# Pressure

11SCI - Mechanics

2020

## Ngā Whāinga Ako

Copy these learning outcomes and the date into your books!

1. Recap forces
2. 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}
1. Calculate the pressure created by a force of $$3N$$ with an area of $$0.5m^{2}$$
2. Calculate the pressure created by a force of $$3N$$ with an area of $$0.25m^{2}$$
3. 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}
1. Calculate the area that a force ($$5N$$) is acting through if it has a pressure of $$7Pa$$
2. Calculate the area that a force ($$7N$$) is acting through if it has a pressure of $$3Pa$$
3. 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}
1. Calculate the force of an object with area $$0.25m^{2}$$ and pressure $$5Pa$$
2. Calculate the force of an object with area $$0.5m^{2}$$ and pressure $$7Pa$$
3. 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:

1. Calculate our weights
2. Find the area of our feet
3. 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 $$0.8ms^{-2}$$.

1. Calculate the net force acting upon Jacob and his bike to cause this acceleration
2. Draw a force diagram showing the forces acting upon Jacob as he accelerates
3. 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