Physics 211
Lecture 5
Video Problem 2

Video Demonstration
1 minutes and 43 seconds running time.

Video Problem #2, Lecture #5: A ball of mass $m$ is subject to a force $F(x) = 24x^2 - 3x$, where $F$ is in N and $x$ is in m. How much work does this force do on the ball while the ball is moving from $x = 3\, \mbox{m}$ to $x = 5\, \mbox{m}$?

Answer: \begin{eqnarray} W_\text{on ball} &=& \int_3^5 F(x)\, dx \\ &=& \int_3^5 (24 x^2 - 3x)\, dx\\ &=& \left. \left(24\frac{x^3}{3} - 3\frac{x^2}{2}\right)\right\vert_3^5\\ &=& \left(8\times 5^3 - 3\times\frac{5^2}{2}\right) - \left(8\times 3^3 - 3\times \frac{3^2}{2}\right) \\ &=& 760\, \mbox{J}. \end{eqnarray} NOTE:The final answer given in the video is 787 J. The answer in the video is wrong, but all of the steps before the final one are correct.