Students will learn the difference between pressure and force and how to calculate the pressure in a variety of problems

### Key Equations

\begin{align*}P = \frac{F}{A}\end{align*} ; Pressure is a force exerted over some area

**Pressure**is often confused with force. Pressure is force spread out over an area; a small force exerted on a very small area can create a very large pressure; i.e., poke a pin into your arm!

#### Example 1

How much pressure does a 340-g Coke can exert on a table if the diameter of the can is 8.0 cm?

*Question:* \begin{align*}P = ? [Pa]\end{align*}

*Given:* \begin{align*}m = 340\ grams = 0.340\ kg\end{align*}

\begin{align*}{\;}\qquad \quad \text{diameter} = 8.0\ cm = 0.08\ m\end{align*}

\begin{align*}{\;}\qquad \quad g = 10\ m/s^2\end{align*}

*Equations:* \begin{align*}P = \frac{F}{A}\end{align*} Area of a circle: \begin{align*}A = \pi \cdot r^2\end{align*}

*Plug n’ Chug:* \begin{align*}P = \frac{F}{A} = \frac{mg}{ \pi \cdot r^2} = \frac{(0.340 \ kg)\left (10 \frac{m}{s^2} \right )}{\pi \left (\frac{0.08 \ m}{2} \right )^2}= \left (\frac{3.4 \frac{kg \cdot m}{s^2}}{5.0 \times 10^{-3} m^2} \right ) = 680 \frac{N}{m^2} = 680 \ Pa\end{align*}

*Answer:* \begin{align*}\boxed{\mathbf{680 \ Pa}}\end{align*}

### Watch this Explanation

### Explore More

- Why does a sharp knife cut so much better than a dull one?
- Every day Fakir likes to spend about an hour meditating on his bed of nails. Fakir’s mass is 60 kg, his bed contains 2000 nails, and each nail point has a surface area of \begin{align*}4 \ mm^2\end{align*}.
- Calculate the total surface area of all the nail points, then convert that area into square meters.
- Calculate the pressure exerted on Fakir by the nails. Compare this to your answer from the previous question.

- Estimate the pressure in Pascals that you exert on the ground when you stand in your bare feet flat compared to 'tippy toes'. Clearly state your assumptions.

**Answers**

- A sharp knife has much less area of contact, so the pressure is greater (pressure is inversely proportional to area).
- a. \begin{align*}0.008 \ m^2\end{align*} b. 75 kPa
- estimates will vary, but expect about a force five times larger for 'tippy toes' due to the smaller area. Discuss in class.