During a practice session for a Grand Prix, two Formula 1 cars collide in the pit lane - Scottish Highers Physics - Question 3 - 2023

To demonstrate that the collision is inelastic, we compare the total kinetic energy before and after the collision.

Before the Collision: Total Initial Kinetic Energy, $E_i$

$E_i = \frac{1}{2} m_1 u_1^2 + \frac{1}{2} m_2 u_2^2$

Substituting the values:

$E_i = \frac{1}{2} (760)(12.0^2) + \frac{1}{2} (840)(4.0^2)$

Calculating:

$E_i = \frac{1}{2} (760)(144) + \frac{1}{2} (840)(16)$

$E_i = 54880 + 6720 = 61600 \ J$

After the Collision: Total Final Kinetic Energy, $E_f$

$E_f = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2$

Substituting the known values:

$E_f = \frac{1}{2} (760)(7.13^2) + \frac{1}{2} (840)(8.5^2)$

Calculating:

$E_f = \frac{1}{2} (760)(50.78) + \frac{1}{2} (840)(72.25)$

$E_f = 19267.2 + 30210 = 49477.2 \ J$

Conclusion: The total initial kinetic energy $E_i$ is greater than the total final kinetic energy $E_f$, indicating that some kinetic energy has been lost. Hence, the collision is inelastic.

To find the average force exerted by car X on car Y during the collision, we use the impulse-momentum principle:

$F \Delta t = \Delta p$

Where:

• $F$ = force (unknown)
• $\Delta t = 0.82 \, s$ (duration of contact)
• $\\Delta p = m \\Delta v$ (change in momentum)

First, find the change in velocity of car Y: $\Delta v = v_f - v_i = 8.5 - 4.0 = 4.5 \, m s^{-1}$

Now find the change in momentum: $\Delta p = m_2 \Delta v = 840 \times 4.5 = 3780 \, kg \, m s^{-1}$

Now substitute into the impulse-momentum equation: $F \times 0.82 = 3780$

Thus, $F = \frac{3780}{0.82} \approx 4609.76 \, N$

Therefore, the magnitude of the average force exerted by car X on car Y is approximately 4610 N.

Tyre walls are designed to enhance safety on racetracks by offering a cushioned barrier that can absorb the impact energy during a collision.

Absorption of Impact Energy

The primary function of the tyre wall is to absorb the kinetic energy of a car that leaves the track. When a car hits the tyre wall, the tyres compress and deform, effectively dissipating the energy of the impact.

Reducing Deceleration Forces

By reducing the forces exerted on the driver through gradual deceleration, tyre walls minimize the risk of injury. This is particularly vital as sudden deceleration can cause severe injuries.

Safety Features

Tyre walls often have layers, with each layer contributing to energy absorption and providing a controlled stop for the car. They can also reconfigure themselves upon impact, ensuring that the deceleration experienced by the driver is as moderate as possible.

Concluding Statement

In summary, tyre walls protect drivers by cushioning collisions, absorbing energy, and reducing the risk of high deceleration forces that could be harmful.