TP PHYSIQUE 1 (Pratical Work in Mechanics)

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 :



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




3. Give the numerical values of the following quantities with their corresponding units :
   $b= ....................$ , $\Delta d=....................$ , $\Delta b=....................$ .


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 $k=(............. \pm .............) ....$.


6. Can the repairer replace the defective spring ? Explain. We give : $g = 9.81 m/s^2$.