SPH4U: Dynamics

Teacher Demonstration: The Force of Air Resistance and the Speed of an Object

TopicsAir Resistance/ Development of Relationships From Experimental Data

Timingpreparation: less than 5 minactivity: one period

Specific Expectations: SPH4U

IntroductionMost of us know from experience that the force of friction caused by air resistance increases as the relative speeds increases. The purpose of this activity is to develop a proportionality statement, and then an equation, that describes the relationship between air resistance and the speed of an object.Assign this activity to a group of three or four students as an example of how physicists determine relationships. Other groups would be exploring other relationships. This is an effective introduction to the course that can be completed during the first week of class. Students can present their results to the class electronically.

Materialsone helium balloon on a string, ribbon or stick masking tapea supply of identical paper clips scissors, to remove bits of tape, stick or ribbon from the balloon system until it is neutrally buoyantone metre stick one stopwatch safety glasses

Safety ConsiderationsPieces of rubber balloon can be a choking hazard and some people have latex allergies. Pieces of burst balloon or deflated balloons should be picked up and disposed of appropriately.Wear safety glasses in case the balloon bursts.

ProcedurePreparation

1. Make the helium balloon neutrally buoyant by removing or adding mass as needed. Part of the stick or ribbon can be removed or tape or paper clips may be added. The balloon will be neutrally buoyant when the balloon neither rises nor falls when released.

2. Set up a data table with headings: Frictional Force (N), Velocity (m/s) and another column for rearranged data.

Predict/Explain3. Ask students to work in pairs as they participate in this demonstration.4. Explain that you will be adding one or more paper clips to the bottom strip.5. Instruct the pairs to predict how adding paper clips will create a change to the

neutrally buoyant balloon with an explanation to justify the prediction.Observe

6. Use a balance to find the mass of a paper clip. Use Fg = mg to calculate the weight of the paper clip.

7. Attach an additional paper clip to the neutrally buoyant balloon system. Now when the balloon is released it should initially accelerate downward but soon it will attain a constant (terminal) velocity as the force of friction balances the weight of the added mass.

8. Estimate the distance the balloon falls for it to attain its terminal velocity.9. Determine the balloon systems terminal velocity by selecting a convenient vertical

distance measured with the metre stick and dividing by the time required for the balloon system to fall that distance once it is up to speed. Give the balloon a head start greater than the distance estimated in step #4 before you start to measure time and distance.

Explain10. Ask students to share their explanations of the phenomenon.11. Guide students to recognize the balance of forces apparent in this demonstration.

The magnitude of the force of air resistance is equivalent to the weight of the added paper clip.

Further Analysis12. Repeat steps #3 to #5 at least 5 times so that you have terminal velocities for a

good range of frictional forces. 13. Use graphical analysis to determine the relationship between the force of air

resistance and the speed of the balloon system falling through the air.

DisposalAny pieces of balloon, tape, ribbon or string should be placed in the regular garbage.

What happens?The graphical analysis should indicate that Ff α V2 and Ff = kV2

How does it work? One model for air resistance takes on the form Ff = C1V + C2V2

The first term takes into account the viscosity of air and the friction associated with the (sticky air) sliding around the balloon. It is the dominant term for small objects like dust and oil droplets (used in Millikan’s Oil Drop Experiment) and depends on the circumference of the balloon. The second term is involved with the collisions the balloon makes with the air as it pushes the air out of the way. It depends on the cross-sectional area and is the dominant term for large objects (like our balloon)

Teaching Suggestions/HintsIt is assumed that students are well versed in graphical techniques used to determine relationships before attempting this activity. Students should do the graphical analysis manually during the period to see if the results show a consistent trend. This allows the teacher to quickly monitor and make suggestions if required.

Select the balloon that best suits your needs: a. a simple uncoated rubber balloon will leak helium rapidly and will need

frequent adjustments to keep it neutrally buoyant. It will usually last less than 24 hours.

b. a rubber balloon which has been treated with a gel coating inside the balloon will last for many days and needs much less frequent adjustment

c. a Mylar balloon can last for months and will remain stable over a period once adjusted. Mylar balloons do not contain latex and are best suited for a situation where that is important.

Next Steps1. A class presentation by the group using for example PowerPoint and/or Excel is a

good team builder in the early part of the course.2. As with any relationship it is fun to extrapolate and predict values beyond the

range of those testeda. How fast would the balloon have to move to produce a force of friction of 1.0

N? Can this be verified?b. How many newtons would friction exert on the balloon if you held it out a

window of a car going down the highway at 100 km/h? Is the value reasonable? Can it be verified?

3. This provides a good place to guide students to discuss the limits of extrapolation for this relationship.

Additional ResourcesNelson Physics 12 Appendix A5.5 Analyzing Experimental Data

Specific ExpectationsSPH4U

A1.1 formulate relevant scientific questions about observed relationships, ideas, problems, or issues, make informed predictions, and/or formulate educated hypotheses to focus inquiries or research

A1.5 conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and using appropriate materials and equipment safely, accurately, and effectively, to collect observations and data

A1.6 compile accurate data from laboratory and other sources, and organize and record the data, using appropriate formats, including tables, flow charts, graphs, and/or diagrams

B2.4 predict, in qualitative and quantitative terms, the forces acting on systems of objects (e.g., masses in a vertical pulley system [a “dumb waiter”], a block sliding off an accelerating vehicle, masses in an inclined-plane pulley system), and plan and conduct an inquiry to test their predictions

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