Open Educational Resources

Problems: Chapter 3

1- For the couple forces shown in the figure, show that the following general relation holds. What property can you conclude?
Hint: Use CVN, with the z component = 0. Note that F=10\rm N.

    \[\bold r_A\times\bold F + \bold r_B\times\ (-\bold F) = \bold r_{BA}\times\bold F = \bold r_{AB}\times (-\bold F)\]


    \[\begin{split}\bold r_A\times\bold F + \bold r_B\times\ (-\bold F) &=-22\bold k\\\bold r_{BA}\times\bold F&=-22\bold k\\\bold r_{AB}\times (-\bold F)&=-22\bold k\end{split}\]

2- Determine the couple moment produced by the couple forces shown.


    \[\bold M_{\text{couple}}= (4\bold i - 3\bold j + 4 \bold k)\text{N.m}\]