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: Convert given diameters to meters and calculate the areas of the pistons. The diameter of the small piston is d_1 = 20 mm = 0.02 m. The area of the small piston is: A_1 = ( d_1^2)/(4) = (0.02 m)^24 = × 0.0004 m^24 = 0.0001 m^2 The diameter of the large piston is d_2 = 100 mm = 0.10 m. The area of the large piston is: A_2 = ( d_2^2)/(4) = (0.10 m)^24 = × 0.01 m^24 = 0.0025 m^2 Step 2: Apply the principle of pressure balance in the hydraulic jack. According to Pascal's principle, the pressure at the same horizontal level in a continuous fluid is equal. Since the large piston is h = 1 m below the small piston, the pressure at the level of the large piston will be higher than the pressure at the level of the small piston by an amount equal to h, where is the specific weight of the liquid. The pressure exerted by the small piston at its level is P_1 = (F_1)/(A_1). The pressure exerted by the large piston at its level is P_2 = (W)/(A_2). The pressure balance equation is: P_2 = P_1 + h Substituting the expressions for P_1 and P_2: (W)/(A_2) = (F_1)/(A_1) + h Step 3: Substitute the known values into the pressure balance equation. We are given F_1 = 400 N, = 9810 N/m^3, and h = 1 m. (W)/(0.0025 m)^2 = 400 N0.0001 m^2 + (9810 N/m^3)(1 m) Step 4: Solve for W. Multiply both sides by A_2: W = A_2 ( (F_1)/(A_1) + h ) W = (0.0025 m^2) ( 400 N0.0001 m^2 + 9810 Pa ) W = (0.0025 × (400)/(0.0001 )) N + (0.0025 × 9810) N W = ((0.0025 × 400)/(0.0001)) N + (0.0025 × 9810) N W = ((1)/(0.0001)) N + (0.0025 × 9810) N W = 10000 N + (0.0025 × 3.14159265 × 9810) N W ≈ 10000 N + 77.040 N W ≈ 10077.04 N The weight W that can be lifted is approximately: 10077.04 N Drop the next question.