Solving Hydraulic Lift & Friction Force Problems

AI Thread Summary
To solve hydraulic lift problems, it's essential to understand the relationship between force, area, and distance, particularly how they relate to the smaller and larger pistons. For the hydraulic lift, raising the larger piston requires applying a force proportional to the combined areas of both pistons and the distance the larger piston is raised. In the second problem, the frictional force between the plug and the wall needs to be determined, but confusion arises regarding the source of friction and the implications of the lake's volume remaining constant. Clarification on the setup of the problems and the assumptions made is necessary for accurate problem-solving. Understanding these principles is crucial for successfully tackling hydraulic lift and friction force challenges.
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Homework Statement



1)

Consider the hydraulic lift which has a smaller piston of area A1 and a larger piston area A2. Initially the two pistons are not moving.

Show that in order to raise the larger piston by a distance d2, it is necessary to apply a force △F = ρg(A1 + A2)d2 on a smaller piston
2)

The water in the lake behind a wall is 15 m deep. A horizontal pipe 4 cm in diameter passes through the wall 6 m below the water surface, which is blocked by a plug. Assume the volume of lake is so large that its surface remains constant even when water flows out of the wall.
Find the frictional force between the plug and the wall.

The Attempt at a Solution



1) for this question , i can only think about the relation of the area , force and distance , but i cannot group them up and form the equation as the question stated

F1 * d1 = F2 * d2
A1 * F2 = A2 * F1

2) i don't know where the friction come from and seems don't know what's going on in this question...
 
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For the first question, is there a picture given? Can you describe the picture?

For the second question... I don't understand this part: "Assume the volume of lake is so large that its surface remains constant" surface area?
 
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