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OlgaM077 [116]
3 years ago
11

A certain spring stretches 3 cm when a load of 15 n is suspended from it. how much will the spring stretch if 30 n is suspended

from it (and it doesn't reach its elastic limit)?

Physics
2 answers:
Jet001 [13]3 years ago
7 0

Extension of the spring is 6 cm

\texttt{ }

<h3>Further explanation</h3>

<em>Hooke's Law states that the length of a spring is directly proportional to the force acting on the spring.</em>

\boxed {F = k \times \Delta x}

<em>F = Force ( N )</em>

<em>k = Spring Constant ( N/m )</em>

<em>Δx = Extension ( m )</em>

\texttt{ }

The formula for finding Young's Modulus is as follows:

\boxed {E = \frac{F / A}{\Delta x / x_o}}

<em>E = Young's Modulus ( N/m² )</em>

<em>F = Force ( N )</em>

<em>A = Cross-Sectional Area ( m² )</em>

<em>Δx = Extension ( m )</em>

<em>x = Initial Length ( m )</em>

Let us now tackle the problem !

\texttt{ }

<u>Given:</u>

initial extension of the spring = x = 3 cm

initial load = F = 15 N

final load = F' = 30 N

<u>Asked:</u>

final extension of the spring = x' = ?

<u>Solution:</u>

<em>We will use </em><em>Hooke's Law</em><em> to solve this problem:</em>

F : F' = kx : kx'

F : F' = x : x'

15 : 30 = 3 : x'

1 : 2 = 3 : x'

x' = 2 \times 3

\boxed {x' = 6 \texttt{ cm}}

\texttt{ }

<h3>Learn more</h3>
  • Young's modulus : brainly.com/question/6864866
  • Young's modulus for aluminum : brainly.com/question/7282579
  • Young's modulus of wire : brainly.com/question/9755626

\texttt{ }

<h3>Answer details</h3>

Grade: College

Subject: Physics

Chapter: Elasticity

Alik [6]3 years ago
4 0
Initially, the spring stretches by 3 cm under a force of 15 N. From these data, we can find the value of the spring constant, given by Hook's law:
k= \frac{F}{\Delta x}
where F is the force applied, and \Delta x is the stretch of the spring with respect to its equilibrium position. Using the data, we find
k= \frac{15 N}{3.0 cm}=5.0 N/cm

Now a force of 30 N is applied to the same spring, with constant k=5.0 N/cm. Using again Hook's law, we can find the new stretch of the spring:
\Delta x =  \frac{F}{k}= \frac{30 N}{5.0 N/cm}=6 cm
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