Troubleshooting a Virtual Work Problem

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SUMMARY

The discussion focuses on troubleshooting a virtual work problem involving the equation of virtual work: [du = 0] - Pdx + mg dh. The user expresses confusion regarding the derivation of the solution provided in the forum. Key elements include the hydraulic force P acting at the extension point and the gravitational force mg related to the car and platform. The user is advised to connect the differential height change (dh) to the differential distance (ds) that the piston moves, emphasizing the geometric relationship necessary for solving the problem.

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https://www.physicsforums.com/attachment.php?attachmentid=65907&stc=1&d=1390369310

I've been stuck on doing my revision on this problem.

The equation of the virtual work, from what I deduce is

[du = 0] -Pdx + mg dh

However the answer given is
https://www.physicsforums.com/attachment.php?attachmentid=65908&stc=1&d=1390369325

I'm not unfamiliar to these types of question as I've done quite a few of them. But, I just couldn't understand how'd the answer arrive to that.

I know P, is the force acting at the hydraulic extension at bc, and mg is the downward force of the car and the platform.
 

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You need to relate dh to a change in ds, a differential distance the piston moves. This is just geometry.
 

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