Video: Calculating the Absolute Error of a Gravitational Acceleration Measurement

In an experiment, the acceleration due to gravity at the surface of the Earth is measured to be 9.90 m/s². Find the absolute error in the measurement using an accepted value of 9.81 m/s².

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Video Transcript

In an experiment, the acceleration due to gravity at the surface of the Earth is measured to be 9.90 meters per second squared. Find the absolute error in the measurement using an accepted value of 9.81 meters per second squared.

So we have here these two values indicating the acceleration due to gravity at Earth’s surface. One, the measured value, that we’ll call 𝑔 sub m, is 9.90 meters per second squared. We’re to compare this to the accepted value of gravity’s acceleration, we’ll call it 𝑔 sub a, of 9.81 meters per second squared. In our comparison, we specifically want to solve for the absolute error of our measured value.

To do this, we can recall that the absolute error of a measured value is equal to the difference between a measured value and an accepted value and then, if that number is negative, taking the absolute value of it. To apply this relationship, we’ll substitute 𝑔 sub a as our accepted value, and we’ll use 𝑔 sub m as our measured value. So, the absolute value of 𝑔 sub a minus 𝑔 sub m is equal to 9.81 meters per second squared minus 9.90 meters per second squared. And the absolute value of that difference is equal to 0.09 meters per second squared. This is the absolute error in our measured value.

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