Question

How does the work needed to stretch a spring 2 cm compare to the work needed to stretch it 1 cm.A.Same amount of workB.twice the workC.4 times the work D.8 times the work

Answer 1

The work required to stretch a string is given by the following equation:

`W=(1)/(2)kx^2`

Where:

`\begin{gathered} k=\text{ string constant} \\ x=\text{ distance the string is stretched} \end{gathered}`

If the string is stretched 2 cm then we substitute the value of "x = 2" in the formula, we get:

`W_2=(1)/(2)k(2)^2`

Solving the square and simplifying:

`W_2=2k`

Now, if the string is stretched 1 cm we get:

`W_1=(1)/(2)k(1)^2`

Solving the operations:

`W_1=(1)/(2)k`

Now, we determine the quotient between W2 and W1:

`(W_2)/(W_1)=(2k)/((1)/(2)k)`

Simplifying we get:

`(W_2)/(W_1)=4`

Now, we multiply both sides by W2:

`W_2=4W_1`

Therefore, the work required to stretch the string 2 cm is 4 times the work to stretch it 1 cm.