Physics C Mechanics
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Lab Activity: Kinematics
Include these in your lab report:
1. The title of the lab activity
2. The date the lab activity was performed
3. The goal(s) of the lab activity
4. A description of the lab activity (procedures and a sketch)
5. Data collected in the lab activity
6. Analysis of data and sample calculations
7. Analysis of error (see below for details)
8. Argument analysis (see below for details)
9. Conclusion(s) (What did you learn?)

It is very important that at the end of this experiment you answer the questions regarding experimental error. Do not skip this section. Questions about experimental error will be a part of the AP* Physics 1 exam.

Goal: Determine the validity of the kinematic equations for a marble or ball rolling down a ramp.

Materials:
1. A heavy marble (steel sphere preferred)
2. Two long pieces of wood (preferably two meter sticks)
3. Books or a box of Kleenex
4. A ruler (preferably a meter stick)
5. A protractor (optional)
6. A stopwatch (or a cell phone with a stopwatch function... or you can use the virtual stopwatch at http://www.online-stopwatch.com/)

Activity:
     Set up a ramp system (2 pieces of wood set close enough together to create a grove-like track) as you see in the images below. If you are not using meter sticks to make the ramp, use the ruler to mark a line at the starting point and at 70 cm from the starting point. Using your protractor, measure the angle of the ramp (θ). If you don’t have a protractor, use your ruler to measure the height and length of the ramp to calculate the angle trigonometrically.

     Now, using the stopwatch, measure the time it takes for the marble to roll 70 cm down the ramp. Make sure that you release the marble (from rest) at the exact instant you start the watch. Stop the watch the moment the 70 cm mark is reached. Record your measurement in a data table such as the one you see below. Repeat this procedure for 7 trials all at different angles. Use angles between 3 degrees and 15 degrees.
rramp1

ramp2

Data Table:

   Trial       Ramp Angle      Measured Time (s)      Calculated Time (s)      % difference  
1
2
3
4
5
6
7


Analysis:
     The acceleration that the marble undergoes is related to the gravitational acceleration that we discussed in the presentations. The magnitude of the acceleration of the marble on the ramp can be calculated by the following equation:

a = (5/7)gsinθ
where θ is the angle of the ramp and g = 9.8 m/s2
The derivation of this equation can be done using an analysis of force and Newton's Laws described in a future lesson.

(Note: The acceleration would be a = gsinθ if the marble only slid down the ramp and did not roll. Because the rolling involves both linear movement down the ramp and rotation at the same time, the linear acceleration is diminished somewhat.)

     Use this acceleration in the 2nd kinematics equation to calculate the time it “should” take for the marble to roll 70 cm. Record your calculations for each angle you used in the lab.

Error Analysis:
     Calculate the percent difference between your measured and calculated times (use calculated time as the reference value) for each trial using the following formula:
C = Calculated Time
M = Measured Time

% difference = [(M – C)/C] x 100%


     There is a good chance that your % difference will be fairly high. Please don't be concerned about that...it's not a problem as long as you can hypothesize the reasons for the difference. Think about why there might be a difference between the measured times and the calculated times. Record your thoughts in the error analysis section of the lab report. Do not simply state that "human error" is the cause of the difference. Be specific as to the sources of error. 

     Finally, examine the data shown below that could have been recorded for multiple attempts to make the measurements associated with one of the trials in this experiment. This data may or may not be similar to the data you collected.

 Attempt  Measured Time (s)  Measured Angle (degrees)
 1  1.57  5.2
 2  1.48  5.1
 3  1.65  5.1
 4  1.47  5.0
 5  1.62  5.1

     Now read the two claims listed below. In the argument analysis section of the lab report identify which claim you think is correct. Support your chosen claim with evidence and justify the connection between the claim and the evidence with text-based and mathematical reasoning. You need to utilize the concept of relative standard deviation, as discussed in the Error Analysis presentation, to satisfactorily support your claim.

Claim 1: The uncertainty in the measurement of time is larger than the uncertainty in the measurement of angle.
Claim 2The uncertainty in the measurement of angle is larger than the uncertainty in the measurement of time.

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