A metal wire of resistance R is cut into two pieces of equal length. The two pieces are connected together side by side. Part A
1 answer:
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<h2>Answer:</h2>
400N/m
<h2>Explanation:</h2>When n identical springs of stiffness k, are attached in series, the reciprocal of their equivalent stiffness (1 / m) is given by the sum of the reciprocal of their individual stiffnesses. i.e
= ∑ⁿ₁ [
] -----------------------(i)
That is;
=
+
+
+ . . . +
-------------------(ii)
If they have the same value of stiffness say s, then equation (ii) becomes;
= n x
-----------------(iii)
Where;
n = number of springs
From the question,
There are 3 identical springs, each with stiffness of 1200N/m and they are attached in series. This implies that;
n = 3
s = 1200N/m
Now, to calculate the effective stiffness,m, (i.e the stiffness of a longer spring formed from the series combination of these springs), we substitute these values into equation (iii) above as follows;
= 3 x
=
=
Cross multiply;
m = 400N/m
Therefore, the stiffness of the longer spring is 400N/m