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 using the formula:

$p = mv$

Using the values: m = 1.5 \times 10^2 \text{ kg}, v = 30.56 \text{ m/s}\n Thus,

$p = 1.5 \times 10^2 \times 30.56 \approx 4584 \text{ kg m/s}$

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

$p_{\text{barrier}} = p \cos(20°)$

Thus:

$p_{\text{barrier}} \approx 4584 \cos(20°) \approx 4308.07 \text{ kg m/s}$

So, the component of momentum is approximately 4308 kg m/s.

Initially, the vehicle's kinetic energy is approximately 700 kJ as calculated earlier. After the collision, the vehicle continues along the barrier, retaining a portion of its kinetic energy.

1. The speed along the barrier can be calculated as: $v' = v \cos(20°)\n v' \approx 30.56 \cos(20°) \approx 28.84 \text{ m/s}$

2. The new kinetic energy is: $KE' = \frac{1}{2} m (v')^2 = \frac{1}{2} \times 1.5 \times 10^2 \times (28.84)^2 \approx 620 \text{ kJ}$

3. The energy lost is: $\Delta KE = KE - KE' \approx 700 \text{ kJ} - 620 \text{ kJ} = 80 \text{ kJ}$

Hence, we have shown that the kinetic energy lost in the collision is about 80 kJ.

To determine if the safety barrier passes the test, we analyze the movement of the test vehicle after the collision. If the vehicle moves more than 1.5 m towards the other carriageway, the barrier fails.

1. As the vehicle maintains its path along the barrier, we consider the deceleration due to the barrier's force.

2. Assuming the average force from the barrier is 60 kN, we can calculate the distance moved before stopping due to stopping force: $F = ma, \text{ where } F = 60,000 \text{ N} \text{ and the mass } m = 150 \text{ kg}.$ Hence, $a = \frac{F}{m} = \frac{60000}{150} = 400 \text{ m/s}^2$

3. Using kinematics, the distance (s) the vehicle could move is: $s = \frac{v^2}{2a} \text{ with } v = 28.84 \text{ m/s}$ $s \approx \frac{(28.84)^2}{2 \times 400} ext{ which is less than } 1.5 m.$

Thus, the barrier will indeed pass the test.

When comparing a steel safety barrier and a solid concrete wall, it is pivotal to assess the forces involved during a collision:

1. The steel barrier deforms upon impact, which absorbs a significant portion of the collision's energy, thereby reducing the forces transmitted to the dummies. This elastic deformation helps to gradually reduce the speed of the vehicle, minimizing injury risk.

2. Conversely, a solid concrete wall is rigid and does not deform, which would lead to a more abrupt stop for the vehicle. This implies greater forces impinging on the dummies, likely resulting in more severe injuries.

3. In conclusion, while structures must meet safety standards, a steel barrier would generally be more effective in minimizing harm to dummies during impact as it dissipates energy through deformation.