Exercises: Vector addition of forces

A problem states: "the wind pushes the sail of a windsurf board with a force of $120\ \text{N}$ towards the north-east."

1. a) State the magnitude, direction and sense of this force.
2. b) Explain why force is a vector quantity: what information would be lost if we only gave its magnitude?

The two auxiliary thrusters of a space probe ignite simultaneously and push in the same direction and sense with forces of $250\ \text{N}$ and $400\ \text{N}$. Calculate the resultant force on the probe and draw a diagram in your notebook representing the two forces and the resultant.

In a tug-of-war game at a local festival, the home team pulls to the left with a force of $380\ \text{N}$ and the visiting team pulls to the right with $350\ \text{N}$. The situation is shown in the figure.

1. a) Calculate the magnitude of the resultant force on the rope.
2. b) State which team the rope will start moving towards and justify your answer.

A painting hangs stationary on a museum wall.

1. a) What is the vector sum of all the forces acting on it? Give reasons for your answer.
2. b) What would happen to the painting if this sum were no longer zero?

A flowerpot of $1.2\ \text{kg}$ hangs at rest from a rope on the porch of a house. Take $g \approx 10\ \text{m/s}^2$.

1. a) Calculate the weight of the flowerpot.
2. b) What force does the rope exert on the flowerpot? Justify your answer by applying the equilibrium condition for a particle, $\sum \vec{F} = 0$.