Question

Question #10432

Answer 1

`tau=1764 Nm`

Explanation:

Torque can be expressed by the equation:

`tau=vecF*r*sinphi`

Where `vecF` 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=90kg` and `r=2m`. The force is given by the force of gravity acting on the pirate, `mg`.

`vecF=vecF_G=mg=(90kg)(9.8m/s^2)=882N`

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.

`=>tau=(882N)(2m)sin(90^o)`

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

`=1764 Nm`