# Forces

## Recap of National 5

### In the National 5 course, Forces were covered in great detail. The following facts were covered :-

### 1. A Force can be seen as a push, a pull, or a twist.

### 2. A Force can change the shape, Speed or direction of an object.

### 3. A Force has the units of Newtons.

## Measuring Forces

### In National 5, A Force was measured with a Newton-Balance. A Newton Balance consists of a Spring with an attached scale. As Force is applied, the Spring is extended.

## Balanced Forces

### When two identical Forces act in opposite directions, they cancel each other out.

## Newton's First Law

### The above understanding of Forces allowed Isaac Newton to develop the 1st of his three laws of Forces :-

### "An object will remain at rest or travel in a straight line with a constant speed, unless an unbalanced Force acts upon it"

## Terminal Velocity

### When a skydiver jumps out of a plane, they accelerate (see unbalanced Forces below). After a short time, however, they reach their maximum Speed. This maximum Speed is called their Terminal Velocity.

### This happens because the two forces acting on the skydiver are balanced.

### The Air Resistance that they experience is equal in size and in opposite direction to their Weight :-

### Note - By changing their body shape (making themselves more streamlined), the skydiver can alter their air resistance, changing their terminal Velocity.

## Unbalanced Force

### When an object experiences an unbalanced Force, the object will accelerate. This can either be cause by only one Force acting (as in the diagram below), or by two unequal Forces acting in opposite directions.

## Newton's Second Law

### The above understanding of Forces allowed Isaac Newton to develop the 2nd of his three laws of Forces :-

### "An unbalanced Force acting on an object will cause the object to Accelerate. The size of that Acceleration will depend on the size of the Force and the mass of the object."

### The above law is more commonly described as the formula below :-

### F = m x a

### Where :-

### F = Unbalanced Force (N)

### m = Mass of object (kg)

### a = Acceleration of object (ms^{-2})

## Example 1 -

### A Truck of mass 2000 kg is acted upon by two Forces as shown in the diagram below:-

### Calculate :-

### 1. The unbalanced Force acting on the object.

### 2. The Acceleration experienced by the object.

### Unbalanced Force = 50000 - 45000

### = 5000 N (to the right)

### F = m x a

### a = F / m

### a = 5000 / 2000

### a = 2.5 ms^{-2}

### Note - Force is a Vector, so a direction must be given

## Motion Case Study : Skydiving

### The video below shows how the motion of a skydiver is affected by the changing forces they experience:-

### The following Velocity-Time graph shows the motion of a skydiver during a jump. By observation of the graph, it is possible to identify key times in the jump process :-

## Resultant Vectors

### So far in this section, the focus has been on Forces acting in the same plane, however Forces (and all other Vectors) can act in multiple planes. In order to understand the effect of Forces acting in different planes, the components of the Forces must be found.

### The diagram above shows how any vector can be split into two components :-

### F = Resultant Force

### F_{horizontal } = Component of Force acting in the horizontal direction

### F_{vertical} = Component of Force acting in the vertical direction

### In order to find the components of a vector, Trigonometry can be used.

## Example 1 -

### What are the components in the horizontal and vertical direction of a Force of 35 N acting at an angle of 25° upwards from horizontal ?

### F_{horizontal }= 35 cos25

### F_{horizontal }= 31.7 N

### F_{vertical }= 35 sin25

### F_{vertical }= 14.8 N

### Note - The above method can be used to calculate the component of any vector. This will be especially useful in the Projectile motion section.

## Forces on a Slope ( Frictionless )

### When an object is on a horizontal surface, its Weight acts vertically downwards and the object remains stationary.

### If the surface is tilted at an increasing angle, the object will begin to move. This is because when the slope is at an angle, a component of Weight acts down the slope, causing the object to move.

### By again applying Trigonometry to find the components of the Weight the following can be found :-

## Example 2 -

### A 2 kg block is placed on a slope at an angle of 15° to the horizontal. Calculate the Force acting down the slope, and therefore the Acceleration of the block.

### W_{down slope} = mg sin

### W_{down slope} = (2x9.8) sin15

### W_{down slope} = 5.1 N

### Acceleration = F / m

### Acceleration = 5.1 / 2

### Acceleration = 2.6 ms^{-2}

### Note - If the dimensions of the ramp are given, then by using the equations of motion, the Speed at various parts of the ramp can be found.