LAB: FREE-FALL - acceleration due to gravity - reaction time -

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PURPOSE

 

Observe a falling body, compute the acceleration due to gravity, find your reaction time.

 

DISUSSION

 

If an object undergoes a constant acceleration along a straight a line you know:

                Equ1 :            d= ______  +  ________

 

With a the acceleration, t the time elapsed and V1 the initial velocity at t=0s.

Also, if the acceleration is constant, the velocity increases at a constant rate and if we call V2 the final velocity and Vav the average velocity we have:

 

Equ2:                                Vav = (V1 + V2 ) /2     

      

Indeed, V increases at a constant rate so he average is just in the middle of all the velocities. For example, if the velocity increase by 10m/s every second and if the initial velocity is 20m/s and if the motion lasts 3 s:

V(t=0) = 20, V(t=1) = 30, V(t = 2) = ____  , V2( t= 3) = ______________

 

So V av = __________________ 

 

 

For any motion, accelerated or uniform, you can compute the average velocity Vav just using the total displacement d and the total time elapsed t:

 

Equ3:                            Vav = ___________       d is the displacement and t the time elapsed.

 

In this lab an object will fall only acted upon by its weight. V1 = 0m/s at t = 0m/s. (It will fall from the table so it was at rest at t=0s). In that case (V1=0) :

 

Using Equ2 and Equ3 and using V1 = 0 show that V2 = 2d / t        Equ4

d is the total displacement covered during the time t. V2 is the final velocity.

 

___________________________________________________________________

 

 

 

 

 

You also know that, if the acceleration is constant:

 

Equ5    V2 = _____________    (with V1=0, t is the time elapsed and a is the acceleration)

 

So if you plot V2 versus the time t , the slope is the _______________________

Hint: V2 is on the y-axis and t is on the x-axis. V2 is the y and t is the x.

 

 

In this lab, you will measure the distance d the mass has fallen during time intervals t according to a timing device. This data will enable you to calculate the instantaneous velocity V2 for different t and d using Equ4 V2 = 2d /t .

 

Plotting V2 versus time t and using Equ5 you will find an experimental value for the acceleration g by finding the slope of the line V2 versus time t .

 

PART I: compute an experimental g (gravity)

 

PROCEDURE:

 

Step1: Set up the timing device such as the mass is ready to fall. The piece of tape is attached to the mass and pass through the device. The park timer will mark the tape at equal time interval T = 1/60s. As the mass will accelerate toward the ground it will leave a trail of mark. The time interval between each spot = 1/60s.

 

Step2: Start the timer and drop the mass. Stop the mass when the mass hits the floor. Remove the tape.

 

Step3: Repeat step2 so each partner has his/her own tape to work one.

 

Step4: write a zero below the first distinguishable dot. Number every subsequent dot consecutively 1, 2, 3, 4 , 5… Stop at the last distinguishable dot. Disregard the end where all the dots are packed together.

 

Step5: draw perpendicular lines through each dot.

 

Step6: Carefully measure (cm) the distance between dot 0 and 1, then the distance between do 0 and dot 2, then the distance between dot 0 and dot 3 …..record the measurements in table1. Also, find the time elapsed for each distance measured. Remember 1/60 s elapsed between each mark. For each interval find V2 using     Equ4 V2= 2d/t. record in table1

 

 

ANALYSIS

 

Step1: Plot velocity V2 versus time t.  V2 is along the Y axis and t is along the X axis.  Trace the best fit line. (regression line). You can use the TI if you know how. Because the first spark was probably not made at the actual time of release, the line on your graph will probably have a y-intercept . Find the slope and record it:

 

g exp = ____________ cm/s/s

 

This is an experimental value for g =918cm/s/s the acceleration due to gravity.

 

Step2: Use the calculated g and the accepted g (918cm/s/s) to compute the experimental error.

 

% error = ___________________________________-

 

Step3: Was the purpose of this lab accomplished ? Why and why not ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PART II: find your reaction time

 

DISCUSSION

 

From Equ1 d = _____ + ______      If V1 = 0  then d = _______  that will be Equ6

 

Suppose you know a = g (918cm/s/s) and d is given, can you use Equ6  to solve for t ?

 

t  = ________  (use g and d). You will use this equation for PARTII.

 

PURPOSE

 

Use the Equ6 to find your reaction time.

 

PROCEDURE

 

What is your reaction time? One way to measure your reaction time is to have another person hold a meter stick vertically from the top while you position your thumb and index finger at the 50cm mark.  The other person will drop the meter stick (UNANNOUNCED) and you will catch it with your thumb and finger. Accelerated by gravity (g), the stick will fall a distance (d) during your reaction time (t). Knowing d and g and Equ6 you can find the reaction time. Every one in your group should try. You will find out whose has the best reaction time. Record the data in table 2

PLEASE FILL THE BLANKS/ THIS IS AN INDIVIDUAL WORK.

A BLANK NOT FILLED = -5%. TRY TO BE NEAT. LABEL YOUR GRAPH.

TABLE 2:

 

d = _____________ cm     USE g = 918cm/s/s

TABLE1: (add more rows if necessary)