## Ngā Whāinga Ako

Copy these learning outcomes and the date into your books!

- Recap forces
- Explain force and pressure in terms of everyday situations. Use $P = F/A$.

## L17 Mahi Tuatahi

Calculate the **net** force acting upon these objects:

## Pātai Tahi

What does an unbalanced force do to the motion of an object?

### Whakatika Tahi

It causes the object to accelerate (or de-accelerate).

We know this because of the equation

\begin{aligned}
force &= mass\times acceleration \

F &= m \times a
\end{aligned}

## Pātai Rua

For the followig equation give the **name** and **unit** for each variable in the equation.

\begin{aligned} & F = m \times a \end{aligned}

### Whakatika Rua

- F stands for
**force**and has units**Newtons (N)** - m stands for
**mass**and has units**kilograms (kg)** - a stands for
**acceleration**and has units**meters per second squared ($ms^{-2}$)**

## Pātai Toru

- What do you think of when you think of pressure?
- What affects the pressure exerted by an object?

### Pātai Whā

The most classic case of pressure is sharpening a knife. Why do we sharpen knives? What does sharpening a knife change about the knife?

# Pressure / *Pēhanga*

Pressure is defined as: *the amount of force per square meter*.

\begin{aligned}
pressure &= \frac{force}{area} \

P &= \frac{F}{A}
\end{aligned}

- Force is measured in
**Newtons (N)** - Area is measured in
**meters squared ($m^{2}$)**

\begin{aligned} & P = \frac{F}{A} \end{aligned}

- Therefore, pressure is measured in Newtons per meters squared ($\frac{N}{m^{2}}$ OR $Nm^{-2}$)
- This is also known as a Pascal (Pa): $Pa = \frac{N}{m^{2}} = Nm^{-2}$

## Calculating Pressure

\begin{aligned} & P = \frac{F}{A} \end{aligned}

- Calculate the
**pressure**created by a force of $3N$ with an area of $0.5m^{2}$ - Calculate the
**pressure**created by a force of $3N$ with an area of $0.25m^{2}$ - Calculate the
**pressure**created by a force of $3N$ with an area of $0.125m^{2}$

### Ngā Whakatika

\begin{aligned}
P &= \frac{F}{A} \

\text{1. } &P = \frac{3}{0.5} = 6Pa \

\text{2. } &P = \frac{3}{0.25} = 12Pa \

\text{3. } &P = \frac{3}{0.125} = 24Pa
\end{aligned}

## Calculating Area

\begin{aligned} & P = \frac{F}{A} \end{aligned}

- Calculate the
**area**that a force ($5N$) is acting through if it has a pressure of $7Pa$ - Calculate the
**area**that a force ($7N$) is acting through if it has a pressure of $3Pa$ - Calculate the
**area**that a force ($10N$) is acting through if it has a pressure of $3Nm^{-2}$

### Ngā Whakatika

\begin{aligned}
A &= \frac{F}{P} \

\text{4. } &A = \frac{5}{7} = 0.71m^{2} \

\text{5. } &A = \frac{7}{3} = 2.33m^{2} \

\text{6. } &A = \frac{10}{3} = 3.33m^{2}
\end{aligned}

## Calculating Force

\begin{aligned} & P = \frac{F}{A} \end{aligned}

- Calculate the
**force**of an object with area $0.25m^{2}$ and pressure $5Pa$ - Calculate the
**force**of an object with area $0.5m^{2}$ and pressure $7Pa$ - Calculate the
**force**of an object with area $0.75m^{2}$ and pressure $10Pa$

### Ngā Whakatika

\begin{aligned}
F &= P \times A \

& \text{7. } F &= 0.25 \times 5 = 1.25N \

& \text{8. } F &= 0.5 \times 7 = 3.5N \

& \text{9. } F &= 0.75 \times 10 = 7.5N
\end{aligned}

## Pressure Whakamātau

We are going to:

- Calculate our weights
- Find the area of our feet
- Calculate the pressure we all exert on the ground!

## L18 Mahi Tuatahi (2018 Exam)

Jacob bikes down The Flying Nun. He and his bike have a mass of $82kg$ and he accelerates at $0.8ms^{-2}$.

- Calculate the
**net force**acting upon Jacob and his bike to cause this acceleration - Draw a force diagram showing the forces acting upon Jacob as he accelerates
- Describe the size and direction of the forces compared to each other (horizontal and vertical)

## Exam Question (2018)

Giovanni is running a 100m sprint. Each of his feet have a surface area of $200cm^{2}$ ($0.0200m^{2}$), which sink into the track. Together, his feet exert a pressure of $13000Pa$. Calculate Giovanni’s weight.

### Whakatika

Because **weight** is a force, we know that we are looking for $F$.

\begin{aligned}
P &= 13000Pa
A &= 0.02m^{2} \times 2 = 0.04m^{2} \

F &= P \times A \

F &= 13000 \times 0.04 \

F &= 520N
\end{aligned}

## Extra Work

**Homework:**Education Perfect due Monday 29th 11:25am- sciPAD Page 46