L20: Mahi Tuatahi (2016 Exam)

• Rhiana is riding a horse along New Brighton Beach. Each of the horse’s hooves have a surface area of $0.0044m^{2}$ which sink into the sand when the horse stops. The horse exerts a total pressure of $200155Pa$.
• Calculate the weight of the horse.
• Equation
• Substitute
• Solve

Te Whakatika

A horse has four hooves, so the total surface area that the horse is exerting pressure through is $A = 0.0044 \times 4 = 0.0176m^{2}$

\begin{aligned} P &= \frac{F}{A} \
200155 &= \frac{F}{0.0176} \
200155 \times 0.0176 &= F = 3522.728N \end{aligned}

Ngā Whāinga Ako

1. Give the symbols and units for kinetic energy
2. $E_{k} = \frac{1}{2}mv^{2}$

Kinetic Energy

What is Kinetic Energy?

Kinetic energy is the energy that an object possesses due to its velocity!

Calculating Kinetic Energy

Kinetic energy depends on the mass and velocity of an object.

\begin{aligned} E_{k} &= \frac{1}{2} \times mass \times \text{velocity squared} \
E_{k} &= \frac{1}{2} \times m \times v^{2} \end{aligned}

What does $v^{2}$ mean?

• It means $v \times v$
• This means we can also write the equation like this, if you find it easier:

\begin{aligned} & E_{k} = \frac{1}{2} \times m \times v \times v \end{aligned}

Pātai Tahi

Mr LeSueur rides his bike to work at $32km/h$ ($8.89ms^{-1}$). Both he and his bike have a combined mass of $80kg$. Calculate his kinetic energy.

Whakatika Tahi

We know $m=80kg$ and $v=8.89ms^{-1}$, and we are looking for $E_{k}$.

\begin{aligned} E_{k} = \frac{1}{2} \times 80 \times 8.89^{2} \
E_{k} = 3161.284J \end{aligned}

Pātai Rua

Sophie is skiing down Upper Fascination at Mt Hutt, and is trying to go really fast. Her combined mass is $60kg$ and she is moving at $60km/h$ ($16.67ms^{-1}$). Calculate her kinetic energy.

Whakatika Tua

We know $m=60kg$ and $v=16.67ms^{-1}$, and we are looking for $E_{k}$.

\begin{aligned} E_{k} = \frac{1}{2} \times 60 \times 16.67^{2} \
E_{k} = 8336.667J \end{aligned}