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Answer :
Final answer:
To find the maximum mass that a hydraulic lift can lift on the output piston, we apply Pascal's principle and the relationship between force and area, then use the force to calculate the mass based on gravitational acceleration.
Explanation:
The subject of the question involves understanding the principles of a hydraulic lift and applying them in a physics problem that relates force, pressure, and the area of the pistons. The problem presented requires calculating the maximum mass that a hydraulic lift can lift on the output piston given a certain force exerted on the input piston.
We can solve this by using Pascal's principle, which states that pressure is transmitted undiminished in an enclosed static fluid. The formula for pressure is P = F/A, where P is the pressure, F is the force, and A is the area on which the force is applied. For hydraulic systems, the pressure exerted on the smaller piston is the same as the pressure exerted on the larger piston. Thus, F1/A1 = F2/A2, where F1 and F2 are the forces on the smaller and larger pistons, respectively, and A1 and A2 are their corresponding areas.
To find the area of each piston, we use the formula A = πr^2, where r is the radius of the piston. Therefore, the area of the input piston (A1) with a diameter of 8.35 cm is A1 = π * (8.35/2)^2. Similarly, for the output piston (A2) with a diameter of 36.3 cm, A2 = π * (36.3/2)^2. Given that F1 = 825 N, we rearrange the equation F1/A1 = F2/A2 to solve for F2, which is the force exerted by the larger piston.
After calculating F2, we can then find the maximum mass (m) that can be lifted using the relationship F = m * g, where g is the acceleration due to gravity (9.8 m/s^2). By rearranging to solve for m, we get m = F2 / g. This gives us the maximum mass that can be supported by the lift at the output piston.
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