Data sheet: Include a photocopy of data sheet page of the handout.

Note: The MEAN acceleration (using STAT button on the acceleration

versus time plot) should be written into your data table.

 

Analysis:

 

In your report, you are really interested in how A and  slope m from

curve fits  and the MEAN acceleration (using STAT button on the

acceleration versus time plot) relate. The relationships would confirm

the consistency with a linear relationship. These values were found

using  curve fit and the STAT tools.  You also  recorded the velocity

versus time using the EXAMINE tool. All these aspects of the procedure

may support the case for a linear relationship between velocity and

time, consistent with Galileo.

 

FOLLOW THESE INSTRUCTIONS:

 

The answers to Analysis questions 1, 2, 3, 4, 5 and 6  should be

included in the your report. The preliminary questions should be answered on separate sheets.

 

 

ANALYSIS QUESTIONS (IN LAB HAND OUT):

 

1 and 2 are self evident. Show calculations, using sig. fig. rules:

http://library.thinkquest.org/10796/ch1/ch1.htm .

In 1 , show your  computations of the increases in speed.
For example,
if you had speed 3 = 0.4651 and speed 2 = 0.3933, you would compute,

 0.4651

-0.3933
  0.0718 m/s

 

3. Note that the answer to question 3 asks you to present evidence of

Galileo's idea that there was a quadratic relationship between the

distance and the time. Your evidence is the linear relationship between

the speed and time. Remember, that linear relationship can be shown to

be equivalent to the quadratic relationship by using basic algebra. Your

evidence of the linear relationship between speed and time was given by

the answer to 2. ( We use speed and velocity interchangeably given that

the motion  was in a straight line in the positive direction i.e. down

the incline.)  You should also state that there was a linear

relationship as revealed by the curve fit value m and how close it was

to the MEAN value of the acceleration obtained by using the STAT tool.

Compare the two using the percent error (PE): PE = |m - MEAN|*100%/m.
Example: Suppressing units, if m = 0.3596 and MEAN acceleration = 0.3576, then:
PE = |m - MEAN|*100%/m = |0.3596 – 0.3576|*100%/0.3596 =
0.0020*100%/0.3596 = (0.005561735)*100% = 0.5561735% = 0.56 %
abiding by the rules for sig. figs. shown here at this link:

http://library.thinkquest.org/10796/ch1/ch1.htm.

 

 

4. Note that the answer to question 4 asks you to find the slope by

finding the  rise over the run using the first and last data values,

abiding by the rules for sig. figs. shown here at this link:

http://library.thinkquest.org/10796/ch1/ch1.htm.

 

4. continued.

Example:
If speed 6 = 0.6741 m/s and speed 1 = 0.3178 m/s, then the
acceleration = (0.6741 – 0.3178) m/s /(time 6 – time 1)=
(0.6741 – 0.3178) m/s/(time 6 – time 1)= 0.3563 m/s/(1 s)=
0.3563 m/s2. Note 1 s means exactly one second. 

 

 

5. Note that the answer to question 5 asks you to find the relationship

between constant A from curve fit  and the slope you found by answering

4, abiding by the rules for sig. figs. shown here at this link:

http://library.thinkquest.org/10796/ch1/ch1.htm.

 

What is the relationship? Using the slope from 4 and A, compute ratio  R

= (slope)/A and   compare this ratio with the actual relationship

(slope)/A = 2. Find the percent error: PE = |R - 2|*100%/2.

Example:

Slope from part 4  = 0.3563 and A = 0.1814 , where we suppress the units.
Ratio R =  0.3563/0.1814 = 1.964167585, where we underline the 2 digit in the 1/1000 place of the final  answer to show it has 4 sig. figs.
Then PE = (2.000 – 1.964167585)*100%/2.000  = (100%)*0.035832415/2 =
1.79162075% = 1.8 %

 

6. Note that the answer to question 6 asks you to find the relationship

between  the constant m from curve fit  and the constant A  found by

answering 5. What is the relationship? Using m and A, compute ratio  R'

= m/A and   compare this ratio with the actual relationship m/A = 2.

Find the percent error: PE = |R' - 2|*100%/2.

Also find the relationship between  the constant m from curve fit and

the slope found in 4. What is the relationship? Compare the two using

the percent error: PE = |m - slope|*100%/m.

See examples in the previous part.

Make both comparisons abiding by the rules for sig. figs. shown here at

this link: http://library.thinkquest.org/10796/ch1/ch1.htm.