Question

problem 6: a simple bow can be modeled as an ideal spring. if one needs 250 n to draw the bow 0.45 m, find the work required to draw the bow a distance of 0.5 m.

Explanation:

Step1: Find the spring - constant (k)

According to Hooke's law $F = kx$. Given $F = 250\ N$ and $x = 0.45\ m$, we can solve for $k$: $k=\frac{F}{x}$.
$k=\frac{250}{0.45}=\frac{2500}{4.5}=\frac{5000}{9}\ N/m$

Step2: Calculate the work - done (W)

The work - done in stretching a spring is given by the formula $W=\frac{1}{2}kx^{2}$. Now, with $k = \frac{5000}{9}\ N/m$ and $x = 0.5\ m$, we substitute these values into the formula:
$W=\frac{1}{2}\times\frac{5000}{9}\times(0.5)^{2}$
$W=\frac{1}{2}\times\frac{5000}{9}\times0.25=\frac{1250}{18}\approx69.44\ J$

Answer:

$69.44\ J$