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user100 [1]
3 years ago
5

Using hooke's law find the elastic constant of a spring that stretches 2 cm when 4newton force is applied to it

Physics
1 answer:
Kay [80]3 years ago
3 0

<u>Answer:</u>

2N/cm

<u>Step-by-step explanation:</u>

According to the Hooke's Law, the force required to extend or compress a spring is directly proportional distance you can stretch it, which is represented as:

F=kx

where, F is the force which is stretching or compressing the spring,

k is the spring constant; and

x is the distance the spring is stretched.

Substituting the given values to find the elastic constant  k to get:

F=kx

4=k(2)

k=\frac{4}{2}

k=2

Therefore, the elastic constant is 2 Newton/cm.

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Answer:

The extension of the second wire is   e_2 = 0.0024 \  m =  2.4 mm

Explanation:

From the question we are told that

    The length of the wire is L  = 3 \ m

     The elongation of the wire is  e =  1.2mm =  \frac{1.2}{1000} =  0.0012 m

        The tension is F  =  200 \ N

       The length of the second wire is  L_2   =  6 \ m

     

Generally the Young's modulus(Y) of this material is  

        Y  = \frac{stress}{strain }

Where stress =  \frac{F}{A}

    Where A is the area which is evaluated as  

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        Y  = \frac{\frac{F}{\pi r^2 } }{ \frac{e}{L}  }

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              F * L   =  constant   * r^2 e

Now the ration between the first and the second wire is

         \frac{F_1}{F_2}  * \frac{L_1}{L_2} =  \frac{r*2_1}{r^2}  *  \frac{e_1}{e_2}

Since tension , radius are constant

   We have

           \frac{L_1}{L_2} =   \frac{e_1}{e_2}

substituting values

          \frac{3}{6} =   \frac{0.0012}{e_2}

          0.5 e_2 =  0.0012

         e_2 = \frac{ 0.0012  }{0.5}

          e_2 = 0.0024 \  m =  2.4 mm

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