TP Physique1

Experience : A scale repairer wants to replace a defective spring in a scale. The spring must have a stiffness constant and a negligible mass. In his workshop, he found a spring of negligible mass but its stiffness constant is unknown.

Using Hook's Law :   , 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 :

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- Give the numerical values of the following quantities with their corresponding units :

  b =                               ; Δd =                             ;  Δb =

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

5- Calculate the spring stiffness constant and put it in the form k = (......... ±   ….......) .........

6- Can the repairer replace the defective spring  ? Explain.  We give   :   g = 9.81 m/s²  .