PART 1. Simple Visual Reaction Time (VRT)

a. Use the following procedure to collect reaction time data:

Use Safari and go to: ReactionTimer.html, collect and write down the data in sets of 10 trials.

b. Collect fifty reaction time values for your dominant hand.

c. Collect ten reaction time values for your non-dominant hand.

d. Enter your data on an Excel Spreadsheet- remember to label all data carefully.

e. Use the Excel procedure described at the end of the handout to find the average value, standard deviation and SDOM of the 50 VRT in step b (T1).

f. Repeat step e for the first ten and also for the last ten VRT taken in step b (T2) and (T3).

g. Repeat step e for the ten VRT in step c (T4).

h. COMPARE

Your results are (with right number of significant figures!):

T2 (first 10) and T1 (all 50)

T2 (first 10) and T3 (last 10)

T2 (first 10 dom.) and T4 (10 non dom)

Also ask a classmate his/her value for T1 (T1') , and compare it with your T1.

i. Show a sample calculation for T2.

You should state your results as:

T = (BEST ESTIMATE) +/- (UNCERTAINTY)

where

BEST ESTIMATE = AVERAGE = TAV

UNCERTAINTY= SDOM (Standard Deviation of the Mean) =

PART 2. Another VRT determination

a. Have your partner release a meter stick "unexpectedly," vertically from rest. Position your dominant hand index and thumb fingers about a cm apart on each side of the meter stick as close as possible to the 0 mark. Record the positions xi at which you grab the meter stick (which are the distances fallen by the meterstick during your reaction time). Repeat ten times (N = 10), and then switch roles with your partner. Find the most probable (average) value, XAV, and the standard deviation of your readings.

State your result for X as Best Estimate +/- Uncertainty, where:

BEST ESTIMATE = AVERAGE = XAV

UNCERTAINTY= SDOM (Standard Deviation of the Mean)

NOTE: Make sure that the number of significant figures in your stated result is consistent with your position data.

b. Determine the value of t (=VRT) obtained from the relationship between distance fallen x and free-fall time t:

==> .....................(Eq.1)

Use the accepted value for g at Sewanee:

and state your result for t as Best Estimate +/- Uncertainty, where:

BEST ESTIMATE =

and the UNCERTAINTY =

This looks fine, but what is ε _t ?

Using error propagation formulas (see ERROR ANALYSIS):

where the relative error ε is defined as ε =UNCERTAINTY/BEST ESTIMATE:

Note that in the special case (like ours) in which one error dominates ( ), then the error propagation formula simplifies to:

(notice that the factor 1/2 comes from the square root relationship between t and x)

so that:

Δt = (1/2) * (Δx/x_AV) * t₀

c. Compare this value for t with the value of T1 obtained in Part 1.

Do they agree or disagree? That is, do the respective ranges of values overlap significantly? Explain your answer very carefully.

d. What simplifying assumptions are made to be able to write Eq. 1?

e. Imagine you are a Physics Consultant.

Which of the techniques (Part 1 or Part 2) would you recommend as a better experimental technique to measure VRT?

Could you propose a better method?

EXCEL HINTS

0. Create in Column 1 a list of numbers 1-50, and in Column 2 enter your VRT data (50 dominant, 10 non dominant).

1. Select a cell in Column 3 . Select fx in the tools bar.

Select average value. Click on next button. Use 'shift -click' to select the first ten cells for the argument ( ) of average value. Click on finish.

2. Repeat step 1 to find the standard deviation--stdev. In the next cell, divide this value by SQRT(N) (10 or 50 depending the case) to obtain the SDOM (which is the uncertainty).

3. Repeat steps 1 and 2 with all 50 cells selected and then for the last ten selected.

4. When you are finished select "Quit" under the File menu (command q).

6. If you want to work on the workbook again, you can open it either by 'double-clicking' on its icon in the window or by starting Excel and using "Open" in the File menu (command o).