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monitta
3 years ago
14

A 10-cm-long spring is attached to theceiling. When a 2.0 kg mass is hung from it,the spring stretches to a length of 15 cm.a.Wh

at is the spring constant k?b.How long is the spring when a 3.0kg mass is suspended from it?

Physics
2 answers:
alekssr [168]3 years ago
8 0

(a) 392 N/m

Hook's law states that:

F=k\Delta x (1)

where

F is the force exerted on the spring

k is the spring constant

\Delta x is the stretching/compression of the spring

In this problem:

- The force exerted on the spring is equal to the weight of the block attached to the spring:

F=mg=(2.0 kg)(9.8 m/s^2)=19.6 N

- The stretching of the spring is

\Delta x=15 cm-10 cm=5 cm=0.05 m

Solving eq.(1) for k, we find the spring constant:

k=\frac{F}{\Delta x}=\frac{19.6 N}{0.05 m}=392 N/m

(b) 17.5 cm

If a block of m = 3.0 kg is attached to the spring, the new force applied is

F=mg=(3.0 kg)(9.8 m/s^2)=29.4 N

And so, the stretch of the spring is

\Delta x=\frac{F}{k}=\frac{29.4 N}{392 N/m}=0.075 m=7.5 cm

And since the initial lenght of the spring is

x_0 = 10 cm

The final length will be

x_f = x_0 +\Delta x=10 cm+7.5 cm=17.5 cm

Rzqust [24]3 years ago
6 0

(a) The spring constant of the spring is 392 N/m

(b) Length of the spring is 17.5 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 length of spring = Lo = 10 cm

mass of object = m = 2.0 kg

extension of the spring = x = 15 - 10 = 5 cm = 0.05 m

mass of second object = m' = 3.0 kg

<u>Asked:</u>

a. spring constant of the spring = k = ?

b. length of spring = L = ?

<u>Solution:</u>

<h3>Part a.</h3>

F = kx

mg = kx

k = mg \div x

k = 2.0 ( 9.8 ) \div 0.05

\boxed {k = 392 \texttt{ N/m}}

\texttt{ }

<h3>Part b.</h3>

F' = kx'

m' g = k x'

x' = ( m' g ) \div k

x' = ( 3.0 (9.8) ) \div 392

x' = 0.075 \texttt{ m} = 7.5 \texttt{ cm}

\texttt{ }

L = Lo + x'

L = 10 + 7.5

\boxed {L = 17.5 \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

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