A horizontal locking pin is used to support a scientific sensor package on a marine research vessel's hull.
A specialized two-pronged alignment tool is used to rotate and secure the pin. The separation between the prongs of the tool is 1.5×10−2 m1.5 \times 10^{-2}\text{ m}1.5×10−2 m. The prongs exert equal and opposite forces on the head of the pin. The magnitude of each force is 340 N340\text{ N}340 N, as shown in Figure A.
Calculate the magnitude of the torque of the couple produced by these forces.
torque=\text{torque} = torque= ............................ N m\text{N m}N m
The sensor package of mass MMM is then suspended from the pin at a specific position, as shown in Figure B.
The internal sleeve of the vessel's hull exerts a maximum downward retaining force of 72 N72\text{ N}72 N on the embedded section of the pin at a distance of 5.0×10−2 m5.0 \times 10^{-2}\text{ m}5.0×10−2 m from the outer edge of the hull. The suspended sensor package exerts a downward force FFF on the pin at a distance of 8.0×10−3 m8.0 \times 10^{-3}\text{ m}8.0×10−3 m from the outer edge of the hull. An upward reaction force RRR acts on the pin at the outer edge of the hull, which behaves as a pivot. The mass of the pin itself is negligible.
Use the principle of moments to calculate the maximum mass MMM of the suspended sensor package. Take g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2.
mass=\text{mass} = mass= ............................ kg\text{kg}kg
