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
4.1: Momentum is the product of an object's mass and its velocity. 4.2: Step 1: Analyze the graph between t = 10 s and t = 20 s. From the graph, the momentum of object A is constant at 50 kg·m·s^-1 between t = 10 s and t = 20 s. This means the change in momentum ( p) during this interval is zero. Step 2: Use the relevant equation. The net force acting on an object is given by the rate of change of momentum: F_net = ( p)/( t) Since p = 0 between t = 10 s and t = 20 s: F_net = (0)/( t) = 0 Therefore, the net force acting on object A is zero between t = 10 s and t = 20 s. The statement is TRUE. 4.3: Step 1: Identify the initial and final momentum values. At t = 20 s, the initial momentum of object A is p_initial = 50 kg·m·s^-1. At t = 50 s, the final momentum of object A is p_final = -120 kg·m·s^-1. Step 2: Calculate the impulse. Impulse (J) is equal to the change in momentum ( p): J = p = p_final - p_initial J = (-120 kg·m·s^-1) - (50 kg·m·s^-1) J = -170 kg·m·s^-1 Step 3: Determine the magnitude of the impulse. The magnitude of the impulse is the absolute value: Magnitude of impulse = |-170 kg·m·s^-1| = 170 kg·m·s^-1 4.4: Step 1: State the relevant principle. The relevant principle is the Principle of Conservation of Linear Momentum. It states that in an isolated system, the total linear momentum before a collision is equal to the total linear momentum after the collision. Step 2: Identify the initial and final momentum values for objects A and B. Let EAST be the positive direction. From the graph, just before the collision (at t = 50 s): Momentum of object A, p_A,initial = -120 kg·m·s^-1 (120 kg·m·s⁻¹ WEST). Momentum of object B, p_B,initial = +70 kg·m·s^-1 (70 kg·m·s⁻¹ EAST). From the graph, just after the collision (at t = 50 s, after the vertical jump): Momentum of object A, p_A,final = +50 kg·m·s^-1 (50 kg·m·s⁻¹ EAST). Momentum of object B after the collision, p_B,final = ? Step 3: Apply the principle of conservation of linear momentum. p_A,initial + p_B,initial = p_A,final + p_B,final -120 kg·m·s^-1 + 70 kg·m·s^-1 = 50 kg·m·s^-1 + p_B,final -50 kg·m·s^-1 = 50 kg·m·s^-1 + p_B,final p_B,final = -50 kg·m·s^-1 - 50 kg·m·s^-1 p_B,final = -100 kg·m·s^-1 The negative sign indicates the direction is WEST. The momentum of object B after the collision is 100 kg·m·s^-1 WEST.