To use the definition of acceleration to directly measure an object's free fall acceleration

Introduction: A direct measurement of the free fall acceleration requires the measurement of the velocity of a falling object at two instants of time as well as the measurement of the time interval between these two instants. If the two velocities are denoted v_i (which occurs at time t_i ) and v_f (which occurs at time t_f ), the acceleration is given by a = (v_f - v_i)/(t_f – t_i) .

In practice, v_i and v_f must each be determined by timing the fall of the object through a short distance. In this experiment, the timing is left to a computer, triggered by the passage of the object through a photogate. The object is a strip of Plexiglas divided into three regions (see diagram). Two opaque regions of lengths, d_a and d_c, are separated by a longer transparent region of length, d_b. The strip is held vertically and dropped through a photogate, consisting of a diode which emits infrared radiation and a transistor which detects that radiation. As the strip falls through the photogate, the light path is first blocked, then unblocked, then blocked, then unblocked.

The time intervals measured by the computer will be denoted as follows:

Dt_a = the time interval from the instant when edge O passes through the photogate to the instant when edge A passes through the photogate,

Dt_b = the time interval from the instant when edge A passes through the photogate to the instant when edge B passes through the photogate,

Dt_c = the time interval from the instant when edge B passes through the photogate to the instant when edge C passes through the photogate.

Prepare the pre-lab individually as you would a homework assignment. During the lab, each student will take two trials each of their own data and will write their own report. This is an individual--not a group--lab.

Pre-lab: Answer the questions thoroughly so that you will be prepared to take data and be able to complete your report within a single class period.

1) The velocities, v_i and v_f , are determined by dividing the width of the corresponding region, d_a or d_c, by the corresponding time interval, Dt_a or Dt_c. Are these velocities, v_i and v_f, average or instantaneous velocities? Explain.

2) Why are we measuring average velocities instead of instantaneous velocities?

3) Now imagine that a clock starts running at the instant that edge O passes by the photogate. Assume that the clock reads time=0 initially. Using the definitions of Dt_a, Dt_b, Dt_c above, what time does the clock read when

a) edge A passes by the photogate?

b) edge B passes by the photogate?

c) edge C passes by the photogate?

4) Even though v_i is an average velocity, the strip actually has this velocity at a certain instant of time (as read by the clock). At what instant t_i (in terms of Dt_a, Dt_b, Dt_c) does the strip have this velocity? Explain your answer and use a v-t graph as well as words.

5) According to the clock, at what time t_f (in terms of Dt_a, Dt_b, Dt_c) does the strip have velocity v_f? Explain your choice.

6) Combining your results from questions 1,4 and 5 and using the definition of acceleration, write an equation for the acceleration of the strip in terms of d_a, d_c, Dt_a, Dt_b, Dt_c only.
 
 

Setup: The photogates have already been connected to a computer. Follow the instructions below to use the computer.

1) If using a computer with a hard drive, select [Physics] from the main menu and Precision Timer from the [Physics] menu.

2) When the program logo appears, press [Enter]. When prompted, you will need to select the Game Port Interface. The main menu should then appear.

3) When the main menu appears, select S - photogate status check. Photogate 1 should have an "Unblocked" status. If this is not the case, ask for help. Otherwise, return to the main menu.

4) Select t - miscellaneous timing modes and then b - bounce timer.

Data: Remember, each person must obtain two trials of data for analysis. Use the following procedure.

1) Record the letter of the Plexiglas strip that you use.

2) Sketch the strip the way you will hold it before dropping. Note which end is labeled "1". Measure the lengths of the three regions on the strip to the nearest 0.0005 m and record them next to the corresponding regions on your sketch.

3) Place a piece of foam on the floor where you intend to drop the Plexiglas strip. This is to keep the strip from breaking when hitting the floor. Hold the strip vertically just above the gate. Release the strip and note the three time intervals that appear on the screen. Record the results in a data table like the one below; then do another drop. If, for any of the drops, the strip does not fall vertically, ignore the data and try again. Once you have data for two good drops, go on to the analysis.
 

Time (s):	Dta	Dtb	Dtc
Trial 1
Trial 2

 

Analysis:

1) Restate your formula for acceleration from pre-lab #6.

2) Using each set of three times and the formula that you obtained in the pre-lab, calculate the acceleration of the strip. Show your substitutions clearly, and round your results to the correct number of significant figures.

3) Note how your results compare to the expected value for the free fall acceleration. Give one reason each why one might obtain a result a) lower b) higher than the expected value. Explain how your reasons contribute to error. Avoid giving minor reasons and things that you could have easily corrected (such as mistakes in calculations, breaking the beam prematurely).
 
 

Summary:

Include a concise summary/conclusion to your lab, as always.