How Many Licks to Get to the Center of a Tootsie Pop?

Tootsie Roll Pop - How Many Licks does it take?

Instructions:
This activity will take two class periods to collect and analyze the data. Time will also be needed outside the class for writing the final report.
Objective:
In this activity you will determine the rate of change of volume of a Tootsie Roll Pop (TRP) as you consume it.
Equipment:
• Tootsie Roll Pop
• Dental Floss & Ruler
• Graphing Calculator or Spreadsheet

Data Collection:
• Step 1: Determine the initial circumference of the TRP and calculate the radius. (Assume it is a perfect sphere.)

• Step 2: Place it in your mouth and carefully suck for 30 seconds.

• Step 3: Measure the circumference and record.

• Step 4: Repeat step two and three a total of 10 times after the initial reading.

• Step 5: Record your measured data in a table, and add columns that calculate the radius and the volume.

Data Analysis:
• Step 1: Graph a scatter plot of the radius as a function of time to see how the radius changes with time. Use this graph to determine the rate of change of the radius (dr/dt) of the TRP from your mouth power.   (Determine the equation of the trend line for your data).

• Step 2: Graph the volume as a function of time so you see how the volume can be modeled as a function of time.   Determine the equation of a trend line that best fits this data.

• Step 3: Use your estimated value of dr/dt and what you learned about related rates to determine a general formula for the rate of change of the volume of the TRP.

• Step 4: Using your data and formula, predict   EMBED Equation.DSMT4   at t = 5 minutes.
• Step 5: Using your data, predict how long it will take for the volume of the TRP = 0.   You have some flexibility in your answer, considering there is a tootsie roll in the center, but you must support your answer.

Sample data:

BONUS:   In a spreadsheet, create additional columns that estimate the dr/dt and dv/dt for each 30 seconds.   Also add a column that calculates...