Question

The force required to compress a non-standard spring as a function of displacement from equilibrium x is given by the equation F(x) = ax2 - bx, where a = 45 N/m2, b = 8 N/m, and the positive x direction is in the compression direction of the spring. Write a general equation in terms of given variables for the work required to compress thai spring from equilibrium to any point xp.​

Answer 1

Answer:

The equation which define the work done by spring is w = 45 x³ - 8 x²

Explanation:

Given as :

The force is the function of distance x

I.e F(x) = a x² - b x

where

a = 45 N/m²

b = 8 N/m

Now, Wok done = Force ×displacement

I.e W = F . ds

So , W = (a x² - b x) × x

or, W = (45 x² - 8 x) × x

Or, w = 45 x³ - 8 x²

So, the equation which define the work done by spring is w = 45 x³ - 8 x²

Hence The equation which define the work done by spring is w = 45 x³ - 8 x²  Answer

Answer 2

The equation for work required to compress the spring is,

                                  $W(x)=45x^{3}-8x^{2}$

Force in spring :

The force function is given that,

             $F(x)=ax^{2} -bx$ where $a=45N/m^{2},b=8N/m$

So that,  $F(x)=45x^{2} -8x$

Work done is given as,

       $Workdone=Force*Displacement$

Displacement is given as x.

      $W(x)=(45x^{2} -8x)*x\\\\W(x)=45x^{3}-8x^{2}$

Learn more about the work-done here:

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