A car of mass 120 kg, moving to the right at a velocity of 25 m·s⁻¹, collides with the back of a construction vehicle loaded with cement bags and moving in the same direction at a velocity of 6.25 m·s⁻¹ - NSC Technical Sciences - Question 4 - 2021 - Paper 1

The principle of conservation of linear momentum states that the total linear momentum of an isolated system remains constant in magnitude and direction, provided that no external forces act on it.

In an isolated system with no external forces acting on it, the net external force is zero. Therefore, the magnitude of the net external force acting on the system is:

0 N

To find the mass of the construction vehicle, we apply the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

1. Calculate the total momentum before the collision:

   • Car's momentum: $m_1 v_1 = (120 ext{ kg} imes 25 ext{ m/s}) = 3000 ext{ kg·m/s}$
   • Construction vehicle's momentum: $m_2 v_2 = m_2 imes 6.25 ext{ m/s}$
   • Total momentum before: $p_{initial} = 3000 + m_2 imes 6.25$

2. Calculate the total momentum after the collision:

   • Car's momentum after: $m_1 v_1' = 120 ext{ kg} imes 7.45 ext{ m/s} = 894 ext{ kg·m/s}$
   • Construction vehicle's momentum after (including cement bags): $p_{final} = (m_2 + 100) imes 8.45$

3. Setting initial momentum equal to final momentum: $3000 + m_2 imes 6.25 = 894 + (m_2 + 100) imes 8.45$

After rearranging and solving for $m_2$, we find:

• The mass of the construction vehicle is approximately: $m_2 ext{ kg}$

To determine if the collision is elastic, we check if kinetic energy is conserved.

1. Calculate total kinetic energy before the collision:

   • Kinetic energy of the car: $KE_{car} = 0.5 imes 120 ext{ kg} imes (25 ext{ m/s})^2$
   • Kinetic energy of the construction vehicle: $KE_{vehicle} = 0.5 imes m_2 imes (6.25 ext{ m/s})^2$
   • Total kinetic energy before: $KE_{initial} = KE_{car} + KE_{vehicle}$

2. Calculate total kinetic energy after the collision:

   • Kinetic energy of the car after: $KE_{car ext{ after}} = 0.5 imes 120 ext{ kg} imes (7.45 ext{ m/s})^2$
   • Kinetic energy of the construction vehicle after: $KE_{vehicle ext{ after}} = 0.5 imes (m_2 + 100) imes (8.45 ext{ m/s})^2$
   • Total kinetic energy after: $KE_{final} = KE_{car ext{ after}} + KE_{vehicle ext{ after}}$

3. If $KE_{initial} eq KE_{final}$, then the collision is inelastic.