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# Pressure and Force

## Pressure is a force spread out over an area. A small force applied over a very small area can exert a large force.

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Pressure and Force

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!

Key Equations

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

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

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

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

g=10 m/s2\begin{align*}{\;}\qquad \quad g = 10\ m/s^2\end{align*}

Equations: P=FA\begin{align*}P = \frac{F}{A}\end{align*} Area of a circle: A=πr2\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*}

### Review

1. Why does a sharp knife cut so much better than a dull one?
2. 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*}.
1. Calculate the total surface area of all the nail points, then convert that area into square meters.
2. Calculate the pressure exerted on Fakir by the nails. Compare this to your answer from the previous question.
3. 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.

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

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