Trolley X of mass 1,2 kg travels at 8 m·s⁻¹ east and collides with trolley Y of mass 0,5 kg which is initially at rest - NSC Physical Sciences - Question 4 - 2022 - Paper 1

To calculate the velocity of trolley Y immediately after the collision, we apply the principle of conservation of momentum:

$ext{Total initial momentum} = ext{Total final momentum}$

This can be expressed as:

$m_X v_{X_i} + m_Y v_{Y_i} = m_X v_{X_f} + m_Y v_{Y_f}$

Inserting the values:

$1.2 ext{ kg} imes 8 ext{ m·s}^{-1} + 0.5 ext{ kg} imes 0 = 1.2 ext{ kg} imes 4 ext{ m·s}^{-1} + 0.5 ext{ kg} imes v_{Y_f}$

Calculating the left side:

$9.6 ext{ kg·m·s}^{-1} = 4.8 + 0.5 v_{Y_f}$

Solving for $v_{Y_f}$:

$9.6 - 4.8 = 0.5 v_{Y_f}$

v_{Y_f} = rac{4.8}{0.5} = 9.6 ext{ m·s}^{-1}

Thus, the velocity of trolley Y immediately after the collision is 9.6 m·s⁻¹ east.

To calculate the average net force, we will use the formula:

F_{net} = rac{ ext{change in momentum}}{ ext{time}}

The change in momentum for trolley Y is given by:

$ext{change in momentum} = m_Y (v_{Y_f} - v_{Y_i})$

Inserting the values:

$= 0.5 ext{ kg} (9.6 ext{ m·s}^{-1} - 0) = 4.8 ext{ kg·m·s}^{-1}$

If we assume the collision lasts for a short time, let’s assume the time duration is $0.1 ext{ s}$ (based on context):

Thus, average net force:

F_{net} = rac{4.8 ext{ kg·m·s}^{-1}}{0.1 ext{ s}} = 48 ext{ N}

Therefore, the average net force that trolley X exerts on trolley Y during the collision is 48 N.

The collision is inelastic. This can be concluded because the kinetic energy is not conserved during the collision.

To determine this, we can compare the total kinetic energy before and after the collision.

Before the collision:

E_k = rac{1}{2} m_X v_{X_i}^2 + rac{1}{2} m_Y v_{Y_i}^2

= rac{1}{2}(1.2)(8^2) + 0 = 38.4 ext{ J}

After the collision:

E_k' = rac{1}{2} m_X v_{X_f}^2 + rac{1}{2} m_Y v_{Y_f}^2

= rac{1}{2}(1.2)(4^2) + rac{1}{2}(0.5)(9.6^2)

Calculating:

= rac{1}{2}(1.2)(16) + rac{1}{2}(0.5)(92.16)

$= 9.6 + 23.04 = 32.64 ext{ J}$

Since the total kinetic energy after the collision (32.64 J) is less than the kinetic energy before the collision (38.4 J), it confirms that the collision is inelastic.