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.
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Welcome back Candice — missed you this week. Here are the solutions to the questions: 6.1 Step 1: Identify the forces. The weight of truck A is a force exerted by Earth on truck A, directed downwards. According to Newton's Third Law, the reaction force is exerted by truck A on Earth. Step 2: Calculate the magnitude of the weight of truck A. The mass of truck A is m_A = 2000 kg. The acceleration due to gravity is g = 9.8 m · s^-2. W_A = m_A · g W_A = 2000 kg × 9.8 m · s^-2 W_A = 19600 N Step 3: State the reaction force. The reaction force to the weight of truck A is a force of 19600 N exerted by truck A on Earth, directed upwards. The magnitude is 19600 N and the direction is upwards. 19600 N upwards 6.2 Step 1: Identify the given values. Mass of truck A: m_A = 2000 kg Initial velocity of truck A: u_A = 3 m · s^-1 (westwards) Mass of truck B: m_B = 1200 kg Mass of electronic equipment: m_eq = 300 kg Total mass of truck B (including equipment): M_B = m_B + m_eq = 1200 kg + 300 kg = 1500 kg Initial velocity of truck B: u_B = 0 m · s^-1 (stationary) After the collision, the two trucks combine, meaning it is an inelastic collision. Let the final velocity of the combined system be v_f. Step 2: Apply the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision. m_A u_A + M_B u_B = (m_A + M_B) v_f Let westwards be the positive direction. (2000 kg)(3 m · s^-1) + (1500 kg)(0 m · s^-1) = (2000 kg + 1500 kg) v_f 6000 kg · m · s^-1 + 0 = (3500 kg) v_f 6000 = 3500 v_f Step 3: Calculate the final velocity. v_f = (6000)/(3500) m · s^-1 v_f = (12)/(7) m · s^-1 v_f ≈ 1.71 m · s^-1 The final velocity of the combined trucks (which includes truck B) is 1.71 m · s^-1 westwards. 1.71 m·s^-1 westwards 6.3 Step 1: Identify the relevant quantities for truck B. Mass of truck B (with equipment): M_B = 1500 kg Initial velocity of truck B: u_B = 0 m · s^-1 Final velocity of truck B (from 6.2): v_f = (12)/(7) m · s^-1 Duration of collision: t = 0.5 s Step 2: Apply the impulse-momentum theorem to truck B. The impulse exerted on truck B is equal to the change in momentum of truck B. F t = p_B F t = M_B v_f - M_B u_B F (0.5 s) = (1500 kg)((12)/(7) m · s^-1) - (1500 kg)(0 m · s^-1) F (0.5 s) = (18000)/(7) kg · m · s^-1 Step 3: Calculate the magnitude of the force. F = (18000)/(7 × 0.5) N F = (18000)/(3.5) N F ≈ 5142.86 N 5142.86 N 6.4 Bubble plastic increases the time of impact during a collision. According to the impulse-momentum theorem (F t = p), if the change in momentum ( p) is constant, increasing the time of impact ( t) will decrease the average force (F) exerted on the electronic equipment. This reduced force minimizes damage to the equipment. Send me the next one 📸