Question #10432

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Question #10432

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Answer 1 · 2017-03-08T01:06:55

$τ = 1764 N m$ $tau=1764 Nm$

Explanation:

Torque can be expressed by the equation:

$τ = \to F \cdot r \cdot sin ϕ$ $tau=vecF*r*sinphi$

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

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

$\to F = {\to F}_{G} = m g = (90 k g) (9.8 \frac{m}{s^{2}}) = 882 N$ $vecF=vecF_G=mg=(90kg)(9.8m/s^2)=882N$

We assume an angle $ϕ = 90^{o}$ $phi=90^o$ , 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.

$\Rightarrow τ = (882 N) (2 m) sin (90^{o})$ $=>tau=(882N)(2m)sin(90^o)$

$= (882 N) (2 m) (1)$ $=(882N)(2m)(1)$

$= 1764 N m$ $=1764 Nm$

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Question #10432

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