This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Okay Maths, let's tackle this momentum problem. 4.1 The principle of conservation of linear momentum states that in an isolated system (where no external forces act), the total linear momentum before a collision or interaction is equal to the total linear momentum after the collision or interaction. 4.2 The problem states that Ball A and Ball B move towards each other. The change in momentum of ball A ( p_A) is given as 2.4 kg·m·s^-1 to the LEFT. During the collision, ball B exerts a force on ball A. This force causes the change in momentum of ball A. Since p_A is to the LEFT, the force on A must have been to the LEFT. This means ball B hit ball A from the right. If ball B hit ball A from the right, and they were moving towards each other, then ball A must have initially been moving to the RIGHT. 4.3 Step 1: Define a positive direction and identify given values. Let's choose RIGHT as the positive direction. • Mass of ball B, m_B = 0.3 kg • Initial speed of ball B, v_iB = 15 m·s^-1. Since ball B moves towards ball A (which is initially moving right), ball B's initial velocity is to the LEFT. So, v_iB = -15 m·s^-1. • Change in momentum of ball A, p_A = 2.4 kg·m·s^-1 to the LEFT. So, p_A = -2.4 kg·m·s^-1. Step 2: Apply the impulse-momentum theorem relationship between the two balls. According to Newton's Third Law, the impulse exerted by ball A on ball B is equal in magnitude and opposite in direction to the impulse exerted by ball B on ball A. Therefore, the change in momentum of ball B ( p_B) is equal in magnitude and opposite in direction to the change in momentum of ball A ( p_A). p_B = - p_A p_B = -(-2.4 kg·m·s^-1) p_B = +2.4 kg·m·s^-1 This means the change in momentum of ball B is 2.4 kg·m·s^-1 to the RIGHT. Step 3: Calculate the final velocity of ball B using the change in momentum formula. The change in momentum for ball B is given by: p_B = m_B v_fB - m_B v_iB Substitute the known values: 2.4 kg·m·s^-1 = (0.3 kg) v_fB - (0.3 kg)(-15 m·s^-1) 2.4 = 0.3 v_fB + 4.5 Step 4: Solve for v_fB. 0.3 v_fB = 2.4 - 4.5 0.3 v_fB = -2.1 v_fB = (-2.1)/(0.3) v_fB = -7 m·s^-1 The negative sign indicates that the final velocity of ball B is to the LEFT. The velocity of ball B after the collision is 7 m·s^-1 to the LEFT. Last free one today — make it count tomorrow, or type /upgrade for unlimited.