Suppose that 2 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 46 cm.
(a) How much work is needed to stretch the spring from 40 cm to 42 cm?

Question

Suppose that 2 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 46 cm.
(a) How much work is needed to stretch the spring from 40 cm to 42 cm?

ganeshie8 · Answer

$\large    F = -kx$

$\large  W =  \int_0^x -kx dx  =  \frac{kx^2}{2} $

ganeshie8 · Answer

substutute x = 46-32 = 14, and find the value of k

ganeshie8 · Answer

W = 2J, when x = 14 :

2 = k*14^2/2
k = ?

mony01 · Answer

is k=2/98?

ganeshie8 · Answer

yes, u may simplify further by canceling 2 if u want.. 
but it doesnt matter

ganeshie8 · Answer

so the required equation for Work doen is :

W = kx^2/2

W = 2/98 * x^2/2

W = x^2/98

ganeshie8 · Answer

(a) How much work is needed to stretch the spring from 40 cm to 42 cm?


plugin x = 42-40 = 2

ganeshie8 · Answer

W = 2^2/98 = 4/98 J

mony01 · Answer

so the answer is 4/98?

ganeshie8 · Answer

yup !
simplify a bit canceling 2 if u want..

mony01 · Answer

it says its wrong