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
d) Given: Mass of aircraft, m = 500 kg Radius of circular path, r = 2000 m Speed, v = 120 m/s i) Step 1: Calculate the centripetal acceleration. The formula for centripetal acceleration is a_c = (v^2)/(r). a_c = (120 m/s)^22000 m a_c = 14400 m^2/s^22000 m a_c = 7.2 m/s^2 The centripetal acceleration is 7.2 m/s^2. ii) Step 1: Calculate the centripetal force. The formula for centripetal force is F_c = m a_c. F_c = (500 kg)(7.2 m/s^2) F_c = 3600 N The centripetal force is 3600 N. e) Given: Initial velocity of ball, v_i = 0 m/s (stationary) Final velocity of ball, v_f = 60 m/s Contact time, t = 15 milliseconds = 15 × 10^-3 s Mass of ball, m = 4.5 × 10^-2 kg i) Step 1: Calculate the change in momentum of the ball. The formula for change in momentum is p = m(v_f - v_i). p = (4.5 × 10^-2 kg)(60 m/s - 0 m/s) p = (4.5 × 10^-2 kg)(60 m/s) p = 2.7 kg·m/s The change in momentum of the ball is 2.7 kg·m/s. ii) Step 1: Calculate the average force. The formula for average force is F_avg = ( p)/( t). F_avg = 2.7 kg·m/s15 × 10^-3 s F_avg = 180 N The average force is 180 N. f) Given: Weight of car, W = 10,000 N Linear velocity, v = 72 Km/h Centripetal force, F_c = 40,000 N Assume acceleration due to gravity, g = 9.8 m/s^2. i) Step 1: Define centripetal force. Centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle, and is responsible for maintaining the circular motion. ii) Step 1: Convert linear velocity to m/s. v = 72 Km/h × 1000 m1 Km × 1 h3600 s v = 20 m/s Step 2: Calculate the mass of the car. The formula for weight is W = mg, so m = (W)/(g). m = 10000 N9.8 m/s^2 m ≈ 1020.41 kg Step 3: Calculate the radius of the circular path. The formula for centripetal force is F_c = (m v^2)/(r). Rearranging for r: r = (m v^2)/(F_c) r = (1020.41 kg)(20 m/s)^240000 N r = (1020.41 kg)(400 m^2/s^2)40000 N r = 408164 N·m40000 N r ≈ 10.20 m The radius of the circular path is 10.20 m. iii) Step 1: Calculate the angular velocity of the car. The relationship between linear velocity and angular velocity is v = r. Rearranging for : = (v)/(r) = 20 m/s10.20 m ≈ 1.96 rad/s The angular velocity of the car is 1.96 rad/s. Send me the next one 📸