## 2D Forces & Friction

When a force is applied, and it is not pointed in the direction of motion, it can be **resolved** to find the component that does point in the direction of motion. For example, imagine when a person is sweeping the floor, the direction of motion is horizontal but a diagonal force is being applied – we can split this force into two components: the one that works horizontally and the one that works vertically. This is known as **resolving a force** and we can use trigonometry to do it (remind yourself of how to use SOHCAHTOA).

We can also use the triangle law for vector addition that we learned about in AS Maths to help find resultant forces – see Example 1.

### Inclined Planes

Similarly, if the direction of motion is on an **inclined plane**, such as a ball rolling down a hill, we can resolve the forces that work vertically and horizontally (such as the weight of the ball) into the direction of the plane of motion and the one perpendicular to it. See Example 2.

### Friction

Up until now, all of the forces working on a moving object modelled as a particle have been on a smooth plane. This means that we have been ignoring the force of **friction** which opposes motion when the surface has some roughness to it. The amount of roughness the surface possess is quantified by the **coefficient of friction**, usually called . The coefficient of friction is 0 () for a smooth surface but for a rough surface and the rougher the surface the larger the value of .

Calculating the force of friction is dependent on the other forces in play. Imagine you would like to push a bag of potatoes along a rough floor (or up a rough plane). If you apply a gentle push of say 1 Newton, friction will oppose the direction of motion and will also be equal to 1 Newton. As you apply more force to move the bag of potatoes, friction () will also increase to that force until it reaches its maximum value at which point the bag will begin to move. The maximum value of friction is , where is the reaction force – the one that stops an object from sinking into the surface it lies on. So, if an object is moving (or about to move) then , otherwise it is calculated from the other forces acting on the object to obtain equilibrium – see Example 3. Note that when an object has acceleration (), the usual equation of motion () applies where friction is now included in the resultant force ().

Friction can be applied in examples using **connected particles**, such as pulleys, when one of the particles is moving along a rough surface as in Example 3. Other examples may use friction acting on rigid bodies, as opposed to objects modelled as particles. These examples may also require the use of **moments** (see moments) – see Example 4.