Question

Table 1 show the data collected by a motion sensor for a ball, initially at rest, then allowed to freely fall straight downward. Table 1 Time, t(s) | Distance from the sensor (m) | t²(s²) | Displacement, ?y(m) 0 | 0.872 | | 0.10 | 0.922 | | 0.20 | 1.061 | | 0.30 | 1.287 | | 0.40 | 1.635 | | 0.50 | 2.079 | | 1. Fill in the t², and the displacement columns. Remember that displacement is direct line length directed from the initial position to the current position. (8 points) 2. Plot displacement vs time (?y vs. t). This means that ?y is the ordinate (vertical axis) and t is the abscissa (horizontal axis). (6 points) 3. Plot ?y vs. t². Then draw a Best-Fit Line through the data points. Find the value of the slope of this line, and its units. (show calculation, and units together on the graph paper) (10 points) 4. What physical quantity (velocity, acceleration, etc.) does the slope of this graph represent? (Please note; you are NOT being asked to describe the relationship between displacement and the square of the time shown by the graph) Here is a hint: The magnitude of the displacement of a freely falling mass with the initial velocity of zero is given by (6 points) 5. From the value of your slope determine your experimental value for g. (6 points) 6. Find the percent error of the experimental value of g, using g = 9.81 m/s² as the accepted value. (2 points)

          Table 1 show the data collected by a motion sensor for a ball, initially at rest, then allowed to freely fall straight downward.

Table 1
Time, t(s) | Distance from the sensor (m) | t²(s²) | Displacement, ?y(m)
0 | 0.872 | | 
0.10 | 0.922 | | 
0.20 | 1.061 | | 
0.30 | 1.287 | | 
0.40 | 1.635 | | 
0.50 | 2.079 | | 

1. Fill in the t², and the displacement columns. Remember that displacement is direct line length directed from the initial position to the current position. (8 points)
2. Plot displacement vs time (?y vs. t). This means that ?y is the ordinate (vertical axis) and t is the abscissa (horizontal axis). (6 points)
3. Plot ?y vs. t². Then draw a Best-Fit Line through the data points. Find the value of the slope of this line, and its units. (show calculation, and units together on the graph paper) (10 points)
4. What physical quantity (velocity, acceleration, etc.) does the slope of this graph represent? (Please note; you are NOT being asked to describe the relationship between displacement and the square of the time shown by the graph) Here is a hint: The magnitude of the displacement of a freely falling mass with the initial velocity of zero is given by (6 points)
5. From the value of your slope determine your experimental value for g. (6 points)
6. Find the percent error of the experimental value of g, using g = 9.81 m/s² as the accepted value. (2 points)

Table 1 show the data collected by a motion sensor for a ball, initially at rest, then allowed to freely fall straight downward.

Table 1
Time, t(s) | Distance from the sensor (m) | t²(s²) | Displacement, ?y(m)
0 | 0.872 | |
0.10 | 0.922 | |
0.20 | 1.061 | |
0.30 | 1.287 | |
0.40 | 1.635 | |
0.50 | 2.079 | |

1. Fill in the t², and the displacement columns. Remember that displacement is direct line length directed from the initial position to the current position. (8 points)
2. Plot displacement vs time (?y vs. t). This means that ?y is the ordinate (vertical axis) and t is the abscissa (horizontal axis). (6 points)
3. Plot ?y vs. t². Then draw a Best-Fit Line through the data points. Find the value of the slope of this line, and its units. (show calculation, and units together on the graph paper) (10 points)
4. What physical quantity (velocity, acceleration, etc.) does the slope of this graph represent? (Please note; you are NOT being asked to describe the relationship between displacement and the square of the time shown by the graph) Here is a hint: The magnitude of the displacement of a freely falling mass with the initial velocity of zero is given by (6 points)
5. From the value of your slope determine your experimental value for g. (6 points)
6. Find the percent error of the experimental value of g, using g = 9.81 m/s² as the accepted value. (2 points)

Added by Katherine H.

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