Question

How much is the moment due to force P about point B. P(unit=N) vector is equal to (150i+260j ) and vector BA (unit=meter) is equal to (0.23i+0.04j)?

Answer 1

The moment (torque) is given by the following equation:

`\vec{\tau} = \vec{r} * \vec{F}\\\vec{r} * \vec{F} = \left[\begin{array}{ccc}\^(i)&\^j&\^k\\r_x&r_y&r_z\\F_x&F_y&F_z\end{array}\right] = \left[\begin{array}{ccc}\^(i)&\^j&\3k\\0.23&0.04&0\\150&260&0\end{array}\right] = \^k((0.23*260) - (0.04*150)) = \^k (53.8~Nm)`

Explanation:

The cross-product between the distance and the force can be calculated using the method of determinant. Since the z-components are zero, it is easy to calculate.