If you are taking this course through PA Homeschoolers, you must submit this lab report.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 C Mechanics exam.

Goal: Determine the validity of the kinematic equations for a toy car rolling down a ramp.

Materials:
1. A toy car with low friction wheels 
2. A long flat piece of wood such as a bookshelf
3. Books to hold the wood
4. A ruler (preferably a meter stick)
5. A protractor
6. A stopwatch (or a cell phone with a stopwatch function)

Activity:

    Set up a ramp system like the one shown below. Use books to support the piece of wood to create a ramp system like the one shown below. Mark a line at the starting point and at 0.70 m from the starting point (the finish line). 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 car to roll 0.70 m down the ramp. Make sure that you release the car (from rest) at the exact instant you start the watch. It may help to use a hold the car in place with a pencil and pull the pencil away from the from of the car to allow it to roll. Holding the car on the top can cause the release to inadvertently push the car slightly up the ramp upon release. Whatever method you choose, make sure that the car is released from rest. Stop the watch the moment the 70 cm mark is reached. Repeat the trial two more times at the same angle. Average the three times and record the average in a data table such as the one you see below. Repeat this procedure for 7 trials all at different angles. Use angles between 5 degrees and 15 degrees.

Data Table:

Analysis:
     The acceleration that the car undergoes is related to the gravitational acceleration that we discussed in the presentations. Although the car is not sliding down the ramp, it's acceleration is very close to that measured when frictionless sliding occurs. The magnitude of the acceleration of the car on the ramp can thus be calculated by the following equation:

a = gsinθ

where θ is the angle of the ramp and g = 9.8 m/s². The derivation of this equation will be shown in a future lesson. 

     Use this acceleration in the 2^nd kinematics equation to calculate the time it “should” take for the car to roll 0.70 m. 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 fair 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 (Chart A) 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.

     Now read the two claims listed below. In the argument analysis section of the lab report identify which claim you think is correct based on the data in Chart A. Do not refer to the data you collected in this activity for this part of the report. 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 2: The uncertainty in the measurement of angle is larger than the uncertainty in the measurement of time.