Velocity Lab

Formal Lab – The Measurement of Velocity

In this experiment, we will determine the velocity of a cart by 2 methods:

·              Photogate timer

·              Ticker tape timer

Each method can be quite accurate, though what is actually being measured by each is worth some discussion. 

Recall that velocity is calculated by knowing the displacement and the amount of time required to traverse it:

v = d / t

Strictly speaking, this is average velocity.  In theory, the average velocity is a mathematical average of all (if that were possible) instantaneous velocity points throughout the trip.

Instantaneous velocity is the type of velocity you receive from a speedometer – it is the velocity at that instant.  In the case where the object moves at a constant rate, the instantaneous velocity (at all points) is equal to the average velocity.  That should be the case (approximately) for this lab.  We will determine the extent to which this idea is true in this lab.  In this lab, you may work in cm OR m – be consistent.

Procedure

1.      Set up a path for your car to travel – 1 meter should be long enough.  Place your motorized car on it.

2.      Attach a piece of timer tape to the card and ready the cart for motion.

3.      Place a photogate timer at some point along the cart’s path.  Place a flag on the cart – it must break the light gate fully.  Ready the photogate for timing.  Measure the width of the flag for future reference.

4.      Set the tape timer and note the frequency of operation.  Turn on the tape timer.

5.      Turn on the car and allow it to run the length of the path.

6.      Remove the tape and write the time value from the photogate on the tape for future reference.

7.      Repeat for 2 different cart trials, using new tapes each time.

Analysis I – the Ticker Tape Timer

·              Examine the ticker tape.  If the car is traveling at a uniform velocity, how should the dots appear?  Verify that this does occur. 

·              Starting with the first clear dot, measure the distance that each consecutive dot is from the first dot.  Recall the frequency of the timer – this determines the time intervals.  For example, if it is set at 10 Hz, the time between each dot is 1/10 of a second.  With this in mind, write down the first 30 or so total displacements from the first point.  The corresponding times (for 10 Hz) are 1/10, 2/10, 3/10, and so on.

·              Plot total displacement versus time on a graph.  What type of relationship is it?  Does this seem correct?

·              Find the slope of the graph.  What does this represent?

·              What would a (displacement vs. time) graph of an accelerating car look like?  How about a decelerating car?  How about a car moving backwards with constant velocity?  Draw these in your lab.

Analysis II – the Photogate Timer

·              Calculate the instantaneous velocity of the car using the time and width of flag.

·              Compare, by means of % difference, the velocities from both methods.  Percent difference is found by taking one value minus the other value, divided by the average of the two values, and multiplied by 100.

In your conclusion, discuss the relative accuracy of the two methods and give methods for improving the lab.