Question

A spring has an unstretched length of 10 cm. it exerts a restoring force f when stretched to a length of 11 cm. part a for what length of the spring is its restoring force 3f?

Answer 1

13 cm
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Answer 2

The restoring force in the spring will be $3F$ if it is stretched to a length of $\boxed{13\,{\text{cm}}}$.

Further Explanation:

When a spring is we compressed or stretched, there is a force which develops in the spring restoring force of the spring which tends to bring the spring back to normal length.

The restoring force of the spring is expressed as:

$F= k\cdot\Delta x$                            ......(1)

Here, $F$ is the force developed in the spring due to stretching,   is the spring constant and $11\,{\text{cm}}$ is the change in length of the spring.

$\begin{aligned}\Deltax&= {x_f} - {x_i}\\&= 0.10 - 0.11\\&= 0.01\,{\text{m}}\\\end{aligned}$

Substitute the values of $F$ and $\Delta x$ in equation (1).

$\begin{aligned}F &= k\cdot 0.01\hfill\\k&=\frac{F}{{0.01}} \hfill\\\end{aligned}$

The restoring force of $3F$ is experienced by the spring when the stretched length of the spring should be:

$3F = k.\Delta x$

Substitute $\dfrac{F}{{0.01}}$ for $k$ in above expression.

$\begin{aligned}3F&=\frac{F}{{0.01}} \cdot\Delta x'\\\Delta x' &= 3 \times 0.01\,{\text{m}}\\&=3\,{\text{cm}}\\\end{aligned}$

Therefore, the new length of the spring will be:

$\begin{aligned}L&={x_o} + \Delta x' \\&= 10\,{\text{cm}} + 3\,{\text{cm}}\\&= 13\,{\text{cm}}\\\end{aligned}$

Thus, the restoring force in the spring will be $3F$ if it is stretched to a length of $\boxed{13\,{\text{cm}}}$.

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Work and energy

Keywords:  Spring, unstretched length, compressed, stretched, restoring force, 3F, 11 cm, F=kx, natural length of spring.