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When you pump a hydraulic floor jack, the lever does not go directly up. It swings around its pivot point.

This motion-on-a-circle action means that the point being lifted will move sideways, relative to the original place where you planted the wheels of the hydraulic floor jack.

The movement of the wheels in turn means that the hydraulic floor jack must be positioned on a smooth floor, and that all wheels must be well lubricated. Failure to pay attention to this (wheels stuck, for example) means you'd be lifting your vehicle sideways, possibly damaging the beam you're lifting, or the vehicle could fall (potentially leading to a nasty accident).

(a) Is my understanding of the use a hydraulic floor jacks accurate? (b) Is that (one of) the difference(s) between a $50 jack and $500 one?

Anecdote: The jockey wheels on a bicycle's derailleurs are almost always built without ball bearings. One has to go to the very top of the range of bicycle derailleurs to find components using ball bearings.

(c) Is this the case here as well, and buying a reliable, safe hydraulic floor jack requires wheels with ball bearings? (d) What else should one be looking for when shopping for a hydraulic floor jack? Lifting a ~1500-2000 kg vehicle (the majority of sedans, hatchbacks, and SUVs) — or ~3000-4000 lb — should be amply supported on even the weakest two-ton hydraulic floor jacks.

The crux of the question is part (c) above. Parts (a), (b), and (d) are for "extra credit". They educate the pupils rather than just have them memorize a quick knowledge bit, and they confirm that the teacher is knowledgeable and will not just provide a one-word answer.

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Your description of the movement of the floor jack is accurate.

Due to this movement, one must also take into consideration the contact point with the vehicle or load being lifted. The forces applied to the system if the wheels do not properly compensate for the lever action can cause the contact pad to slip from the load. This may be the most destructive failure point.

For (b), it's probably a good idea to present links and/or images of the $50 floor jack and the $500 floor jack as there may be other features contributing to the price difference.

For (c), the working environment is a factor, specifically the surface from which the load is being lifted. An ordinary concrete driveway is typically less smooth than the working bay of a repair facility and would thus benefit from larger wheels and bearings, while smaller wheels without bearings (bushings can work well) would be sufficient on a repair facility surface. The grammar in (c) is a little confusing, by the way.

Question (d) is ambiguous in a fashion. Some situations require a low-profile floor jack and that becomes a non-negotiable cost factor. You'll find that some jacks require one to release or secure the lift/drop valve mounted on the floor jack body, using a part of the handle (less expensive, I own two!) which typically separates from the body, while the more expensive models have this feature addressed by the lifting handle, integrated into the construction.

In the image below from an online shop, the valve which determines lifting and release is a simple screw. The shape of the screw matches a distorted handle end that becomes part of the lever used to pump the hydraulics.

lower cost floor jack detail

In the image below, taken from a Harbor Freight floor jack manual, one can see a reference to a U-joint, which is connected to the pump handle, but does not require that the handle be separated and moved to a valve screw.

HF floor jack with integrated valve

lower cost floor jack detail

Secondary to the question, it's important to note that one does not support a load with a floor jack. One lifts the load to the desired height and supports it with appropriately rated jack stands. You'll find feature-related price variations within that class of tool as well.

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