Springs - Simples Machines?

Factual Questions
1

Wikipedia says that simple machine is any device that only requires the application of a single force to work. It then lists the “traditional” machines as,

[ul]
[li]The inclined plane[/li][li]The wheel and axle[/li][li]The lever[/li][li]The pulley[/li][li]The wedge[/li][li]The Archimedes’ screw[/ul][/li]
A spring (assumed attached at one end and pulled by the other) requires only a single force to work. Would it be safe to call it a simple machine? Would it fall under the category of one of the above. If not, why not on the list? Perhaps the spring not invented when this list was first determined?

2

A spring is a lever.

3

What makes a spring a lever? It’s not listed as one of the examples of levers, again at Wikipedia.

4

Wikipedia has a different definition of simple machine than any I have heard. A simple machine to me is a device with a mechanical advantage. Things like wheels and axles and pullys aren’t simple machines becuase they don’t provide a mechanical advantage. It is the same with springs, there is no mechanical advantage so they are not simple machines.

5

I don’t think a spring performs work. A spring stores and releases potential energy.

6

Patty: I don’t think Wikipedia is saying that the spring is performing work, but rathat that the spring is working, i.e. functioning.

7

rathat, of course, should read as rather.

8

Isn’t Archimedes’ screw technically a variation of the inclined plane?

9

My physics book defines a machine as an intermediate device that transfers work of one place to another and lists the simple machines as:

  1. Lever

  2. Wheel and axle

  3. Pulley

  4. Inclined plane

  5. Screw

  6. Wedge

I would agree with you and say the the screw and wedge are merely examples of inclined planes.

10

A simple machine allows one to perform work (in the physics sense of Force*Distance) by trading force for distance (or vice versa; see the example of the wheel and axle below).

For example, one way to raise a 500kg weight one meter off the ground (you’ve been drafted into loading furniture into a truck for your friend) is to apply a 4900 newton force to the load straight up; this task then requires 4900 joules of work. Most humans could not apply a force this great by themselves, so they employ a simple machine to trade some of force required for distance. Rolling the load up a 5 degree inclined plane, for example, means you only need to apply ~427 Netwons of force–the equivalent of lifting ~43 kilograms–but the plane needs to be 11.5 meters long at 5 degrees incline to raise the load 1 meter, so you need to apply this force over 11.5 meters. Lifting 43kg over 11.5 meters still produces the same amount of work–4900 Joules.

Alternatively, you could use a block and tackle, where force is traded for the length of rope you need to pull. A 10-pulley block and tackle would cut the force needed to raise the load by a tenth, but also increases the amount of rope you need to pull by a factor of ten. Similar translations of force-to-distance occur in the other four machines:

  • The lever–if the fulcrum is closer to the movee than the mover–provides a greater force at the object to be moved at a cost of greater distance to swing the mover’s end of the lever than the amount of swing at the object’s end.

  • The wheel-and-axle allows a stronger force to be applied at the axle for the price of having the circular distance at the outer edge of the wheel be longer.

  • If a wedge is driven between two objects, a smaller force pressed at the back of the wedge is translated into a greater force driving the objects apart at the cost of driving the wedge in a greater distance than it spreads the objects apart.

  • The screw–although apparently only a rotary version of the wedge or inclined plane–refers I think to Archimedes screw, which is the only one of the simple machines directly applicable to the movement of a flow of water. This is why I think it is listed separately (no cite, just a guess).

The wheel and axle is one of the few examples where it is more common for the machine transfer to go in the other direction: Stronger force applied at the axle (e.g. by a car engine) is used to make the wheel go a greater distance than the spinning axle could cover.

11

It is possible to gain mechanical advantage at the ends of a taut rope by deflecting the middle - a little pull on the middle (perpendicular to the rope itself) translates to a shorter, but more forceful pull at the ends. What category does this one belong in? It’s a bit like a wedge, only pulling instead of pushing.

12

Unless I mistake what you mean by “mechanical advantage”, I don’t know what you mean about wheels and axles not providing such. Motion on the edge of the wheel is high-distance and low-torque, while at the axle it’s high-torque and low-distance. Just try removing the steering wheel from your car and turning the steering shaft with your bare hands.

13

You’re describing a lever.

14

By “bit like a wedge”, I presume you mean the resultant force is (more or less) perpendicular to the direction of the applied force. I don’t know for sure, but I’ll bet the machines are classified as to how the force is transferrred: wheel-and axle is same-direction rotary-to-rotary force, lever is opposite direction rotary-to-rotary force, screw is rotary-to-linear, wedge transfers forces perpendicularly (but so does the inclined plane), and the pulley–err, maybe this isn’t such a hot idea :slight_smile:

15

Well, yes, but with torque rather than force. I didn’t say that it wasn’t a lever, but was just rebutting treis’ assertion that a wheel-and-axle provided no mechanical advantage.

16

Dunno… .it just seems somewhat analogous to a lever.

For an example of this, you could measure the force on the end ropes of a hammock; it will be greater than the force applied by the weight of the person in the hammock, but will be applied across a shorter distance.

17

:smack: D’oh! I mean analogous to a wedge, and I was responding to CJJ* in that last post. :smack: :smack: :smack:

18

Note that all simple machines display the quality of either redirecting the force vector (wedge, pulley, inclined plane), amplifying the magnitude of force (lever and fulcrum, wheel and axle), or both (screw). All are, in concept, rigid, inelastic, frictionless elements that can be modeled algebraically as a time-independent element of a system. The spring, however, relies upon material elasticity and (it can be demonstrated) always displays some degree of mechanical hysteresis, and whose properties vary with respect to an initial time and condition. Ergo, like a rope/cable it is not a “simple machine” in the strict fundamental mechanics definition, though springs in various forms are one of the oldest elements of real-world mechanisms.

The difference between a wedge and an inclined plane, I think, is that with the former it is considered the primary dynamic element in the system, whereas the inclined plane is assumed to be fixed to ground and simply displays reactions to other elements. A trival distinction, perhaps, given that both mechanisms redirect forces in essentially the same way, but that’s been the traditional breakdown. By the same measure, a pulley is merely a wheel and axle turned around; instead of the axle attached to the load and the wheel in contact with the ground, the wheel is connected to the load (typcially by a cable, but it could be a direct mechanical contact as in a cam or a gear) and the axle is rigidly connected to ground. A screw, however, not only redirects the force vector in a different direction but also translates it from linear force to torque or vice versa, so its is fair to distinguish the screw from a wedge.

The idea behind the “simple machines” is that they comprise all force-redirecting or -amplifying elements of more complex mechanisms like four-bar mechanisms, Scotch yokes, block-and-tackle, et cetera. They are not an exhaustive list of all machine elements, but rather just those that are time- and property-invariant.

Mangetout’s example of the rope, for instance, assumes that exists some additional constraint that keeps the ends of the rope from simply moving in the direction of the applied force but allows it to move in the perpendicular direction. This implies some additional mechanism, like a track, a pulley, or some other device to redirect the force or apply a reaction; thus, a rope is not a simple machine.

Stranger

19

Pshhh… that’s the way real men drive.

20

Are you sure? I’m no physics whiz, but drive edge-on into a concrete freeway barrier at 100kph and the barrier will act as a wedge to split your car in two, despite being fixed to the ground. Aren’t scissors just parallel wedges moving in opposite directions?

I would say the primary difference between a wedge and an inclined plane is that an inclined plane cannot be used to focus force on a point in the way a wedge can.

You can use a wedge as an inclined plane, to shim something up, but you can’t use an inclined plane to split firewood.

Of course, I could be wrong.