A particle in equilibrium has three forces of magnitudes $5 \mathrm{N}, 6 \mathrm{N}$ and $F \mathrm{N}$ acting on it in the horizontal plane in the directions shown. Find the values of $F$ and $\theta .$

A lightshade of mass $2 \mathrm{kg}$ is hung from the ceiling by two strings. One is fixed with tension $8 \mathrm{N}$ at $20°$ to the vertical. The other is fixed with tension $T \mathrm{N}$ at an angle $\theta$ to the vertical.

By modelling the lightshade as a particle, draw a force diagram for this situation.

A lightshade of mass $2 \mathrm{kg}$ is hung from the ceiling by two strings. One is fixed with tension $8 \mathrm{N}$ at $20°$ to the vertical. The other is fixed with tension $T \mathrm{N}$ at an angle $\theta$ to the vertical.

Resolve horizontally to find a value for $T\sin \theta$ and resolve vertically to find a value for $T\cos \theta .$

A lightshade of mass $2 \mathrm{kg}$ is hung from the ceiling by two strings. One is fixed with tension $8 \mathrm{N}$ at $20°$ to the vertical. The other is fixed with tension $T \mathrm{N}$ at an angle $\theta$ to the vertical.

Hence, find the values of $T$ and $\theta .$

A ship is being blown by a breeze with a force of $100 \mathrm{N}$ on a bearing of $280°$, as shown in the diagram. It is pulled by a rope attached to the shore with force $50 \mathrm{N}$ on a bearing of $170°.$ A tugboat holds it in place. Find the size and bearing of the force $F$ applied by the tugboat.

A wooden block of weight $20 \mathrm{N}$ is at rest on a horizontal surface. It is pulled by a force of $30 \mathrm{N}$ acting at $10°$ above the horizontal, as shown in the diagram, and remains at rest because of a horizontal frictional force, $F.$

Draw the force diagram for this situation.

A wooden block of weight $20 \mathrm{N}$ is at rest on a horizontal surface. It is pulled by a force of $30 \mathrm{N}$ acting at $10°$ above the horizontal, as shown in the diagram, and remains at rest because of a horizontal frictional force, $F.$

Find the size of $F$ and the size of the normal contact force.

A winch is dragging a caravan along a horizontal road at constant velocity. The caravan has mass $750 \mathrm{kg}$. The winch provides a force of $850 \mathrm{N}$ and acts at angle $\theta$ above the horizontal, as shown in the diagram. There is friction of $700 \mathrm{N}.$

Draw the force diagram for this situation.

A winch is dragging a caravan along a horizontal road at constant velocity. The caravan has mass $750 \mathrm{kg}.$ The winch provides a force of $850 \mathrm{N}$ and acts at angle $\theta$ above the horizontal, as shown in the diagram. There is friction of $700 \mathrm{N}.$

Find the value of $\theta$ and size of the normal contact force.