Pressure

11SCI - Mechanics

Finn LeSueur

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
  • sciPAD Page 46