State the principle of conservation of linear momentum and apply it to a system of two boys and a trolley.

2014 Exemplar Paper 1 Q 4 4.1 The principle of conservation of linear momentum states that: The total linear momentum of an isolated system remains constant in both magnitude and direction. 4.2 Step 1: Identify the given values and set up the system. System: Two boys + trolley. Initial state: Trolley and boys are at rest. Mass of each boy = m Total mass of boys m_boys = 2m Mass of trolley m_trolley = 4m Initial velocity of boys u_boys = 0 m/s Initial velocity of trolley u_trolley = 0 m/s Final velocity of boys v_boys = 2 m/s (Let's take this direction as positive) Final velocity of trolley v_trolley = ? Step 2: Apply the principle of conservation of linear momentum. P_initial = P_final m_boys u_boys + m_trolley u_trolley = m_boys v_boys + m_trolley v_trolley (2m)(0) + (4m)(0) = (2m)(2 m/s) + (4m) v_trolley 0 = 4m + 4m v_trolley 4m v_trolley = -4m v_trolley = (-4m)/(4m) v_trolley = -1 m/s The negative sign indicates that the trolley moves in the opposite direction to the boys' jump. The final velocity of the trolley is 1 m/s in the opposite direction 4.3 If the two boys jump off the trolley one at a time, the velocity of the trolley will be GREATER THAN that calculated in QUESTION 4.2. --- 2015 Limpopo Prelim Paper 1 Q5 5.1 The relationship between impulse and change in momentum is that impulse is equal to the change in momentum of an object. Mathematically, Impulse (F t) = Change in momentum ( p = m v). 5.2 No, the total momentum is NOT conserved during this collision. Reason: The system (soccer ball + player's head) is not an isolated system because there is an external force acting on it from the player's body (connected to the ground). 5.3 Step 1: Identify the given values for the soccer ball. Mass of ball m = 0.5 kg Initial velocity of ball u = 6 m/s (Let's take the initial direction as positive) Final velocity of ball v = -9 m/s (headed directly back, so opposite direction) Time of contact t = 0.02 s Average force F = ? Step 2: Calculate the change in momentum of the ball. p = m(v - u) p = (0.5 kg)(-9 m/s - 6 m/s) p = (0.5 kg)(-15 m/s) p = -7.5 kg·m/s Step 3: Apply the impulse-momentum theorem to find the average force. F t = p F (0.02 s) = -7.5 kg·m/s F = (-7.5)/(0.02) F = -375 N The magnitude of the average force exerted by the soccer player's head on the ball is 375 N 5.4 The force exerted by the soccer player's head on the ball will be GREATER THAN the force calculated in question 5.3. Reason: A non-compressible ball will experience the same change in momentum ( p) but over a shorter contact time ( t) because it deforms less. Since F = ( p)/( t), a smaller t for the same p results in a larger force F.