Safety barriers are used on UK motorways to prevent vehicles crossing from one carriageway to the other carriageway - AQA - A-Level Physics - Question 5 - 2019 - Paper 1

The momentum ($p$) of the vehicle can be calculated as:

$p = m v$

Using the mass and the calculated speed:

$p = (1.5 \times 10^3) \left(\frac{110}{3.6} \right) \approx 46,500 \text{ kg m/s}$

The component of momentum along the safety barrier (at an angle of 20°) is given by:

$p_{\text{barrier}} = p \cos(20°)$

Calculating this:

$p_{\text{barrier}} \approx 46,500 \times \cos(20°) \approx 43,780 \text{ kg m/s}$

To find the kinetic energy lost, we first calculate the kinetic energy after the collision.

The test vehicle moves along the barrier with speed:

$\text{Speed along barrier} = v \cos(20°) \approx \frac{110}{3.6} \cos(20°) \approx 28.7 \text{ m/s}$

Then, the kinetic energy after collision is:

$KE_{\text{after}} = \frac{1}{2} (1.5 \times 10^3) (28.7)^2 \approx 620\text{ kJ}$

Thus, the energy lost is:

$\text{Energy lost} = KE_{\text{initial}} - KE_{\text{after}} = 700 - 620 = 80 \text{ kJ}$

The barrier can apply an average force of 60 kN, which is equivalent to 60,000 N.

We can calculate the work done by this force during the collision:

$\text{Work} = \text{Force} \times \text{Distance} = 60,000 \times 1.5 \text{ m} = 90,000 \text{ J} = 90 \text{ kJ}$

Since the maximum allowable deformation is 1.5 m, and the work done exceeds the kinetic energy lost (80 kJ), it suggests:

• The barrier can withstand the impact, as the damage is less than the force exerted. Therefore, the barrier passes the test.

The steel safety barrier, which deforms during the impact, will absorb a portion of the kinetic energy, thus reducing the forces experienced by the dummies. In contrast, the solid concrete wall does not deform, meaning that the dummies would experience a greater impact force. This leads to higher potential for injury. Therefore, the steel barrier is likely to cause less damage to the dummies compared to the solid concrete barrier.