LAB 2

Plotting Motion Diagrams

OBJECTIVES

1.Practice graphing and interpreting position, velocity and time data.

2.Measure the acceleration of a freely falling object.

3.Practice using Excel to fit a curve

EQUIPMENT

Freefall apparatus, spark timer, meter stick, ruler, and special graph paper.

PROCEDURE

Part 1: Plotting position vs. time for a falling object

  1. Obtain a record of a falling ball's positions at regularly spaced time intervals (1/60 s) on a spark tape.Hints: (i) Make sure that the Freefall apparatus is leveled and (ii) ball's position go all the way to the bottom of the tape.
  2. Circle the marks and number them sequentially, starting with 0 (start 0 on the three mark). These labels correspond to t = 0 s, t = 1/60 s, t = 2/60 s, etc.
  3. Measure the position of each of the marks, relative to the “0” mark. Record this data in a neat table (labeled t(1/60 s) and y(cm)) in your lab report.
  4. From your time and position height, plot a full-page graph on the Distance vs. Time graph paper (see attachment). Put position “y” on the vertical axis, and time “t” on the horizontal axis. Draw a smooth curve through the data points that best represents the data (do not draw a curve that purposely connects the dots - that is incorrect).

Answer the Question:

  • Do the data points lie along a straight line? If not, what does this mean? Remember that you are measuring position, not velocity or acceleration.
  1. Determine the instantaneous speed of the ball at four selected times by measuring the slope of a line tangent to the y vs. t curve at each of the four points. (Hint: circle the locations where the instantaneous speeds are to be measured.)Don’t forget the 1/60 s units on the time axis.

∆t(s) / ∆y(cm) / v(cm/s)
1
2
3
4

Answer the following questions:

  • Are the slopes of a line tangent changing as the time of flight increases? If so, what does this mean?
  • Is the falling ball accelerating? Use your data results in the above table to justify this?

Part 2: Plotting velocity vs. time for a falling object

  1. Plot the instantaneous velocity vs. time on a separate graph (see attachment)and again draw a smooth curve through the data points that best represents the data (do not draw a curve that purposely connects the dots - that is incorrect).

Answer the Questions:

  • Why do your four speed values not lie exactly along a straight line?
  • Is your best fit line a linear line? If so, what does this mean about the velocity and acceleration of the ball? Explain.
  1. Determine the slope of this line to determine the value of “g,” the acceleration of gravity. Don’t forget the 1/60 s units on the time axis.
  2. Compare your result gexpt with the accepted value of gaccepted= 981 cm/s2 using the percent difference:

How do they compare?

Part 3: Using Excel to Find the Acceleration Due to Gravity

  1. With the help of the instructor
  • setup and organized a data table for plotting the velocity vs. time
  • plot velocity vs. time using a scatter plot
  • use theTrendline function to determine the linear equation that best fits the data and determine the slope of this line.
  • compare the acceleration due to gravity values obtain in Part (2)and the Excel value.
  1. If time allows, put your result on the board and on a Results Sheet at the front of the room so that you can get a class average gavg and a standard deviation σg using Excel. Perform the following analysis:
  • Set up and draw a “confidence interval” gavg± σg . Does gaccepted fall in-between or outside the confidence interval? If it falls in-between, then the accepted value is consistent with the class' experimental results. If it falls outside, the accepted value is not consistent.