INTRODUCTION TO PHYSICS PRACTICAL WORK

Experience 

A scale repairer wants to replace a defective spring in a scale. The spring must have a stiffness constant \( k=(3.00 \pm 0.05) N/m \) and a negligible mass. In his workshop, he found a spring of negligible mass but its stiffness constant is unknown.

Using Hook's Law :  \( F=k \times d \) , where \( F \) represents the force applied to the spring, \( k \)   the stiffness constant and \( d \) the elongation, he was able to calculate the value of \( k \) . As a result, he hung different masses on the spring and measured its elongation. Hook's law simplifies to : 

\( d= \frac{g}{k} m \)             (1)

The measurements are reported in the table below.

Questions

  1. By comparing the physical equation (1) with the mathematical formula  \( y=bx \) , establish the following identifications : 
     \( x= .....................\)\( y= ..................... \) , \( b= ..................... \)   

  2. Complete the table below :

  3. i \( m_i (kg) \) \( d_i(m) \) \( m_i d_i (…) \) \( m_i^2 (…) \) \( bm_i(…) \) \( (d_i-bm_i )^2(…) \)
    1 0.010 0.03290
    2 0.020 0.06650
    3 0.040 0.13280
    4 0.060 0.19940
    5 0.080 0.26590
    \( n=... \)

    \( \sum_{i=1}^{n} m_i d_i \)

    \(= ....................\)

    \( \sum_{i=1}^{n} m_i^2 \)

    \(= ....................\)

    \( \sum_{i=1}^{n} (d_i-bm_i )^2 \)

    \(= ....................\)


  4. Give the numerical values of the following quantities with their corresponding units :
    \( b= .................... \) , \( \Delta d=.................... \) , \( \Delta b=.................... \) .

  5. On the same graph sheet, represent the experimental points \( d=f(m) \), the error bars as well as the line of slope \(b\).

  6. Calculate the spring stiffness constant and put it in the form \( k=(............. \pm .............) .... \).

  7. Can the repairer replace the defective spring ? Explain. We give : \(g = 9.81 m/s^2 \).

Modifié le: dimanche 17 décembre 2023, 00:23