If we look at our daily lives we rarely think about how to do things. Whether we are opening a bottle or moving an object, we can do so without thinking about how much work goes into it. Many tasks that once took considerable effort to accomplish can now be done practically with no effort at all.
How can we be so effortless? The answer is through the use of simple machines – the basic components of all machines! Simple machines are neat devices invented over several hundred years that can increase our force, change the direction of our efforts or increase the distance we apply our efforts, meaning we can do work with significantly less effort.
So what is work in the scientific sense, and how do these devices often described as basic alter our ability to do work? In physics, work is defined as energy transferred when force moves an object through a distance. To describe work mathematically, we would use:
W= F × d × cos(θ)
Where:
- W is the work done
- F is the total force acting
- d is the distance travelled by an object acted upon
- θ is the angle between the force vector and the distance vector
So we can tell that to do work we need to apply a force and have the object moved through a distance. Simple machines do not magically remove the amount of work needed to move an object (as per the laws of conservation of energy).
They do this by manipulating the dependence between force and distance; you can do the same work with a smaller amount of force – at a larger distance, or just change the direction of the force to a more suitable.
Let’s take a light-hearted look at the six classical simple machines so see how they work together to help us do work easier.
1. Lever: The Power of Leverage
Imagine this. You’re trying to pick up large, heavy rock (and I hope it doesn’t want to move while you’re pushing it!). You probably won’t be as successful as you would like to be simply relying on strength.
However, there is now a large, solid bar and a pivot point (called the fulcrum) piping up, and you may have a better shot of lifting the rock. This is the basic concept of the lever, a rigid bar that is free to rotate about a fixed point.
Levers use the principle of moments (or torques). Moment is just defined as the turning effect of a force about the pivot, and is calculated with:
τ=F×r×sin(ϕ)
Where:
- τ is the moment
- F is the force applied
- r is the distance from the pivot point to where we are applying the force (called the lever arm)
- ϕ is the angle between the force vector and the lever arm
We can achieve a mechanical advantage (MA)Mechanical advantage is defined as a ratio of the output force (the force the machine applies to something it is moving) to the input force (the force we apply to the machine):
MA= Fout / Fin
There are three classes of levers depending on where the fulcrum, effort, and load are located:
- First class levers: where the fulcrum is located between the effort and load (for example: seesaw, crowbar, scissors). Normally a first class lever can provide a mechanical advantage greater than, equal to, or less than one, depending on where the fulcrum is located.
- Second class levers: where the load is located between the fulcrum and the effort (for example: wheelbarrow, nutcracker, bottle opener). A second class lever will always provide a mechanical advantage greater than one, meaning we can lift or move heavy loads with less effort than dragging.
- Third class levers: where the effort is located between the fulcrum and the load (for example: tweezers, fishing rod, human forearm). A third class lever will always be less than one; while they do not provide any amplification of force they do allow for either an increased distance or speed of the load.
2. Wheel and Axle: Rotation to Our Advantage
The wheel and axle consists of a wheel attached to a central rod or axle that rotates as one unit. When a force is applied on the rim of the wheel the axle will rotate. Applied to the axle will also get rotation.
So if for example we had to move something, we could push it. However, using a wheel to roll it would minimize friction compared to dragging it. For most of us the wheel and axle may be one of the easiest machines to understand.
With an example, The larger radius of the knob (the wheel) lets you apply less force over a greater distance to create more torque on the smaller radius of the spindle (the axle), allowing you to work the latch with ease.
The mechanical advantage of a wheel and axle is determined by the radius of the wheel (R) vs the radius of the axle (r):
MA= R/r
If you have a larger wheel compared to the axle you will have a greater mechanical advantage, and this will allow you to turn the axle easier or lift a load that is attached to the axle (just think of a winch).
3. Pulley: Changing Direction and Gaining Advantage
A pulley is a grooved wheel with a rope or cable that runs along the groove. Pulleys can function by themselves or in succession to lift heavy loads. Pulleys basically work by changing direction of the force making it more convenient to lift an object.
Fixed pulley: A single pulley that is attached to a fixed position (for example, a flagpole pulley). There is no mechanical advantage with this pulley and there is no amplification of force (MA = 1), however we are able to pull downward on the rope to lift the load upward. Therefore, it can be more comfortable and allows us to use our body weight as mechanical advantage.
Movable pulley: A pulley that is attached to the load itself. One end of the Essentially a single pulley gives you a mechanical advantage of 2, meaning you applied 50% of the force needed to lift the object (for now don’t consider the weight of the pulley or friction). For a single movable pulley, means you need to pull the rope 2 times the distance of the object.
Pulley systems (block and tackle): Utilizing fixed and movable pulleys we can assemble a pulley system. A pulley system can provide a larger mechanical advantage than a single pulley system. The mechanical advantage of a pulley system is usually close to the total number of rope segments supporting the movable load. Pulley systems are used to lift large objects, they are commonly used on cranes and elevators and for sailing.
4. Inclined Plane: Easing the Climb
When you lift a heavy object straight up, you are required to overcome the weight of the object in full.
But, if you push (or pull) the same object up an incline (an inclined plane) you are applying lesser force (but over a longer distance).
The incline plane allows you less amount of force to be applied by distributing the work along the longer distance.
The mechanical advantage of an inclined plane is the ratio of length (L) of the slope, to the height (h) of the incline:
MA= L/h
Inclined surfaces that are longer in length and less quick of a slope provide a greater mechanical advantage, therefore making it easier to move the object.
Our examples of inclined planes include ramps for wheelchairs, loading ramps on freight trucks, and even the slopes of hills and mountains.
5. Wedge: The Force of Separation
A wedge is essentially a movable inclined plane with one or two inclined sides that comes to a sharp edge. Wedges are used to separate objects, split materials, or hold things in a stationary position.
When a wedge is pushed or pulled at the wider end, it will create a force that is larger than the applied force that is at an angle perpendicular to the sloping surface(s) of the wedge which creates a force that drives the wedge into the material.
A wedge could also be knives used to cut, axes to split, nails can be used to fasten (held in place), or doorstops that prevent the door from opening or closing.
The mechanical advantage of wedge is a little complicated to determine exactly, because friction and angles are difficult to measure; however, in general, the longer and skinnier the wedge is, it has greater mechanical advantage for separating or splitting.
6. Screw: A Spiral Advantage
A screw is basically an inclined plane that is wrapped around the cylinder. Whenever you turn the screw, you apply a rotational force (torque), which is transformed into a linear force that presses the screw into the material.
The closely spaced threads of the screw can be explained as a long shallow inclined plane, which has significant mechanical advantages.
The mechanical advantage of a screw is based on the circumference of the screw vs. the pitch (distance between adjacent threads).
The finer the thread (smaller pitch), the greater the mechanical advantage; because it would take less force to drive the screw into the material, but require more revolutions.
There are many examples of screws, including wood screws to fasten, bolts and nuts to join, and even the Archimedes’ screw to raise water.
How Simple Machines are a Part of Our Lives?
Far from being antiquated, simple machines are part of numerous devices and systems that are a part of our daily lives.
Complex machines are many simple machines that are combined to perform more complex acts. For example, a car jack is composed of a lever and screw, a bicycle incorporates wheels and axles and levers in the brakes, even a pair of scissors is made of two levers working together.
Understanding simple machines provides insight about the mechanics of our everyday surroundings, but they can also cause us to appreciate the ingenuity of human invention.
Simple machines are elegant devices, conceptualized by need to make work easier, and remain significant in our everyday lives and in advancing technology.
Simple machines assist us in manipulating force and motion, to help overcome obstacles, and perform actions that we could not do without.
By recognizing the context for simple machines, we see there are forces demonstrated in nature, confirming some of the fundamental principles of physics are involved with even the simplest of activities.