- About Us
- Join + Support
- About Us
- Join + Support
When you push the plunger on a syringe, water is forced into a second syringe, extending its plunger and lifting a mechanical arm. The process illustrates aspects of fluid pressure, force, mechanical work, and biomechanics.
The diagram below shows an exploded drawing of the Hydraulic Arm assembly. Refer to this drawing as necessary as you proceed through the steps that follow.
Push on the plunger of the free syringe. What happens? Pull on the plunger. What happens now?
Use the arm to lift a small object. (If the arm tips, put a book or other heavy weight on the base to steady it, or find a lighter object to lift.) How does the force of your push on the free syringe’s plunger compare to the force that the fixed syringe’s plunger exerts on the arm? How do the distances that the two plungers move compare with each other?
Notice carefully how hard you have to push on the plunger to lift a particular object, and notice how far the arm can move the object.
Remove the object, then push water into the fixed syringe so that the arm is elevated as much as possible. Support the elevated arm so that it can’t fall. (You could have a friend hold the arm, or you could support it with a stack of books.) Then raise the free syringe until the end of the tube attached to it is well above the fixed syringe. Keeping the end of the tube raised (to prevent water from coming out when the syringe is removed), remove the 10-mL syringe and replace it with the 1-mL syringe.
Remove the support from the elevated arm. Pull the plunger on the 1-mL syringe until the syringe is full. Replace the object on the hook, and then push the plunger on the 1-mL syringe to lift the object. Notice the difference in how hard you have to push on the plunger to lift the object this time. Notice also how far the object is lifted.
Put the 10-mL syringe back in place at the end of the tube, using the same technique you used to replace it with the 1-mL syringe. Turn the whole device upside down and use the syringe to raise and lower the arm. Compared to the right-side-up position, what’s different about the process of elevating the arm?
When you push on the plunger of the movable syringe, the arm rises; when you pull on the plunger, the arm descends.
Pushing on the plunger applies pressure on the water in the movable syringe. Since the water is confined and incompressible, Pascal’s principle comes into play, telling us that the pressure is transmitted undiminished to all parts of the water and to the walls of its container. Since the plunger of the fixed syringe at the other end of the tube forms part of the “container” for the water, and is the only part of the container that can expand, the pressure causes the plunger in the fixed syringe to move.
Pascal’s principle and a little mathematics can be used to show that—if the syringes are identical—the force you apply to one plunger is transmitted in full to the other plunger (see Math Root, below). Additionally, as you can observe, each plunger moves the same distance.
With the 1-mL syringe, you need to push with less force than with the 10-mL syringe, but the arm is not lifted nearly as far. In accordance with Pascal’s principle, the pressure on the plunger of the 10-mL syringe is the same as the pressure on the plunger of the 1-mL syringe. However, since the area of the 10-mL plunger is far larger than the area of the 1-mL plunger, the force exerted on the 10-mL plunger is far larger than the force you push with (remember, F = pA). The good news is that you have obtained a force advantage, but the bad news is that you’re paying for it with a distance penalty. Mechanical work is the product of force times the distance the force moves through (W = Fd), and this product remains constant.
In the right-side-up position, the plunger pushes on the arm to raise it. But when you turn the whole assembly upside down, the syringe pulls on the arm to raise it, just like your muscles do with your own arms. The muscle that allows your forearm to lift things, called the biceps, is attached near your shoulder and just below your elbow. When the biceps contracts, it has the same effect on your arm as the syringe has on the hydraulic arm when the assembly is upside down. In both cases, a large force is exerted so that a small weight can be lifted, but the weight can be lifted a large distance compared to the distance the force moves (the distance the syringe plunger moves, or the distance your muscles contract).
Hydraulic systems are used in countless applications: brakes and steering on cars; hydraulic lifts and jacks for servicing cars; airplane wing flaps, stabilizer controls, and landing gear; mechanical arms on garbage trucks; blades on bulldozers; and so on.
Pressure is defined as force per unit area (p = F/A). If you divide the force you push with by the area of the plunger that is in contact with the water, you can find the pressure exerted on the water. You can mathematically rearrange p = F/A to become F = pA. This tells you that if you multiply pressure (expressed in pounds per square inch) by area (expressed in square inches) the square inches cancel out, and you are left with force expressed in pounds.
Since the pressure on both plungers is the same, and the areas of both plungers are identical, then the force on both plungers is the same. (In the SI system, force is expressed in newtons.)
Louis Bloomfield. How Things Work: The Physics of Everyday Life (New York: John Wiley & Sons, 1997). There is an excellent discussion of hydraulic elevators on pages 236–237.
John Cameron, James Skofronick, and Roderick Grant. Physics of the Body, 2nd ed. (Madison, WI: Medical Physics Publishing, 1999). Pages 41–50 have a good discussion of the biomechanics of the arm.
Use air pressure to calculate the weight of a car.
Feel atmospheric pressure changes by stepping into a garbage bag.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Attribution: Exploratorium Teacher Institute