Physics Lab: Is This Constant Acceleration?

Discussion:

It would seem (to the uninitiated) that determining if a particular motion is motion with constant acceleration would be a straightforward job. Use a motion detector and look at the graph of acceleration versus time produced by the computer software. Is the graph a horizontal line, or not?

However, it isn't quite so easy in the real world. The motion detector calculates the distance to the object by timing pulses reflected from the object and knowing (hopefully) the speed of the pulses: d = vt/2. Any small discrepancy in timing or reflection will produce a small spike in the position versus time graph, but that usually is not a big problem. The velocity of the object is calculated by the software based on the time between successive positions, so small errors in position are magnified into very noticeable errors in velocity. The velocity versus time graphs produced by motion detector software are often, if not usually, irritatingly irregular. The acceleration of the object is calculated from the velocity calculations, and very noticeable irregularities in the velocity produce ridiculous irregularities in the acceleration - so much so that the acceleration versus time graphs produced by motion detector software are generally unusable. So, much like the party game where the first person whispers something to the person next to them, and so on, what comes out at the end often bears no resemblance to the original message.

Another problem with using software-generated velocity versus time graphs and acceleration versus time graphs is that the calculations that are made on the original data are hidden. How do we know what goes on deep in the bowels of the software? Therefore, it is a good idea to stick to position versus time data and ignore the rest.

So, how do you tell if a motion is motion with constant acceleration, then? Well, if an object moves with constant acceleration, then its motion is described by the kinematics equation

and in particular, if the object starts from rest, v_i =0, so:

.

So, the test for constant acceleration from rest could be "is the displacement of the object proportional to t²?" Fortunately, this question is easy to answer from position versus time data.

In this lab, you will examine several motions and determine if they are motion with constant acceleration. The motions are:

1. The motion of a dynamics cart pulled along a horizontal track by a falling weight.
2. The motion of a dynamics cart on an inclined track.
3. The motion of a falling coffee filter.
4. The bouncing of a basketball.

Equipment:

Notes:

1. Your instructor will give you some hints on setting up each motion, and some equipment may be pre-assembled.
2. In order to save time, each lab group should set up one motion, and then the lab groups can rotate among the set ups. You should record the names of the people who engineered each setup, and make a clearly-labeled sketch of each one (setup, not person...).
3. Remember that your lab book is an as-it-happens record of your lab experiences.
4. Be sure that all original data and calculations makes their way into your lab record.
5. Construct a position versus time-squared graph for each situation. You may use Excel or DataStudio for three of the graphs. Produce one graph "the old-fashioned way" - by hand. Be sure to use graph paper.
6. Your job is to determine whether each motion is motion with constant acceleration. Be sure to tell why you think whatever you think, how confident you are in your conclusions, and why.

The pulley attaches to the end of the dynamics track. You need to stop the timer before the weight hits the floor.
Prop up one end of the dynamics track at a shallow angle, and attach a bumper to the other end. Catch the cart before it hits the bumper - the bumper is a "last resort." What happens if you give the cart an initial velocity up the incline?
Attach the motion detector a ring stand, and c-clamp the ring stand to the lab table. You should be able to record at least two or three bounces of the basketball. Note: The entire motion is certainly NOT motion with constant acceleration, since the ball obviously undergoes very large upward accelerations when it contacts the floor that are not present when it is in the air. Therefore, the question is: "Does the ball have a constant acceleration while it is in the air?"
Place the motion detector on the floor, and orient it so that it detects vertical motion. Drop the coffee filter from directly above the motion detector. If a breeze blows the filter off course, add a few more coffee filters.

last update September 10, 2006 by JL Stanbrough