# Activity: Forces as vectors

#### Aims

• Define a force
• Adding forces vectorially.
• free body diagrams.
• Balancing forces

#### Definition of a Force

A push or a pull

The unit of force is the newton, 1 N is approximately the force required to hold a mass of 100 g.

• When you push a body it can start to move. Why isn't force defined as the quantity that makes things move?

#### Forces as a vector

Imagine two strings attached to some object. Two forces can be applied to the object by pulling on the strings. In my book this was represented by spacemen/women (difficult to tell with those helmets on) pulling a red ball. The reason it is in space is to eliminate all other forces however the spacemen would need to have some sort of rocket pack to prevent them from moving towards the ball.

When two forces are applied to the same object the resultant force can be found by adding the vectors that represent the forces. In the case of the strings the fore is in the direction of the string. If the strings are in 1D then adding the vectors is easy.

• Try dragging the blue dots to change the size of the forces.
• The vector addition is shown in the lower diagram.

Forces are said to be balanced if the resultant is zero. The body is then in equilibrium.

2D perpendicular vectors can be added nose to tail then Pythagoras used to find the resultant.

• Find the resultant of the following. • Use this simulation to check your result.
• What force would balance this pair of forces?

Non perpendicular forces can be added if you consider components. For the two forces shown calculate • the vertical component of the 4 N force
• the vertical component of the 5 N force
• the resultant vertical force
• the horizontal component of the 4 N force
• the horizontal component of the 5 N force
• the resultant horizontal force
• use Pythagoras to find the resultant force
• what force would balance these forces?

Use the simulation below to check your answers and observe the addition of other forces.

#### Newton's first Law of motion

Newton's laws of motion relate the motion of a body with the force that causes the motion the first law says (in simple terms) that things don't move or stop moving unless pushed.

A body will remain at rest or moving with constant velocity unless acted upon by an unbalanced force. Watch out for problems like the last one, the car is traveling along the track at high velocity but since the velocity is constant the forces on it must be balanced (according to Newton), in the next unit you will find out what those forces are.

Newton's 1st law multiple choice

Now do exercise 21-25 on page 54-56

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