Gravitational Acceleration (James Rice)

Author

James Rice

Principle(s) Illustrated

Gravitational force causes all objects to accelerate, but what's surprising is that it's value can be measured even when nothing is in motion. Conversely, when a measuring device is actually accelerating with gravitational acceleration (free fall) the device itself will measure no acceleration at all. This is why objects that are all in free fall each other will have zero acceleration relative to one another. This is demonstrated with the accelerometer features of a smartphone.

Standards

HS-PS2-1.

Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.

Disciplinary Core Ideas: PS2.A: Forces and Motion

Newton’s second law accurately predicts changes in the motion of macroscopic objects.

Science and Engineering Practices: Analyzing and Interpreting Data

Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data.

Analyze data using tools, technologies, and/or models (e.g., computational, mathematical) in order to make valid and reliable scientific claims or determine an optimal design solution.

Empirical evidence is required to differentiate between cause and correlation and make claims about specific causes and effects.

Questioning Script

Prior knowledge & experience:

Essential kinematics equations and concepts
Freefall acceleration near the surface of the earth is -9.81 m/s².
Newton's Second Law of Motion (Optional)

Root question:

Why does the accelerometer data read -9.81 m/s² when the accelerometer is stationary, but reads 0 m/s² when the accelerometer is in free fall?

Target response:

The design of the MEMS (microelectromechanical sensor) that lets the phone measure acceleration is essentially a cantilever system. Whenever the cantilever arm is pulled down by the force of gravity, it generates an electrical current that can be measured by other circuits in the smartphone and which are then encoded as "acceleration". However, when the phone, along with the sensor inside it, is falling, then the cantilever and its housing have no difference in force between them because they are both in free fall. Essentially, during falling, the cantilever doesn't hang from its housing apparatus, so there is no electrical current and no acceleration reading.

Common Misconceptions:

Gravity only works when you are falling, and the rest of the time it just "waits".
Gravity doesn't work when you are rising during a jump, or at the "top" of your jump while you "hang".
Gravity works differently on objects with initial horizontal motion versus objects falling straight down.
Gravity only works when there is air.
Gravity doesn't work in outer space.
Heavy things fall faster than light objects

Photographs and Movies

Cross-cutting Concept: Cause and Effect

Video capture of acceleration data being generated by the accelerometer on a smart phone. Notice the accelerometer readings before, during, and after free fall.

Slow motion video from a smartphone as both the phone and a tennis ball are released from the same height at the same instant. Notice that the phone and the ball essentially fall together. Except for rotation on the part of the phone, the ball seems to "float" in the same position.

Applications to everyday life

In a sense, gravity applies to everything all the time! Practically, people underestimate gravitational acceleration all the time, and it's why people get injured so badly when falling from relatively low heights. However, historically, people have actually thought that the fall itself is the part that can kill, while in reality, to borrow the often quoted phrase, "it's not the falling that hurts, it's the stopping".
All buildings are under the influence of gravity at all times, and while it would seem that buidlings are static objects, it is because gravity is acting all the time that various load-bearing members can weaken over time and fail, even if there is minimal geologic movement underneath the structure.
More directly applicable to this demonstration, the idea that gravitational acceleration is sensed as an acceleration relative to one's inertial frame, has been used by NASA and others to create weightless conditions inside of specially equipped planes called "vomet comets". These planes take simulate the weightless conditions of space travel by flying to very high altitudes and then dropping with near parabolic motion in order to achieve near free fall. By doing so, occupants aboard the plane fall exactly as the plane does so that, relative to the interior of the plane, the occupants experience no acceleration whatsoever, thereby indicating no gravitational force either, and thus they are able to "float".

References

NGSS HS-PS2-1
Wikipedia article on Free Fall

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