AP Physics Kinematics Lab: Stopping Distance

AP Physics Kinematics Lab – Stopping Distance

Purpose

The purpose of this experiment is to explore the relations between initial speed, stopping distance, and stopping time for an object experiencing sliding friction and to evaluate the constant acceleration model for this type of motion.

Procedure

Use a spark timer to record the motion of an object sliding across a tabletop. Prepare a length of timer paper roughly equal to the length of the tabletop or a little longer. Place the timer at one end of the table and set it to spark at 60 hertz. Feed the paper strip through the timer and tape it to the object. Turn the timer on and then set the object into motion directly away from the timer such that it will slide completely to a stop before reaching the end of the table and before the timer paper pulls out of the timer. The goal is to create a strip of timer dots that records the motion of the object sliding freely until it comes to rest. This can be accomplished by giving the object a little pull with your hand and then releasing it. Inspect the strip closely – it should show a clear pattern of deceleration leading to a singular blur of dots that represents the final location at which it came to a complete stop. Label the strip so that you can tell which end is the start and which end is the finish.

Analyses

Use a ruler to measure the strip of dots and complete the data table. Locate the second pair of dots counting back from the final blur and label it point A. Skip the next pair of dots and label the fourth pair as point B. Continue in this fashion labeling every other pair of dots. The table shows for each labeled pair of dots the instantaneous speed, the stopping distance, and stopping time from that point to the end. You should use points A – G at a minimum (i.e. at least six labeled points on the strip). Measure stopping distance to the nearest 0.01 cm from each labeled pair to the center of the final blur. Stopping time is based on number of sparks that occurred from each labeled point to the final blur – calculate the decimal number of seconds using the spark frequency of 60 Hz. To determine the instantaneous speed at a particular pair of dots measure the distance between the pair that precedes it to the pair that follows it (i.e. the unlabeled points) and divide by the amount of time between those two pairs. Although this is the average speed between the two unlabeled pairs it should equate with the instantaneous speed at the labeled pair of dots. (You will be asked to explain this…)

Interpretations

Create appropriate well-labeled graphs, including an appropriate line or curve of best fit and its corresponding equation for each of the following: speed vs. stopping time, speed squared vs. stopping distance.

Based on a constant acceleration model prepare a “curve-straightening” graph illustrating the relation between stopping distance and stopping time and find an appropriate line of best fit and corresponding equation. There is an additional “blank column” in the table that you may use to prepare values for this graph. Make sure this additional column is clearly labeled. Calculate a quantity in this column that can be graphed to produce a straight line (assuming the acceleration is constant).

Questions

1. Consider the speed vs. stopping time graph. (a) Starting with one of the constant acceleration model equations, derive the “theoretical relation” between initial velocity v₀ and the stopping time, t, in terms of the deceleration rate, a (taken to be positive). (b) Based on this result and the equation for the line of best fit what is the deceleration rate of the object?

2. Consider the speed squared vs. stopping distance. (a) Starting with one or more of the constant acceleration model equations, derive the “theoretical relation” between initial velocity v₀ and the stopping distance, d, in terms of the deceleration rate, a (taken to be positive). (b) Based on this result and the equation for the line of best fit, determine the deceleration rate of the object. Show your work.

3. Consider the linear graph that you created that shows the relation between stopping distance and stopping time. (a) Starting with one or more of the constant acceleration model equations, derive the “theoretical relation” between the quantities that you graphed in terms of the deceleration rate, a, (taken to be positive). (b) Based on this result and the equation for the line of best fit what is the deceleration rate of the object?

4. Based on the results of the experiment do you believe it is reasonable to use a constant acceleration model for this type of motion? Explain and refer specifically to results.

5. Consider the method for finding the instantaneous speed of the object at each of the labeled points. Explain or show algebraically and/or graphically why it is reasonable to expect the instantaneous speed at one pair of dots to be equal to the average speed between pairs of dots on either side of it.

6. Discuss error. As always, this means to look for and describe signs of error in the results and explain the most probable sources of error. In other words what are the indicators and evidence showing that error occurred and what problems were responsible? Be specific!

Your report (50 pts.) should consist of the following materials – neatly labeled and in this order:

o Completed data table (8)

o Speed vs. Stopping Time graph with best fit and equation (10)

o Speed Squared vs. Stopping Distance graph with best fit and equation (10)

o Linear graph of your design with best fit and equation (see directions) (10)

o Answers to questions 1 – 6 on separate paper using complete sentences (12)

Data: Kinematics of Stopping Distance

Point	Stopping Distance (cm)	Stopping Time (s)	Instantaneous Speed (cm/s)	Speed Squared (cm²/s²)
A
B
C
D
E
F
G
H

Notes: The instantaneous speed occurs at the indicated point on the strip, whereas stopping distance and stopping time describe the interval from each point to the point on the strip at which the object stopped moving.