data, hypothesize which of these equations is correct Use unit analysis to demonstrate that the equation you selected in part a. is dimensionally consistent:
8 2. Graphing the Appropriate Physics Equation: Complete the table below using the physics equation you selected and then graph the data on the same graph as the observational data. Be certain to show ALL OF the work that supports your graph and include a key that distinguishes between the graph for the data and the graph for the equation. l (m) v (m/sec) 3. Using the Graph to Interpolate the Data: Predict the velocity of the object at a distance of 0.75 m Predict the distance at which the velocity will reach 1.20 m/sec 4. Using the Equation to Extrapolate the Data: Isolate the variable for distance (l) in the physics equation you selected Predict the distance where the object will reach a velocity of 8.64 x 10 3 km/day
9 TIME INTERVAL VERSUS VELOCITY: Data/Graph: Copy the velocity and time interval data from the original data table into the table below. Then graph the data using good graphing techniques and identify the parent function that best describes the relationship between the variables. Velocity (v) (m/sec) Time Interval (w) (sec) Analysis/Predictions: 1. Selecting the Appropriate Physics Equation: One of the following is the equation that describes relationship between the time interval (w) and velocity (v): Note: g = 9.81m/sec 2 and a = m 2 a w 0.102gv w 0.204gv w gv w v Based ONLY on the graph of the data, hypothesize which of these equations is correct Use unit analysis to demonstrate that the equation you selected in part a. is dimensionally consistent:
10 2. Graphing the Appropriate Physics Equation: Complete the table below using the physics equation you selected and then graph the data on the same graph as the observational data. Be certain to show ALL OF the work that supports your graph and include a key that distinguishes between the graph for the data and the graph for the equation. v (m/sec) w (sec) 3. Using the Graph to Interpolate the Data: Predict the time interval of the object for a velocity of 1.0 m/sec Predict the velocity for a time interval 3.2 x 10-8 years 4. Using the Equation to Extrapolate the Data: Isolate the variable for the time interval (w) in the physics equation you selected Predict the time interval when the object reaches a velocity of 8.64 x 10 3 km/day
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