66 - Simple Machines (w/ Adele Musicant!)
66. Simple Machines
Fundamental physical properties govern our lives and how our world operates. Today, we will discuss simple machines and how they have contributed to human advancement. Let’s learn to be scientifically conversational.
General Learning Concepts
1. What are the physical properties that helped develop the need for simple machines?
a. General idea: Simple machines modify motion and force. [2] [3]
i. Motion: The study of how things move; generally thought to be describable from Newton’s laws:
1. First Law: Inertia (Every object persists in its state of rest or uniform motion in a straight line unless acted on by an external force.) Example: roll a ball across a flat surface, ball will continue rolling in a straight line until the forces of air resistance and friction against the floor cause it to stop.
2. Second Law: Forces. Explains how an object’s movement is altered by the application of an external force – the change in movement is dictated by both the net force acting on the object as well as the object’s mass.
3. Third Law: Rockets (for every action, there is an equal and opposite reaction).
ii. Force: Push or pull on an object resulting from interactions with other objects. Can be divided into two categories: contact forces (result from direction interactions between objects – includes friction and spring force) and action-at-a-distance forces (result from indirect interactions, like gravitational force.
1. Abstract; often understandable once it meets resistance. Strength, energy, power, intensity. (An influence tending to change the motion of a body or produce motion or stress in a stationary body).
iii. Work: Energy transfer that occurs when an object is moved by a given distance (the displacement) by some force.
1. W = |F| (cos θ) |d| (W is work, d is the displacement, θ is the angle between the force vector F and the displacement vector d).
2. Work, as you imagine, is not only happening in one dimension, but it is easier to think about the work being done in each dimension separately. Work is measured in the same units as energy, joules.
iv. Friction: Force that resists motion. [2]
1. Not a fundamental force (like gravity or electromagnetism). Instead, it’s believed to be the result of electromagnetic attraction between charged particles in two touching surfaces.
2. Static friction acts before a motion begins its journey and dynamic friction acts upon the object once it has begun moving. Still, friction is required for certain types of movement; if there was no friction, wheels would simply spin in place.
v. Torque: Rotational equivalent of linear force.
1. The measure of force that causes an object to rotate about an axis; allows for objects to acquire angular acceleration (compared to how force allows something to accelerate).
2. Torque is equal to Force times the perpendicular distance from the line of action.
vi. Mechanical advantage: Measure of the force amplification achieved by using a tool.
1. Ratio of the output force (force exerted by the machine) to the input force (force applied to the machine).
2. Used to describe the forces in simple machines. Input and output energy are always the same (law of conservation of energy) but different machines can help you conserve force in different ways.
3. Examples:
a. Mechanical advantage = 1. Flagpole pulley: force remains the same, but the direction of the force changes.
b. Running: You want to climb 1,000 ft, can choose a gentle hill or a steep hill. Running up the gentle hill is easier (will require less input force) but will require you to run a greater distance. The steep hill will get you to 1,000 ft faster (i.e. will minimize total distance run) but will require more input force.
2. Simple machines: Devices with few or no moving parts that make work easier.
a. Types: Simple machines are commonly associated with six main classes: wheel and axle, inclined planes, wedges, levers, pulleys, and screws.
i. Wheel and axle: Changes force by changing the distance over which a force is applied.
1. Can apply force to either the wheel or the axle.
a. Force applied to wheel: Screwdriver. You turn the wheel (handle of the screwdriver), increasing the force on the smaller axle, which turns the screw.
b. Force applied to axle: ceiling fan. Large force is applied to axle, powering the wheel (fan blades) to move over a greater distance and cause the desired air movement.
2. Earliest evidence of wheels on axles was 3200 BC, the Sumerians, but the Chinese independently invented the wheel in 2800 BC.
ii. Inclined plane: Changes force by modulating direction and magnitude of force.
1. A ramp decreases force required but increases distance over which an object needs to be moved.
2. Effects on force are dependent on the angle of the inclined plane. A steeper ramp requires greater input force to move an object but decreases the length the object has to be moved. More gradually sloped ramp decreases input force but increases distance.
iii. Wedge: Changes the direction of forces.
1. Triangular-shaped tool (essentially two inclined planes together, sometimes called a portable inclined plane). Different from an inclined plane because a wedge does work by moving, while an inclined plane stays still.
2. Can be driven under loads to lift, or into a load to split or separate. Essentially, they act to change the direction of the input force (eg. Splitting a log with a wedge and a sledgehammer, or a doorstop that translates force into friction).
3. Longer, thinner wedges have a greater mechanical advantage than shorter, wider wedges. In the case of an axe used to split wood, a long/thin axe would require less input force than a short/wide axe to do the same amount of work.
iv. Lever: Amplifies input force to provide greater output force to lift or move heavy objects.
1. Made up of four major points:
a. Fulcrum (or hinge, where the lever pivots rotationally)
b. Beam (physical lever itself, which pivots on the fulcrum)
c. Load (object being manipulated)
d. Effort (force exerted by a person or machine on the lever)
2. An example of a balanced lever would be two equally weighted people on a seesaw at equal distances from the fulcrum. A non-balanced lever would be using a crowbar to remove a nail.
v. Pulley: Changes the direction of force. Can often be combined to obtain increased mechanical advantage (by trading distance for effort).
1. A pulley is a wheel over which a rope or belt is passed. It is also a form of the wheel and axle.
2. Example: Pulling a bucket out of a well. Instead of pulling the bucket up, you assemble a pulley system, which allows you to pull down, working with the force of gravity instead of against it.
3. Adding more wheels to a pulley system decreases the amount of effort needed to lift the same amount of weight. However, this also increases the distance over which you have to apply force (e.g. the amount of rope you have to pull)
vi. Screw: Converts rotational motion to linear motion. [2]
1. A screw is essentially a long inclined plane (thread) wrapped around a cylinder (shaft).
2. The mechanical advantage of a screw depends on the length and thickness of the screw as well as the space between the threads (pitch).
a. You have a greater mechanical advantage with a screw that has a smaller pitch – you have to turn the screw more times but it takes less effort.
3. Can be used to hold things together (e.g. the screw on a jar lid) or to apply force to objects (as in a vise or a clamp). Screw presses were also used in the Roman Empire to press apples into cider, grapes into wine, and olives into olive oil (walk around the press using a long wooden bar to turn the screw, which then presses down on the apples, grapes, etc., forcing out the juice)
3. What are some spectacular uses for simple machines?
a. The Pyramids: Inclined planes helped build the pyramids. While the distance was farther to move stone slabs, the force required to move the object was lessened.
b. Elevators: Use pulleys to move elevator car up and down elevator shaft. Without it, we likely wouldn’t have the skyscrapers we see in cities around the world today.
4. Fun Tidbits
a. Archimedes of Syracuse: “ "Give me a place to stand," Archimedes is said to have promised, "and I will move the world." In this perhaps apocryphal quote, the Greek mathematician, scientist, and inventor was discussing the principle of the lever and fulcrum, but he could very well have been describing his whole career. In addition to his mathematical studies and his work on buoyancy, Archimedes contributed to knowledge concerning at least three of the five simple machines—winch, pulley, lever, wedge, and screw—known to antiquity. His studies greatly enhanced knowledge concerning the way things work, and his practical applications remain vital today; thus he is aptly named the "father of experimental science." “
b. Simple machines exist in nature! [2]
i. Wedge: Teeth
ii. Lever: Joint at the top of your neck (fulcrum). Muscles at the back of your neck provide input force, resulting in you leaning your head back.
iii. Pulley: Kneecap changes the direction in which the quadriceps tendon pulls on the tibia
iv. Screw: Rather than a ball-and-socket system, the hip joints of some weevils (type of herbivorous beetle) are screws. Allows them to twit their front legs 90 degrees and their hind and middle legs 130 degrees. Thought to help them find better footholds as they search for food in leaf litter on the forest floor.
c. Compound machine example: Your bicycle makes use of nearly every kind of simple machine!
i. Pulley: chain & gears
ii. Wheel and axle: pedals, wheels
iii. Lever: handle bars, pedals
iv. Screw: raise and lower seat, hold various parts together
2) Solicited Questions
a. Why are you talking about simple machines instead of coronavirus?