username@email.com
username@email.com
In this lesson, you will review the concepts of force, inertia, mass, weight, and the three laws of motion developed by Sir Isaac Newton.
The foremost Italian scientist, Galileo, successfully introduced the concept of inertia. His observations paved the way for Newton to formalize the laws of motion, and Newton is often credited as being the father of physics.
To start us off, we will review some terminology. In physics, a force is any external cause for change to occur on a physical system. For example, any push or pull on another object would be considered to be a force.
Friction is the force that acts between two objects that are in contact and move relative to one another. Any two objects, no matter how smooth they are, have some frictional force between them on Earth. If there was no such thing as friction, a moving object would need no force whatsoever to remain in motion. Objects in a vacuum theoretically move without friction.
A ball is dropped from 5 m high and falls towards the Earth. As the ball falls ___________________.
The correct answer is C. Even though they don’t touch each other, the ball and the earth do exert force. The force of the ball pulling on the earth must be the same as that of the earth pulling on the ball.
How can two objects with the same mass have different weights? The terms weight and mass are often used interchangeably and thus are often confused with each other. We think that a heavy object contains a lot of matter, but is this always true? We often determine the amount of matter in an object by weighing it on a scale. This is not an accurate method to determine an object’s mass.
Mass is more fundamental than weight; mass is the measure of the amount of matter in an object and depends only on the number and kind of atoms in the object. Weight, on the other hand, is a measure of the gravitational force acting on an object. There are places where a massive object has no weight, hence weight depends on an object’s location—Earth is by far the most common location considered when weight is discussed and that is why we often confuse the terms weight and mass.
Mass is a measure of the amount of matter in an object and weight is the force exerted by gravity on an object. A person has the same mass at all times, no matter where the person is located. However, the weight of the person can change drastically depending on where the person is. A person weighs more at sea level than he/she does on top of a mountain because the pull of gravity is greater at sea level (closer to the center of the Earth) than it is on the top of a mountain. Similarly, a person weighs more on the Earth than on the moon because the gravity of the Earth is greater (about 6 times) than that on the moon.
What is the difference between mass and weight?
The correct answer is C. Choice A is the reverse of the correct answer. Weight, not mass, is dependent upon the distance from Earth’s center. Mass does not depend on where the object is located, but weight does.
By the time he was 24 years old, Isaac Newton had developed the three laws of motion—the cornerstone of all of physics.
Newton’s First Law of Motion states that every object at rest will remain at rest, and any object in motion will remain in motion (in a straight line at a constant speed) unless acted upon by an outside force.
In other words, an object tends to keep on doing whatever it was already doing unless something else acts upon it. Books on your desk, for example, are in a state of rest unless they are moved in some way. Now consider if the book was in motion on your desk. Let’s say you exerted a quick force on your book trying to slide it off the end of your desk. Most likely, the book would come to a stop before it fell off. This is because of a large frictional force between the book and the desk. The moment you let go of the book, it was in motion and tried to stay in motion, but because of the outside force of friction that acted on the book after you let go, it stopped. Now imagine you took your book to the arcade and slid it across a frictionless air hockey table. The book would slide easily across the table in a straight line probably hitting the side before it stopped. This is because the surface of the air hockey table exerts less friction upon the book.
Whether or not an object was in motion, it resists any change to what it was doing. The object has inertia, the tendency of an object to resist any change in its motion. Newton’s first law of motion is also called the law of inertia. Some objects have more inertia than other objects. For example, if you try to push an elephant and then try to push a beetle, you quickly realize that the elephant is much harder to push because it is more massive. Likewise, when you try to stop an elephant, it is much harder to stop than the beetle. The greater the mass of an object, the greater its inertia, and the greater the force needed to change its motion.
Acceleration describes how quickly the motion of an object changes and that it is equal to the change in velocity of the object per unit time. We also know that if we apply a force to an object, its motion changes. Force and acceleration are not the same thing. Force, as we just covered, is proportional to the object’s mass. The most popular sport in the world gives us a great example. Consider a soccer ball at rest; apply a force with your foot and it starts to move. Since the ball was not moving before you kicked it, it accelerated, or changed its motion. The ball accelerates each time you kick it; force causes acceleration.
Now if you kick the soccer ball and kick the goal post, you will find that the ball accelerates and moves easily while the goal post is much harder to accelerate and move by applying a force. For any given force, the acceleration produced in another object is inversely proportional to the mass of that object. Newton came up with one of the most important laws of nature ever proposed, the Second Law of Motion, which states that acceleration is directly proportional and in the same direction as the force that caused it, and is inversely proportional to the mass of the object that the force is acting on. In equation form, the second law is:
If a force of 2,000 Newtons is applied to a 1,000 kg car. What is the car’s acceleration?
The correct answer is D. The answer is obtained by dividing the force by the mass. Choice A is multiplying mass times force. Choice B is dividing mass by force. Choice C is subtracting mass from force.
Newton also realized that a force is not just a single entity, in and of itself, but is an interaction between two objects. Suppose you place a nail into some wood with a hammer. You strike the nail with the hammer and the nail goes into the wood because of the force exerted on the nail by the hammer. That is only half of the story. What stopped the hammer from moving? Turns out, the nail actually exerted a force on the hammer to stop its motion. So, there was an interaction of two forces: the hammer on the nail, and the nail on the hammer. Newton realized that forces come in pairs, which led him to his third law of motion. Newton’s Third Law of Motion states that when one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. The key idea here is that each force is a part of a system and for every action there is an equal and opposite reaction.
We all know how objects fall to Earth due to gravity, and that gravity is what holds water in a glass of water. That is what gravity does; it is the main interaction between objects. Newton made key observations about how gravity behaves between all objects. He discovered that gravity is universal—it exists everywhere, between all objects, and depends on the masses of the objects and their distance apart.
Newton’s Universal Law of Gravitation states that every object attracts every other object with a force that is proportional to the product of the objects’ masses and inversely proportional to the square of the distance between them. This is why we have equations. In equation form, this law is:
Newton realized that all objects in the Universe are affected by gravity and their gravitational forces act everywhere in the Universe, not just on Earth. The force that makes an apple fall to the ground is the same force that keeps the planets in orbit around the sun and is also the same force that would allow a leaf in California to attract and potentially come into contact with a feather in New York (if there were no other forces like friction or objects in the way to prevent that from happening, no matter the object’s sizes or locations). Nonetheless, the attractive force between the leaf and the feather (and all objects everywhere) is still there. Most of the time, however, this force is only great enough to be noticed when at least one of the objects is massive.
Now imagine a man standing on the ground next to his house: Is the force of attraction between the man and the center of the Earth the same as when he stands on the roof of his house? No. The force of attraction between the man and the center of the Earth (his weight) when he is standing on the ground is more than when he is standing on the roof of his house. The fact that gravity is inversely proportional to the square of the distance between objects is the key here. When the man is standing on the ground, the distance between him and the center of the Earth is less than when he is standing on the roof of his house. His mass and the Earth’s mass are the same whether he is on his roof or not. Because he is farther from the center of the Earth when he is on his roof, the force between him and the center of the Earth is less than when he is on the ground. This difference in force is very slight because the difference in distance is very slight, but it does exist.
Which one of the following equations correctly describes the mathematical nature of the law of universal gravitation?
The correct answer is C. Gravitational force is best described as the product of the masses of the objects divided by their distance squared.
Momentum is the characteristic of a moving object that makes it difficult to stop. Consider a bicycle going 1 km/hr and a train going 1 km/hr. The train has the most momentum and is much harder to stop because it has so much more mass than a bicycle. Consider an automobile going 1 km/hr and an automobile going 100 km/hr. The faster automobile has more momentum and is much harder to stop because it has a higher velocity. So, momentum has something to do with both mass and velocity. The momentum of an object is defined as the product of the mass and velocity of the object, or:
p = m ⋅ v
What is the momentum of a 50 kg object traveling at 25 m/s?
The correct answer is A. The answer is obtained by multiplying the mass of the object by its velocity. Choice B is dividing mass by velocity. Choice C is dividing velocity by mass. Choice D is adding mass and velocity.
Momentum and Newton’s third law of motion lead us to another fundamental law of nature, the Conservation of Momentum. The Law of Conservation of Momentum states that in the absence of external forces, the momentum of a system is conserved—it never changes. Obviously, there is an intimate relationship between inertia and momentum.
The momentum of a system never changes unless it is acted on by outside forces. A system will always have the same momentum before an interaction as it does after the interaction.
If a 2,000 kg automobile moving at 50 m/s collides with another 2,000 kg automobile at rest and they get stuck together from the impact. Immediately after the collision (and ignoring the effects of friction), how fast will the two automobiles be traveling?
The correct answer is B. Multiplying the masses and the velocities before the collision and setting them equal to the product of the masses and velocities after the collision and then solving this equation for the speed of the two automobiles together gives 25 M/s. Choice A is incorrect since the momentum before the collision was not zero.
The scientific definition of work is the product of the force applied to an object multiplied by the distance the object moved under the influence of the force.
In equation form: Work = Force · Distance or
If a 70 N force is applied to an object and raises it 2.0 m vertically, what amount of work was performed on the object?
The correct answer is D. The work performed is equal to the force multiplied by the distance.
Energy is an inherent quality of every system in our Universe—it is all around us. In physics, we describe energy as the amount of work needed to change the state of a system. This could mean changing a substance from a solid to a liquid, changing the volume of a substance, or the total pressure of a system. Although energy is easily transferred from one form to another, it is never lost.
There are two fundamental types of energy, potential and kinetic. When you carried the boxes up the stairs, the work you performed gave the boxes the ability to do their own work. You exerted kinetic energy and gave the boxes potential energy. If you dropped the boxes from where you carried them, they would fall, gain speed, and do work of their own; they would transfer potential energy into kinetic energy.
The Law of Conservation of Energy states that energy cannot be created or destroyed in a closed system. It can be transformed from one form into another, but the total amount of energy is always the same.
If you lift up the 50 kg box, you do work and give it potential energy by virtue of its position relative to the gravitational force of the Earth. If you drop it, the potential energy is converted into kinetic energy, and when the box hits the ground, the kinetic energy is transferred to the ground. But where did the kinetic energy of the box go? The crumpled box just sits there on the ground. It has no ability to do work and it is not moving. Where did the energy go? The energy did not disappear. The energy went into crumpling the box, changing the state of physical materials by breaking literally billions of molecular bonds, and to literally warming up the ground, albeit just a little. All energy is conserved.
Simple machines help us perform work by distributing the components of work into smaller parcels. A combination of simile machines may let you do work in a more efficient manner and in less time. Using a machine requires the same amount of work as not using the machine, but the machine changes the way in which you perform the work. Using a machine makes your work easier by changing one or more of the following factors:
If you use a machine to exert less force, for example, it will increase the distance involved in your work.
If you need to move a 50 kg box up to a high shelf, it is much easier to push it up a ramp than to lift it straight up. If the length of the ramp was twice the distance up to the shelf, you would only have to exert half the force of lifting the box but you would have to push it up the ramp for twice as long as you would spend lifting it. Using a machine makes your work easier but it does not reduce the amount of your work.
You can also use a machine to apply a greater force than you could do by yourself, but you will have to exert a force over a longer distance. When you use a hammer to pry a nail out of a piece of wood, for example, your hand moves a much greater distance than the nail moves when it comes out. But you can actually generate a much greater force over a very short distance by applying less force over a greater distance.
All forces in nature can be classified into four basic types, each with a different relative strength. They are (listed in order of weakest to strongest):
Gravity is one of the two forces that dominate our everyday lives and is probably the most common and recognizable force. Electromagnetism is the other dominant force in our everyday lives. The electromagnetic force acts between all particles that have electric charge. It is attractive for oppositely charged particles, and repulsive for particles of the same charge. The electromagnetic force is the ‘glue’ that holds atoms, molecules, and chemical compounds together. The electromagnetic force is generally responsible for all forces involved when atoms interact. The weak nuclear force is most commonly seen in the beta decay of radioactive particles and named because it is relatively weak (109 times less than that of the strong nuclear force) and limited to distances smaller than an atomic nucleus. The strong nuclear force is the strongest of all forces and it is the ‘glue’ that holds the protons and neutrons together in the nucleus of an atom. Although two protons (both being positively charged) repel each other via the electromagnetic force, the strong nuclear force overcomes the repulsive force within an atom and holds the nucleus together. Even though it operates at very short distances (within the nucleus of an atom), it is incredibly strong relative to the other fundamental forces.
Most of the information we receive gets to us in the form of a wave, such as sound waves, light waves, and radio waves. Most waves travel through something and the material through which a wave travels is called a medium. Waves that require a medium to travel through are called mechanical waves. A wave is a disturbance that transfers energy from one place to another without changing the medium through which it travels. However, not all waves require a medium. Light waves travel from the sun through the vacuum of space to the Earth. Waves that do not require a medium to travel through are called electromagnetic waves. The basic properties of waves are wavelength, frequency, amplitude and speed.
Speed = Frequency · Wavelength
Assuming the medium does not change, the speed of a wave is constant. For example, sound waves in air (of the same temperature and pressure) all travel at the same speed. If the speed of a wave is constant and the frequency increases, the wavelength decreases by the same proportion.
What is the speed of a water wave on a lake that has a wavelength of 0.5 m and frequency 2 hertz?
The correct answer is C. The speed of the wave = the product of 0.5 m and 2 hertz = 1 m/s.
Have you ever driven slightly off the edge of a road in your car and noticed that as soon as your wheels hit the dirt or grass just off the pavement, your car suddenly wanted to turn, rather than continuing in a straight line? This happens because the first wheel to hit the soft shoulder of the road slows down while the other wheels stay the same speed. This change in speed between two different wheels causes a change in direction. Just like this example, when the speed of a wave changes while passing from one medium into another, the direction of the wave changes. This is called refraction.
When light strikes a mirror, the light reflects off the surface. The angles of the incoming light and the reflected light are always
The correct answer is A. The law of reflection states that the angle of incidence equals the angle of reflection. Although it is possible for the angles to add up to 90 degrees, it is not always the case. Under normal circumstances, it would be impossible for the angles to add up to 180 degrees.
The Law of Refraction states that when a wave enters a new medium at an angle other than perpendicular, one side of the wave changes speed before the other side, causing the wave to change direction (or bend relative to a stationary object).
Another interesting characteristic of waves is that they can change their frequency depending on the motion of the wave source. You know this automatically but may not realize why yet. As you read this, try making the sound you might hear of a race car zooming by you. Did you notice that you changed the frequency of the sound as the car approached you and zoomed away from you? You decreased the frequency from a high pitch whine to a low pitch rumble. The motion of the sound source (the race car) causes this phenomenon. This change in frequency due to the motion of the wave source is called the Doppler Effect. Imagine that the sound waves emanating from the race car are much like the ripples in water from a pebble dropped in it. As the car approached the listener, the distance between repeating parts of each wave (wavelength) were compressed, causing more of them to get squished into in a certain time. This caused an actual increase in the frequency of the sound. As the car went away from you, the distance between repeating parts of each wave (wavelength) was stretched out, causing fewer of them to occur in a certain time. This caused an apparent lowering of the frequency of sound.
Perhaps more interesting is that the frequency of the sound does not really change—to the observer it appears to change, but it does not actually change at the source. This is because the frequency of the sound heard literally depends on who is listening. Any one who hears the race car will hear a higher frequency sound as the car approaches and a lower frequency when the car is moving away. Yet the race car driver hears a constant frequency sound. This happens for light as well.
According to the Doppler Shift, what happens to starlight seen on the Earth that has arrived from a star that is moving away from the Earth?
The correct answer is C. A Doppler Shift in starlight arriving at the Earth is the increase in wavelength of an individual color within a star’s light. The star’s motion away from the Earth causes the wavelengths of its light to increase over what it would be if the star were not moving away from the Earth. The increase in wavelength can be used to accurately measure the speed that the star is moving away from the Earth and how far away the star is from the Earth. This information combined with the known speed of light through space is used to calculate the time the star has been moving away from the Earth (its age).
Electromagnetic radiation is wave energy with both electric and magnetic aspects. The spectrum of possible types of electromagnetic radiation is quite broad and includes all of the ways in which humans communicate. There are radio, microwave, infrared, visible light, ultraviolet, X-ray, and gamma rays, listed in order of increasing frequency. These electromagnetic waves are all around us all the time but the only wavelengths our eyes sense is what we are most familiar with: visible light. Only a very small part of the electromagnetic spectrum is visible light.
Radio waves and microwaves are used for the broadcasting of information and entertainment through the air. Microwaves are also used to cook food and propagate cellular telephone transmissions. Infrared waves are otherwise known as heat—for example, the heat from the sun or a flame. Infrared waves are just below the visible light part of the spectrum and although you can feel infrared waves, you cannot see them. Common uses are heat lamps and infrared cameras that can detect heat. Continuing down the spectrum, visible light ranges in both wavelength and frequency. The lower frequency visible light is reddish and then the color changes to orange, yellow, green, blue, and violet as its frequency increases. When white light (all colors mixed together) enters a raindrop, refraction occurs and the different frequencies (colors) in the white light change speeds and bend at different angles while passing through the rain drop causing a rainbow.
Ultraviolet waves have high enough frequencies (and energy) to be hazardous. In small quantities, they are used in the human body to produce vitamins and increase the amount of epidermal melanin, but excessive exposure causes sunburn, eye damage, and changes in tissues and organs (up to and including cancer). X-rays have still higher energy—enough to penetrate soft tissue (but not bone), allowing doctors to see inside a body and diagnose and treat many health problems. X-rays, however, are more dangerous than ultraviolet waves and thus must be used sparingly—which is why you probably get dental X-rays only once a year and wear that heavy lead apron to prevent the rays from entering and damaging your body during the dental X-ray. X-rays are also used in industrial engineering applications such as examining the interior of a concrete and steel structure to see if they are any cracks in the steel supports within the concrete.
Then we get to the potentially dangerous waves, gamma rays that have the shortest wavelengths and highest frequencies (and energy). Because they are the highest energy waves, they have the highest penetrating power on the electromagnetic spectrum. Nuclear radioactivity is primarily the effect of gamma rays, the most powerful of the electromagnetic waves. Because of the penetrating nature and the tissue damage that comes along with it, gamma rays are used to kill cancer cells within a human body. They must be carefully focused to avoid damage to nearby healthy tissue.
As the wavelength of electromagnetic waves decreases, what happens to the frequency and the energy?
The correct answer is A. As the wavelength of electromagnetic waves decreases, the frequency increases because of the law stating that speed = wavelength · frequency. The speed of an electromagnetic wave is a constant (under most conditions) and therefore the wavelength and frequency are inversely proportional to each other. Also, as frequency increases, energy increases. Choice B is incorrect because the frequency does not decrease and the energy does not decrease; choice C is incorrect because the frequency does not decrease; choice D is incorrect because the energy does not decrease.
Have you ever pulled a blanket out of your clothes dryer and found a sock stuck to it? The force of electric charges is what is holding them together. We previously reviewed that parts of atoms called protons and electrons have opposite charges; protons have positive charges and electrons have negative charges.
When two protons come close together, they push each other apart. The same is true for two electrons. However, if an electron and a proton come close together, they attract each other. This is because they have different charges and, in nature, opposite electric charges attract each other. They do so with an electromotive force similar to mechanical forces. Every electric charge has an electric field extending around it that is an invisible region where the object’s electric force is exerted on other charged objects, without the two objects coming into contact. When a charged object is placed within the electric field of another charged object, it is either attracted or repelled depending on the type of charge. The strength of an electric field depends on the distance from the object. The greater the distance from the charged object, the weaker the electric field becomes.
Most objects have no overall or net electric charge, meaning they are neutral, neither positive nor negative. Therefore, there are no electric fields around neutral objects. However, some objects can become charged. While protons are tightly bound in an atom’s nucleus, the outer electrons can sometimes easily move away from their nuclei. An object becomes charged when it loses or gains electrons—negative if it gained electrons or positive if it lost electrons. Such charges do not move or flow—they are static. The accumulation of this kind of charge on an object is called static electricity.
Static electricity on an object does not stay there forever, it discharges. Electrons like to move from charged objects in such a way as to remove the charge on the objects (make them neutral again). When two oppositely charged objects come into close proximity or contact, they discharge in the form of a spark of electricity. You have probably felt the effects of this yourself. Lightning is a dramatic example of static discharge. During thunderstorms, air and water droplets swirl violently and water droplets become charged. To restore their neutral condition, electrons move from an area of excess negative charge to an area of excess positive charge, and produce an intense spark as lightning. Some lightning reaches the ground because negative charges at the bottom of storm clouds may give the ground a positive charge. Electrons will jump from the clouds to the Earth’s surface producing a giant spark.