Question

A spring of spring constant 5N/m is compressed to 6mm, the restoring force is Z × 10 power -2 where Z is​

Answer 1

Answer:

• $\large\bold\red{z=3}$

Explanation:

Given,

• Spring Constant,$\bold{ K = 5 \;N{m}^{-1}}$
• Compression, $\bold{x=6\;mm}$
• Restoring force, $\bold{F=z \times {10}^{-2}\:N}$

To find the value of z,

We know that,

Restoring force in spring is given by the formula,

• $\large\boxed{\large \bold \pink{F = - kx}}$

Now,

We shall use the values in SI Units.

Therefore,

• $\bold{x= 6\times{10}^{-3}\;m}$

Also,

The force is applied on the spring,

Therefore,

It will also apply an equal and opposite amount of force.

Therefore,

• $\bold{F=-z \times {10}^{-2}\:N}$

Now,

Putting the respective values in the formula,

We get,

$= > - z \times {10}^{ - 2} = - 5 \times 6 \times {10}^{ - 3} \\\\ = > z \times {10}^{ - 2} = 30 \times {10}^{ - 3} \\ \\ = > z = \frac{30 \times {10}^{ - 3} }{ {10}^{ - 2} } \\\\ = > z = 30 \times {10}^{ - 3 + 2} \\\\ = > z = 30 \times {10}^{ - 1} \\ \\ = > z = 3$

Hence,

• $\large\bold{z=3}$

Answer 2

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

$\huge{\underline{\underline{\mathfrak{Given \colon}}}}$

• Compression of the spring,c = 6 mm

• Spring Constant,k = 5 N/m

• $\sf{Restoring \ Force,f = z \times {10}^{-2}}$

Restoring Force is given by

$\huge{ \underline{ \boxed{ \tt{ \green{f = - kx}}}}}$

Firstly,

Compression (change in length) of the spring in given in millimetres,we need to change it to metres.

$\large{ \leadsto \ \sf{c = \frac{6}{1000} \: m}} \\ \\ \\ \large{ \leadsto \: \orange{\sf{c = 6 \times {10}^{ - 3} m}}}$

Also,

The spring is getting compressed,thus the restoring force would have negative impact

Substituting the values,we get :

$\large{ \rightarrow \: \sf{ - z \times {10}^{ - 2} = ( - 5) \times 6 \times {10}^{ - 3} }} \\ \\ \large{ \rightarrow \: \sf{ \cancel{ - } \: z = \cancel{ - } \: 30 \times \: {10}^{ - 1} }} \\ \\ \huge{ \rightarrow \: \underline{ \boxed{ \sf{z = 3}}}}$

Thus,the required value of z is 3