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
Morning Candice — let's get this done. Here are the solutions for the collision problem: 3.1: Step 1: Define a positive direction and list the given values. Let "towards the right" be the positive direction. Mass of delivery van (m_v) = 5000 kg Initial velocity of delivery van (v_vi) = +10 m/s Mass of car (m_c) = 2000 kg Initial velocity of car (v_ci) = -15 m/s (moving left) Final velocity of car (v_cf) = +5 m/s (moving right) Step 2: Apply the law of conservation of linear momentum. The total momentum before the collision equals the total momentum after the collision: m_v v_vi + m_c v_ci = m_v v_vf + m_c v_cf Step 3: Substitute the values into the equation and solve for v_vf. (5000 kg)(+10 m/s) + (2000 kg)(-15 m/s) = (5000 kg)v_vf + (2000 kg)(+5 m/s) 50000 kg · m/s - 30000 kg · m/s = (5000 kg)v_vf + 10000 kg · m/s 20000 kg · m/s = (5000 kg)v_vf + 10000 kg · m/s 20000 kg · m/s - 10000 kg · m/s = (5000 kg)v_vf 10000 kg · m/s = (5000 kg)v_vf v_vf = 10000 kg · m/s5000 kg v_vf = +2 m/s The magnitude of the velocity of the delivery van immediately after the collision is 2 m/s. 3.2: Step 1: Calculate the total initial kinetic energy of the system. KE_initial = (1)/(2)m_v v_vi^2 + (1)/(2)m_c v_ci^2 KE_initial = (1)/(2)(5000 kg)(10 m/s)^2 + (1)/(2)(2000 kg)(-15 m/s)^2 KE_initial = (1)/(2)(5000)(100) + (1)/(2)(2000)(225) KE_initial = 250000 J + 225000 J KE_initial = 475000 J Step 2: Calculate the total final kinetic energy of the system. Using v_vf = +2 m/s from 3.1 and v_cf = +5 m/s. KE_final = (1)/(2)m_v v_vf^2 + (1)/(2)m_c v_cf^2 KE_final = (1)/(2)(5000 kg)(2 m/s)^2 + (1)/(2)(2000 kg)(5 m/s)^2 KE_final = (1)/(2)(5000)(4) + (1)/(2)(2000)(25) KE_final = 10000 J + 25000 J KE_final = 35000 J Step 3: Calculate the change in kinetic energy. KE = KE_final - KE_initial KE = 35000 J - 475000 J KE = -440000 J The change in the kinetic energy of the system is -440000 J. 3.3: Since the kinetic energy of the system is not conserved (it changed by -440000 J), the collision is INELASTIC. 3.4: Step 1: Identify the given values and the impulse-momentum theorem for the car. Mass of car (m_c) = 2000 kg Initial velocity of car (v_ci) = -15 m/s Final velocity of car (v_cf) = +5 m/s Collision duration ( t) = 0.4 s The impulse-momentum theorem states that F_avg t = p_c = m_c v_cf - m_c v_ci. Step 2: Substitute the values into the formula and solve for the average force (F_avg). F_avg (0.4 s) = (2000 kg)(+5 m/s) - (2000 kg)(-15 m/s) F_avg (0.4 s) = 10000 kg · m/s - (-30000 kg · m/s) F_avg (0.4 s) = 10000 kg · m/s + 30000 kg · m/s F_avg (0.4 s) = 40000 kg · m/s F_avg = 40000 kg · m/s0.4 s F_avg = 100000 N The magnitude of the force that the delivery van exerts on the car is 100000 N. Drop the next question.