Students take measurements of the force F0 , directed to the left, needed to hold the cart in place as well as the tension FT in the horizontal section of string. The students take three measurements for each force. Write down the sets of measurements that would provide the most precise determination of the correct relationship between the net force and the vector sum of the individual forces exerted on the cart?

Respuesta :

The characteristics of the random error allow to find the result for the best value of the forces is:

  • Using the average values ​​gives the best results.

In a measurement in physics some type of instrument is used, therefore all measurements have a precision due to the minimum amount that can be measured with the given instrument, the correct way to give the measurement is

     m = m ± Δm

     

Where m is the measure and Δm the error due to the appreciation of the instrument.

In the measurement process there are variables type that can affect the results, in general they can be divided into two groups:

  • Systematic errors. They are problems that can be reduced or solved, in general they move the result to a specific side, for example: calibration problems, problems with the measurement method, etc.
  • Random errors. They are variables that change during the measurement that cannot be foreseen or controlled, for example: temperature, humidity, deformation of bodies, etc.

Statistical methods can be applied to the random type of processes to reduce their effect on the final result, one of the most efficient way is to carry out the measurement several times and since the errors are random, if we obtain the average it must be closer to the true value.

       [tex]m_{average} = \frac{\sum m_i}{n}[/tex]  

Where m_i  is each measurement and n is the number of measurements.

As a result it is

        [tex]m = m_{average} \pm \sigma[/tex]

Where σ  is the standard deviation.

It indicates that three measurements were made of each force, suppose that their values ​​are: F₀₁, F₀₂ and F₀₃, and the best value is

       [tex]F_{o \ average} = \frac{1}{3} (F_{o1} + F_{o2} + F_{o3} )[/tex]

For the tension of the body also takes three measurements.

        [tex]F_{t \ averag} = \frac{1}{3} (F_{t1} + F_{t2} + F_{t3} )[/tex]

The best value of the net forces should be obtained using the average values.

        [tex]\Delta F = F_{t \ average} - F_{o \ average}[/tex]  

In conclusion using the characteristics of the random error we can find the result for the best value of the forces is:

  • Using the average values ​​gives the best results.

Learn more here: brainly.com/question/14149934