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
Here are the solutions for question 29: i) The hydraulic lift is an application of Pascal's law. Pascal's law states that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. The correct option is c) Pascal's law. ii) When pressure is applied to an enclosed fluid, it is transmitted unchanged to every portion of the fluid and the walls of the container. This is a fundamental principle of fluid mechanics, known as Pascal's principle. The correct option is d) transmitted unchanged to every portion of the fluid and the walls of the container. iii) For a hydraulic lift, the work done by the input piston is equal to the work done on the output piston (assuming an ideal system). Let A_1 and d_1 be the area and distance moved by piston P1, and A_2 and d_2 be the area and distance moved by piston P2. Given: A_1 = A, A_2 = 2A, d_1 = x. The volume of fluid displaced by piston P1 must be equal to the volume of fluid displaced by piston P2. V_1 = V_2 A_1 d_1 = A_2 d_2 Substitute the given values: A · x = (2A) · d_2 Divide both sides by A: x = 2 d_2 Solve for d_2: d_2 = (x)/(2) The distance moved by piston P2 is (x)/(2). iv) We use Pascal's principle, which states that the pressure exerted on the fluid by the smaller piston is equal to the pressure exerted by the fluid on the larger piston. Let F_1 be the force applied on the input piston and F_2 be the force on the working piston. Let r_1 be the radius of the input piston and r_2 be the radius of the working piston. Given: r_1 = 2 cm r_2 = 6 cm F_2 = 6000 N The area of a circular piston is A = r^2. So, A_1 = r_1^2 and A_2 = r_2^2. According to Pascal's principle: (F_1)/(A_1) = (F_2)/(A_2) Substitute the area formulas: (F_1)/( r_1^2) = (F_2)/( r_2^2) Cancel from both sides: (F_1)/(r_1^2) = (F_2)/(r_2^2) Solve for F_1: F_1 = F_2 ((r_1)/(r_2))^2 Substitute the given values: F_1 = 6000 N × (2 cm6 cm)^2 F_1 = 6000 N × ((1)/(3))^2 F_1 = 6000 N × (1)/(9) F_1 = (6000)/(9) N F_1 = (2000)/(3) N F_1 ≈ 666.67 N Rounding to the nearest whole number, F_1 ≈ 667 N. The force needed is 667 N.