1. Given data

• Total mass of system: $m = 40000\,\text{kg}$
• Initial speed: $72\,\text{km h}^{-1}$
• Compression of shock absorber spring: $x = 1.0\,\text{m}$
• $90\%$ of wagon's energy is lost due to friction

So, only $10\%$ of the initial kinetic energy is stored in the spring.

2. Convert speed into SI units

$v = 72\times \frac{1000}{3600} = 20\,\text{m s}^{-1}$

3. Initial kinetic energy of the system

$KE = \frac{1}{2}mv^2$

$KE = \frac{1}{2}(40000)(20)^2$

$KE = 20000\times 400 = 8.0\times 10^6\,\text{J}$

4. Energy stored in the spring

Since $90\%$ is lost to friction, spring gets:

$10\%\text{ of } KE = 0.1\times 8.0\times 10^6 = 8.0\times 10^5\,\text{J}$

5. Use spring energy formula

$\frac{1}{2}kx^2 = 8.0\times 10^5$

Given $x=1\,\text{m}$,

$\frac{1}{2}k(1)^2 = 8.0\times 10^5$

$k = 1.6\times 10^6\,\text{N/m}$

$k = 16\times 10^5\,\text{N/m}$

6. Final answer

The required value is:

$\boxed{16}$

7. Comparison with stored answer

Stored correct answer = $16$

Our derived answer matches the stored answer.