A car is being cut open by emergency services. What is the purpose of the tools being used and what principles of physics are involved in their operation?

The Jaws of Life tool operates on Pascal's principle for hydraulic systems:

$$P = \frac{F_1}{A_1} = \frac{F_2}{A_2}$$

where $P$ is pressure in Pa (N/m²), $F_1 = 200\ \mathrm{N}$ is input force, $A_1$ is input piston area, $A_2$ is output piston area, and $F_2$ is output force in N.

Input diameter = 2 cm = 0.02 m, so radius $r_1 = 0.01\ \mathrm{m}$.

$$A_1 = \pi r_1^2$$ $$A_1 = \pi (0.01)^2 = \pi \times 0.0001 = 3.14 \times 10^{-4}\ \mathrm{m^2}$$

Output diameter = 20 cm = 0.20 m, so radius $r_2 = 0.10\ \mathrm{m}$.

$$A_2 = \pi r_2^2$$ $$A_2 = \pi (0.10)^2 = \pi \times 0.01 = 3.14 \times 10^{-2}\ \mathrm{m^2}$$

$$F_2 = F_1 \times \frac{A_2}{A_1}$$ $$F_2 = 200\ \mathrm{N} \times 100 = 20000\ \mathrm{N}$$

The output piston exerts $\boxed{20000\ \mathrm{N}}$ on the car door.