Question

Suppose a person pushes thumbtack that is 1/5 centimeter long into a bulletin board, and the force (in dynes) exerted when the depth of the thumbtack in the bulletinboard is x centimeters is given by.
F(x) = 1000 (1 + 2x)^2 for 0 = x = 1/5

Find the work W done by pushing the thumbtack all the way into the board

Answer 1

Work = Force*Distance
Since the given force is not constant, you need to integrate the force function with respect to distance.

At the moment the thumbtack touched the board, x=0 and when it is all the way in the board the distance equals to the length of the thumbtack, which isx=1/5 cm= 0.2 cm =0.002 m (SI units)

Thus, you need to integrate the function from x=0 to x=0.002 m

===1.99 N*m

I only use 0.002 because when x=0 . W=0.