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
Step 1: The Jaws-of-Life model uses a hydraulic system with Pascal's principle for force amplification. Pressure P applied to the input piston is transmitted equally. P = (F_1)/(A_1) = (F_2)/(A_2) where F_1 is input force, A_1 input area, F_2 output force, A_2 output area. Step 2: Given input piston radius r_1 = 0.5 cm = 0.005 m, so A_1 = r_1^2. A_1 = (0.005)^2 = × 2.5 × 10^-5 ≈ 7.85 × 10^-5 \ m^2 Output piston radius r_2 = 1.5 cm = 0.015 m, so A_2 = r_2^2. A_2 = (0.015)^2 = × 2.25 × 10^-4 ≈ 7.07 × 10^-4 \ m^2 Step 3: Mechanical advantage MA = (A_2)/(A_1). MA = 7.07 × 10^-47.85 × 10^-5 ≈ 9 Step 4: Input force from hand pump F_1 = 150 N. F_2 = F_1 × MA = 150 × 9 = 1350 \ N The model exerts a spreading force of 1350 N on the car door. 1350 N