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4. Suppose that the initial height of the object were measured from the top of the object at
the release point to the floor. How would this affect your experimental result for g, that is,
would it be too high or too low? Is this a random or a systematic error? (See Experiment 2
on errors.)

Respuesta :

The kinematics and errors allow to find the correct answers are:

  • Systematic type error
  • The acceleration value is increased

The magnitude measurements have the value and also an uncertainty about the last significant figure, this uncertainty or error when the measurement is carried out by an instrument coincides with the appreciation of the instrument.

Errors can be classified into two types:

  • Systematic, which are errors that influence the measurement in some constant sense either up or down, in general they are due to some problem in the working method
  • Random are errors that cannot be controlled by the experimenter and influence the result in a random direction. Statistical methods can be applied to these errors to decrease their value.

In this case we have an object that has a height h and is released in order to calculate the acceleration, in general the measurement must end when the object reaches the ground.

They indicate that the height measurement is made in the upper part of the object, but when reaching the floor the measurement ends for the lower part of the object, therefore there is a distance equal to the height of the body that has not been taken into account (y = h)

The described error is systematic since it influences the measurement towards a specific side, it can be improved by measuring the height from the lower part of the body.

Let's use kinematics to see the influence of the error on the height

        y = y₀ + v₀ t - ½ a t²

As the body is released, its initial velocity is zero and when it reaches the floor the final height is zero.

       0 = y₀ +0 - ½ a t²

       g = 2 y₀ / t²

Height is wrongly measured from the upper body

       y₀ = y₀_ {real} + h

Where y₀_ {real} which is the initial height, must be measured to the lower part of the body, a is the acceleration and t is the time

       a = 2 (y₀_ {real} + h) / t²

We can see from this expression that the error increases the value of the calculated acceleration

In conclusion, using kinematics and errors, we can find the type of error and where the value increases:

  • Systematic type error
  • The acceleration value is increased

Learn more about Errors and kinematics here:

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