Key Terms
acceleration
accelerometer
constant motion (uniform speed or uniform velocity)
force
friction
gyroscope
inertia
position
speed
velocity
Soon we will be covering topics related to sensors (devices which record data on objects). Some sensors are able to determine whether an object is in the vicinity of a certain space. This implies that the exact location of the object is uncertain. These sensors could indicate, for example, whether someone had entered a room or is standing in a doorway ... useful, but that might not be precise enough. Other sensors may need to be more exact in the data they report. If a sensor is a position sensor, it will be able to give the exact location (to the limits of the measuring instruments) of a given object. This may be required for assembly lines and robotics. Position sensors may give the position in 3-D coordinates, 2-D Cartesian coordinates (x , y) , polar (r , θ) , or simply where an object is on a number line. In short, position is where something is.
Speed is simply how fast something is going. A simple speedometer in a car is an example everyone can relate to. Units can vary, ... miles per hour, feet per second, kilometers per hour, ... or even inches per century. As the units imply, you need to know how far something traveled as well as the time it took to get there. Occasionally, the terms speed and velocity are used interchangeably. There is a difference!
Technically, the velocity implies you also know the specific direction the object is going (and speed does not).
Displacement is more than distance traveled, ... it is distance traveled (as the crow flies from start to finish) as well as the direction moved (such as 50 mph East). So, for example, if you drove your car once around the Indy 500 track, you traveled a distance of 2.5 miles but your total displacement would be zero. Can you see why your speed and velocity would be very different values (no matter how much time you took)? Don't worry, we are not trying to turn you into a physics major, but you can see how easy it is to get confused when using these terms.
Speed and position are somewhat related because if you have data related to position at all times, you can calculate the speed of the object. Technically any sensor that is able to measure position will also be able (with the help of a computer chip), to calculate speed. The same goes for velocity and displacement. If you have accurate data on displacement over time, you can calculate velocity
Most people know that when an object speeds up, it is said to be accelerating. However, anything that speeds up, slows down or changes direction is accelerating. The change in direction is what confuses many students. This is where we need to be more technical and talk about velocity instead of speed. Since direction is an integral part of velocity, any change in direction implies a change in velocity (even if it is moving with constant motion ... such as a car on cruise control moving in a circle). In other words, acceleration implies that the velocity is changing with time.
If you drop an apple, it accelerates towards the ground. At the surface of the earth (and in a vacuum), all objects accelerate at 1 "g". This value is 32 feet per second per second (abbreviated 32 ft/s2). This means that every second the object's velocity grows by 32 feet per second towards the ground. That is, after one second of freefall, an object dropped from rest will be moving at a speed of 32 feet/second. After two seconds, the speed grows to 64 feet per second, etc. If a sensor has precise data on the velocity of an object at any given time, a computer can also (in theory) obtain the acceleration of the object.
Galileo Galilei laid down the fundamental understanding of natural motion when he contradicted the ancient view of the Greeks (Aristotle). Aristotle stated that the "natural" state of motion is the state of rest. This can be observed by sliding a book along a table top ... it eventually comes to rest. Galileo understood that there was a force of friction between the book and the table which altered the "natural" state. He claimed that an object in motion will continue in motion (provided you eliminate the frictional forces). He was correct ... as anyone who has ever played a game of air hockey can attest. Galileo called this property of matter inertia.
You "feel" inertia when you are a passenger in a car. Your head moves back when you take off from a stoplight. You slide to the side when your car turns. It is also the main reason you should always wear a seat belt. When your car suddenly stops, you tend to keep moving forward. In an accident, seat belts and air bags help you safely overcome your tendency to remain moving forward.
Isaac Newton formalized the concepts of Galileo in the form of laws.
Newton's First law of Motion states: An object at rest will remain at rest ... an object in motion will continue in a state of uniform velocity (same speed ... same direction) unless acted upon by some force.
You can easily expand the concept of inertia to spinning objects. Just as objects moving in a straight line tend to keep moving in the same direction, ... spinning objects have the same tendency to keep spinning with the same orientation in space (until acted upon by an outside force). Let's give a few examples where this concept is seen.
The gyroscope is nothing more than a heavy, almost frictionless, spinning top. They are used in airplanes, rockets, space stations and all satellites to maintain orientation and to "know" which way they are pointing.
Courtesy Wikimedia Commons
The same concept of angular inertia helps explain why you have such good balance when riding a bicycle. The wheels (once turning) have angular inertia and help you maintain your orientation.
Let's see if you can discover Newton's Second Law for yourself.
Newton's Second Law of Motion deals with the behavior of matter when an applied force acts on it. Can you guess what it is? Watch the animation below. A force acts on blocks in a frictionless environment. Write something down and look below for Newton's version.
Forces acting on various masses (animation)
.... Keep scrolling down for the answer (make a guess first).
The animation clearly shows that when a force acts on an object, it accelerates. The acceleration is the greatest when a large force acts on a small mass. When a small force acts on a large mass, the acceleration is considerably lower. Newton summarized this observation in the form of the following law ...
Newton's Second Law of Motion - When a force acts on an object, it will accelerate. The greater the applied force, the greater the acceleration. The acceleration also depends on the mass (weight) of the object being accelerated. The greater the mass, the lower the acceleration!
How close was your law? Newton published his "laws" in 1687 in his great work, The Principia.
Actually, anything that speeds up, slows down, or changes direction is considered an acceleration. So whenever you see an object display this kind of motion, you know that an applied force must be acting on it.
Newton formalized his second law in one simple equation:
Where a = acceleration, F is the net force on an object, and m is the mass of the object. It basically says that acceleration is proportional to the applied force and inversely proportional to the mass of the object being accelerated. That is, if F increases, so does a. However, if m increases, a decreases.
Structural engineers, rocket scientists, manufacturers, and architects are just some of the people who need to know how objects behave when accelerated. So how do these designers determine the rates of acceleration on objects? Simple! Attach an accelerometer to your test subject and let it go. Basically, it is a small mass suspended in a box which is supported in all directions by springs (see image below).
If the box is accelerated in one direction, the springs will stretch in the forward direction and compress in the trailing direction. These springs provide the net force to make the mass accelerate (with the box). The more the springs are distorted (from their rest position), the greater the applied force, .. the greater the degree of acceleration. All you need to measure is the force in the spring and you can calculate the acceleration of the object. Later you will see other ways to measure the applied force on the mass without using springs.
An accelerometer in action (animation)
For example, test pilots will black out when experiencing accelerations around 5-8 times the acceleration of gravity (called G-LOC). Don't you think it would be a good idea to have one of these sensors in your jet to let you know when you are approaching this limit?
Accelerometers are built into your smart phone. They are used to determine orientation and adjust the screen accordingly. Etched on a chip only 1/50th of an inch across, the motion of the suspended mass is determined not by forces in springs, but by capacitors (covered in unit 4).
Liquids and gasses obey the same laws as solids, but these laws must be
modified slightly. The motion of solids is dictated by the action of
forces. However, the motion of liquids and gasses are dictated by
pressure. Pressure is nothing more than force over a given area.
Liquids and gasses always move when there is a pressure difference.
Specifically, liquids and gasses move from areas of high pressure toward
areas of lower pressure. You will see some interesting and important
effects which result from the motion of liquids (and gasses) when we discuss the
ways water is distributed to homes and how the wings of an airplane create lift.
When two moving surfaces are in direct contact, they rub against each other and produce heat. We call this (kinetic) friction. No matter how smooth a polished surface appears, on the microscopic scale it looks like a mountain range. As two surfaces move across each other (on the atomic scale) there are small forces of attraction between atoms of one surface and the other. As the surfaces move with respect to each other, close atomic encounters produce a "stick" which must be overcome (yanked away) ... only to find another atomic interaction with the next row of atoms. When the two surfaces are simply resting against each other, the friction between the surfaces is even greater (called static friction) because these "mountains" have a chance to settle deeper into the "valleys" of the other surface. This increases the atomic force of attraction (more "stick"). This is why it is harder to get a crate moving initially than it is to keep it moving along the floor. The subject is a very complex topic in molecular physics. If interested, you can read more about it at link 1.2.a.
Static friction (no motion between surfaces) - the surfaces are
interlocked making it difficult to move initially.
Kinetic friction (motion between surfaces) - this produces heat (try rubbing your
hands together and see what happens) (animation)
All engineers have to deal with friction. It is the reason you cannot simply turn off your engine when moving down a flat, straight section of highway (remember Newton's First Law of Motion?). Moving parts in an engine need to be lubricated with oil to reduce friction. Spinning wheels use roller bearings to reduce friction. Planes, trains and automobiles are designed to minimize friction with the air. Fluids moving through pipes have to deal with friction. Even electrical resistance can be thought of as a form of friction which converts usable energy to wasteful heat. Many devices are carefully engineered to reduce friction to a minimum.
However, in some cases, friction is an absolute necessity. The brakes in your car depend on friction between the drum and shoe (or between pads and rotor in disc brakes) to make your car stop. The treads on tires are designed to maximize the friction between the tire and the road.
©2001, 2004, 2007, 2009, 2016 by Jim Mihal - All rights reserved
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