A traditional pair of scales uses sliding masses of $10 \mathrm{g}$ and $100 \mathrm{g}$ to achieve a balance. A diagram of the arrangement is shown in Figure. The bar itself is supported with its centre of gravity at the pivot. Determine the upwards force of the pivot on the bar.

Figure shows a beam with four forces acting on it.

For each force, calculate the moment of the force about point $\mathrm{P}$.

Figure shows a beam with four forces acting on it.

State whether each moment is clockwise or anticlockwise.

Figure shows a beam with four forces acting on it. State whether the moments of the forces are balanced.

The driving wheel of a car travelling at a constant velocity has a torque of $137 \mathrm{Nm}$ applied to it by the axle that drives the car. The radius of the tyre is $0.18 \mathrm{m}$. Calculate the driving force provided by this wheel.

A force $F$ is applied at a distance $d$ from the hinge $H$ and an angle $x$ to the door.

What is the moment of force $F$ bout the point $H$ ?

The angle between two forces each of magnitude $5.0 \mathrm{N}$ is $120°$.

What is the magnitude of the resultant of these two forces ?

A ship is pulled at a constant speed by two small boats $\mathrm{A} \& \mathrm{B}$ as shown.

The engine of the ship does not produce any force.

The tension in each cable between $\mathrm{A}$ and $\mathrm{B}$ and the ship is $4000 \mathrm{N}$.

(Draw a free-body diagram showing the three horizontal forces acting on the ship.