Question

You have two springs that are identical except that spring 1 is stiffer than spring 2, (k1 > k2). On which spring is more work done?(a) If they are stretched using the same force(b) If they are stretched the same distance

Answer 1

Answer:

Explanation:

Given

Two springs with spring constant $k_1$ and $k_2$

(a)If they are stretched using the same force

Force $F=k_1x_1=k_2x_2$

where $x_1$ and $x_2$ are the extension in the spring

so $\frac{k_1}{k_2}=\frac{x_2}{x_1}$

therefore $x_2 > x_1$

Work done is given by

$W=F\cdot x$

$W_1=F\cdot x_1$

$W_2=F\cdot x_2$

thus $W_2 > W_1$

(b)If they are stretched the same distance

$\frac{F_1}{F_2}=\frac{k_1}{k_2}$

Thus $F_1 > F_2$

For same extension, work done by Force 1 is more

$W_1 > W_2$