A force with magnitude F=a√x acts in the x direction where a = 5.5N/m(1/2). Calculate the work this force does as it acts on an object moving from x=0 to x=3.0m. Calculate the work this force does as it acts on an object moving from 3.0 m to 6.0 m. Calculate the work this force does as it acts on an object moving from 6.0 m to 9.0 m.

Question

anonymous · Answer

$$
W = \int_0^LF\;dx\int_0^La\sqrt{x}\;dx = a\left[\frac{2x^{3/2}}{3} \Bigg|_0^L\right] = \frac{2}{3}aL^{3/2}
$$

anonymous · Answer

In this case, $L = 3.0, 6.0, 9.0$