A ballet dancer balances en pointe, with her full weight of 480 N passing through the tip of one pointe shoe. The tip is in contact with the floor over an area of 50 mm^2. What pressure does the dancer exert on the floor?

Answer: B. Step 1: Recall the pressure formula p = F/A Step 2: Convert the area into square metres The area is given in mm^2, but the formula needs m^2. Since 1 m = 1000 mm: 1 m^2 = (1000 mm)^2 = 1 000 000 mm^2 So: 50 mm^2 = 50/1 000 000 m^2 = 5×10^-…

IGCSE Physics 0625: Pressure from a Small Contact Area (mm² Conversion)

Step 1: Recall the pressure formula

$p = \frac{F}{A}$

Step 2: Convert the area into square metres

The area is given in $\text{mm}^2$ , but the formula needs $\text{m}^2$ . Since $1\text{ m} = 1000\text{ mm}$ :

$1\text{ m}^2 = (1000\text{ mm})^2 = 1\,000\,000\text{ mm}^2$

So:

$50\text{ mm}^2 = \frac{50}{1\,000\,000}\text{ m}^2 = 5\times10^{-5}\text{ m}^2$

Step 3: Substitute into the formula

$p = \frac{480\text{ N}}{5\times10^{-5}\text{ m}^2} = 9\,600\,000\text{ Pa} = 9.6\times10^{6}\text{ Pa}$

Why the other options are wrong

Option	How it arises	Error
$9.6\text{ Pa}$	$480 \div 50$	Area never converted from $\text{mm}^2$ to $\text{m}^2$
$9.6\times10^{4}\text{ Pa}$	$480 \div 0.005$	Area converted using the $\text{cm}^2$ factor ( $\times10^{-4}$ ) instead of the $\text{mm}^2$ factor ( $\times10^{-6}$ )
$1.0\times10^{-7}\text{ Pa}$	$(5\times10^{-5}) \div 480$	Formula inverted (area ÷ force)

Final answers

Pressure $= \boxed{9.6\times10^{6}\text{ Pa}}$ , option B