Sciences with TI-NspireTM

Technology

Module F

Lesson 2: Free fall acceleration

TI-NspireTM Technology

In the previous lesson you learned…

2 | Lesson F.2

What is meant by the scientific method; That students are stimulated to do inquiry based science; That TI-NspireTM Technology can be a great help in inquiry based

learning; How the Vernier DataQuest application can be used to do an

experiment in an easy way; How you can analyze data by using the Vernier DataQuest

application; That TI-NspireTM Technology offers different ways of making a

report of a science experiment.

TI-NspireTM Technology

In this lesson you will:

• Measure the free fall acceleration;

• Investigate the influence of the air during a free fall;

• Use the Vernier DataQuest application and the CBR2 motion sensor.

3 | Lesson F.2

Free fall acceleration

• Near the surface of the Earth, an object in free fall in a vacuum will accelerate at approximately 9.8 m/s2, independent of its mass.

• This is what Newton taught us.• Isn’t it possible to measure this free fall acceleration?

4 | Lesson F.2

Experiment 1

• One of the benefits of having sensors in your school lab is that you can measure this in an easy way.• All you need is a basketball, a motion sensor and the Vernier DataQuest application.• This is how it works:

1. Hold the sensor about 1.5 meters above the ground;

2. Let the basketball fall;

3. Measure the motion of the bouncing ball;

4. Analyze the data.

5 | Lesson F.2

Conclusion

• The curve fit showed us that the position function of one bounce can be written as

• The derivative of this functions is the velocity:

• The derivative of the velocity is the acceleration:

6 | Lesson F.2

2( ) 4.860 12.336 8.806x t t t

( ) 9.72 12.336xv t t

( ) 9.72xa t

Experiment 2

• In the first experiment we have seen that the influence of air resistance on the movement of the ball was negligible.

• What would happen if we investigate the free fall of a coffee filter? • Will the acceleration still be close to 9.8 m/s2?

7 | Lesson F.2

Conclusion

• The curve fit showed us that the position function of the filter can be written as

• The derivative of this functions is the terminal velocity:

• The terminal velocity depends on many factors including mass, drag coefficient, and relative surface area, and will only be achieved if the fall is from sufficient altitude.• The derivative of the velocity is the acceleration:

8 | Lesson F.2

( ) 1.021 0.266x t t

( ) 1.021xv t

( ) 0xa t

Conclusion

• We can conclude that the value of 9.8 m/s2 is only valid, when air resistance can be neglected.

9 | Lesson F.2

In this lesson you learned:

That the Vernier DataQuest application automatically chooses the standard setting at the start of the application, depending on the connected sensor;

To change the collection setup of an experiment with a motion sensor;

That you can select a region of the collected data, before you do a curve fit;

That the derivative of the position function gives the velocity function and that de derivative of the velocity function gives the acceleration function;

That air resistance has an important impact on the free fall acceleration.

10 | Lesson F.2

Congratulations!

You have just finished lesson F.2!

11 | Lesson F.2