Estimate how much work is completed in stretching, Mathematics

Assignment Help:

A spring has a natural length of 20 Centimeter. A 40 N force is needed to stretch and hold the spring to a length of 30 Centimeter. How much work is completed in stretching the spring from 35 Centimeter to 38 Centimeter?

Solution : This illustration will need Hooke's Law to find out the force. Law of Hooke tells us that the force needed to stretch a spring a distance of x meters by its natural length is,

F(x) = k x

Here k < 0 is termed as the spring constant.

The first thing that we require to do is find out the spring constant for this spring. We can do which using the initial information.  A force of 40 N is needed to stretch the spring 30Centimeter -20Centimeter = 10 Centimeter = 0.10meter from its natural length. By using Law of Hooke we have,

 40 = 0.10k     ⇒     k = 400

 Therefore as per Hooke's Law the force needed to hold this spring x meters from its natural length,

 F(x) = 400x

 We need to know the work required to stretch the spring from 35Centimeter to 38Centimeter. First we require converting these in distances from the natural length in meters.  Doing this provides us x's of 0.15meter and 0.18meter.

The work is now,

1046_work2.png


Related Discussions:- Estimate how much work is completed in stretching

Graphs, How do I graph a round robin pool tournment with 6 players using gr...

How do I graph a round robin pool tournment with 6 players using graph theory

What could the dimensions of the floor be in terms of x, Harold is tiling a...

Harold is tiling a rectangular kitchen floor with an area that is expressed as x 2 + 6x + 5. What could the dimensions of the floor be in terms of x? Because area of a rectang

Find the maxima or minima and green theorem, 1) find the maxima and minima ...

1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving

Fractions, If i worked 7 1/3 hours and planted 11 trees how many hours did ...

If i worked 7 1/3 hours and planted 11 trees how many hours did it take to plant each tree?

How to find x?, How can I solve x in a circle? For example.. m

How can I solve x in a circle? For example.. m

What day?, together, pearl and harvey are going to visit their aunt on sund...

together, pearl and harvey are going to visit their aunt on sunday. If Pearl visits their aunt every 6 days, while harvey every 8 days, on what day will they visit their aunt toget

Testing the difference between two sample means-illustration, An observatio...

An observation was made concerning reading abilities of males and females. The observation leads to a conclusion that females are faster readers than males. The observation was bas

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd