Energy conservation in a pendulum (using a measure of centripetal acceleration)

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High School

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FizziQ

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Description

In this activity, students use a smartphone as a pendulum to experimentally confirm the law of conservation of mechanical energy. The analysis includes a theoretical phase which consists in identifying the formula of the centripetal acceleration as a function of the height of the release. During the practical phase, students measure the centripetal acceleration of the smartphone when released at different heights, and check that the relationship is linear. This experiment uses the accelerometer of the smartphone.

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Sample protocol for the student
1. We will verify the law of conservation of energy in the case of the pendulum
2. Write the formula for the potential energy of a pendulum as a function of the height from the low point
3. Write the kinetic energy of the pendulum at the low point
4. Using the conservation of energy theorem, calculate the tangential velocity at the low point as a function of the height
5. Using the relationship between centripetal acceleration and tangential velocity, deduct the tangential acceleration at the low point as a function of the heigh
6. Using a pendulum and your smartphone, calculate for different heights the maximum centripetal linear acceleration reached by the pendulum
7. Enter the data in a table and check graphically that the centripetal acceleration is proportional to the height
8. Document your assumptions, results and conclusions in your experiment notebook by adding text and photos

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