# Question #10432

Mar 8, 2017

$\tau = 1764 N m$

#### Explanation:

Torque can be expressed by the equation:

$\tau = \vec{F} \cdot r \cdot \sin \phi$

Where $\vec{F}$ is the magnitude of the applied force, $r$ is the distance from the point of application to the pivot, and $\phi$ is the angle between the force and radius vectors.

We are given $m = 90 k g$ and $r = 2 m$. The force is given by the force of gravity acting on the pirate, $m g$.

$\vec{F} = {\vec{F}}_{G} = m g = \left(90 k g\right) \left(9.8 \frac{m}{s} ^ 2\right) = 882 N$

We assume an angle $\phi = {90}^{o}$, as the force of gravity acts straight down on the pirate, and the radius, i.e. the plank, is assumed to be perfectly horizontal. This makes a right angle.

$\implies \tau = \left(882 N\right) \left(2 m\right) \sin \left({90}^{o}\right)$

$= \left(882 N\right) \left(2 m\right) \left(1\right)$

$= 1764 N m$