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Mars2501 [29]
3 years ago
8

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?

Physics
2 answers:
jarptica [38.1K]3 years ago
8 0

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}}}.

Learn More:

1. How far must you compress a spring with twice the spring constant to store the same amount of energy? brainly.com/question/2114706

2. Max and Maya are riding on a merry-go-round that rotates at a constant speed brainly.com/question/8444623

3. It's been a great day of new, frictionless snow. Julie starts at the top of the 60 brainly.com/question/3943029

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.

rjkz [21]3 years ago
4 0
13 cm
just solved the same question on mastering physics<span />
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