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Newton’s Laws – Intro to Dynamics Newton's First Law (Law of Inertia) Let's restate Newton's first law in everyday terms: An object at rest will stay at rest, forever, as long as nothing pushes or pulls on it. An object in motion will stay in motion, traveling in a straight line, forever, until something pushes or pulls on it. The "forever" part is difficult to swallow sometimes. But imagine that you have three ramps set up as shown below. Also imagine that the ramps are infinitely long and infinitely smooth. You let a marble roll down the first ramp, which is set at a slight incline. The marble speeds up on its way down the ramp. Now, you give a gentle push to the marble going uphill on the second ramp. It slows down as it goes up. Finally, you push a marble on a ramp that represents the middle state between the first two -- in other words, a ramp that is perfectly horizontal. In this case, the marble will neither slow down nor speed up. In fact, it should keep rolling. Forever. Which person in this ring will be harder to move? The sumo wrestler or the little boy? According to Newton's first law, the marble on that bottom ramp should just keep going. And going. Physicists use the term inertia to describe this tendency of an object to resist a change in its motion. The Latin root for inertia is the same root for "inert," which means lacking the ability to move. So you can see how scientists came up with the word. What's more amazing is that they came up with the concept. Inertia isn't an immediately apparent physical property, such as length or volume. It is, however, related to an object's mass. To understand how, consider the sumo wrestler and the boy shown above. Let's say the wrestler on the left has a mass of 136 kilograms, and the boy on the right has a mass of 30 kilograms (scientists measure mass in kilograms). Remember the object of sumo wrestling is to move your opponent from his position. Which person in our example would be easier to move? Common sense tells you that the boy would be easier to move, or less resistant to inertia. You experience inertia in a moving car all the time. In fact, seatbelts exist in cars specifically to counteract the effects of inertia. Imagine for a moment that a car at a test track is traveling at a speed of 55 mph. Now imagine that a crash test dummy is inside that car, riding in the front seat. If the car slams into a wall, the dummy flies forward into the dashboard. Why? Because, according to Newton's first law, an object in motion will remain in motion until an outside force acts on it. When the car hits the wall, the dummy keeps moving in a straight line and at a constant speed until the dashboard applies a force. Seatbelts hold dummies (and passengers) down, protecting them from their own inertia. Interestingly, Newton wasn't the first scientist to come up with the law of inertia. That honor goes to Galileo and to René Descartes. In fact, the marble-and-ramp thought experiment described previously is credited to Galileo. Newton owed much to events and people who preceded him. Before we continue with his other two laws, let's review some of the important history that informed them. Newton’s Laws – Intro to Dynamics Newton's Second Law (Law of Motion) You may be surprised to learn that Newton wasn't the genius behind the law of inertia. But Newton himself wrote that he was able to see so far only because he stood on "the shoulders of Giants." And see far he did. Although the law of inertia identified forces as the actions required to stop or start motion, it didn't quantify those forces. Newton's second law supplied the missing link by relating force to acceleration. This is what it said: When a force acts on an object, the object accelerates in the direction of the force. If the mass of an object is held constant, increasing force will increase acceleration. If the force on an object remains constant, increasing mass will decrease acceleration. In other words, force and acceleration are directly proportional, while mass and acceleration are inversely proportional. Technically, Newton equated force to the differential change in momentum per unit time. Momentum is a characteristic of a moving body determined by the product of the body's mass and velocity. To determine the differential change in momentum per unit time, Newton developed a new type of math -- differential calculus. His original equation looked something like this: F = (m)(Δv/Δt) where the delta (Δ) symbols signify change. Because acceleration is defined as the instantaneous change in velocity in an instant of time (Δv/Δt), the equation is often rewritten as: F = ma The equation form of Newton's second law allows us to specify a unit of measurement for force. Because the standard unit of mass is the kilogram (kg) and the standard unit of acceleration is meters per second squared (m/s 2), the unit for force must be a product of the two -- (kg)(m/s2). This is a little awkward, so scientists decided to use a Newton as the official unit of force. One Newton, or N, is equivalent to 1 kilogram-meter per second squared. There are 4.448 N in 1 pound. So what can you do with Newton's second law? As it turns out, F = ma lets you quantify motion of every variety. Let's say, for example, you want to calculate the acceleration of the dog led shown below. Figure 1 Figure 2 Figure 3 If you want to calculate the acceleration, first you need to modify the force equation to get a = F/m. When you plug in the numbers for force (100 N) and mass (50 kg), you find that the acceleration is 2 m/s2. Notice that doubling the force by adding another dog doubles the acceleration. Oppositely, doubling the mass to 100 kg would halve the acceleration to 2 m/s2. If two dogs are on each side, then the total force pulling to the left (200 N) balances the total force pulling to the right (200 N). That means the net force on the sled is zero, so the sled doesn’t move. Newton’s Laws – Intro to Dynamics Now let's say that the mass of the sled stays at 50 kg and that another dog is added to the team. If we assume the second dog pulls with the same force as the first (100 N), the total force would be 200 N and the acceleration would be 4 m/s2. Finally, let's imagine that a second dog team is attached to the sled so that it can pull in the opposite direction. This is important because Newton's second law is concerned with net forces. We could rewrite the law to say: When a net force acts on an object, the object accelerates in the direction of the net force. Now imagine that one of the dogs on the left breaks free and runs away. Suddenly, the force pulling to the right is larger than the force pulling to the left, so the sled accelerates to the right. What's not so obvious in our examples is that the sled is also applying a force on the dogs. In other words, all forces act in pairs. This is Newton's third law…. Speaking of which! Newton's Third Law (Law of Force Pairs) Newton's third law is probably the most familiar. Everyone knows that every action has an equal and opposite reaction, right? Unfortunately, this statement lacks some necessary detail. This is a better way to say it: A force is exerted by one object on another object. In other words, every force involves the interaction of two objects. When one object exerts a force on a second object, the second object also exerts a force on the first object. The two forces are equal in strength and oriented in opposite directions. Many people have trouble visualizing this law because it's not as intuitive. In fact, the best way to discuss the law of force pairs is by presenting examples. Let's start by considering a swimmer facing the wall of a pool. If she places her feet on the wall and pushes hard, what happens? She shoots backward, away from the wall. Figure 1 Figure 2 That's one heck of a force! A baseball player shatters his bat. Clearly, the swimmer is applying a force to the wall, but her motion indicates that a force is being applied to her, too. This force comes from the wall, and it's equal in magnitude and opposite in direction. Next, think about a book lying on a table. What forces are acting on it? One big force is Earth's gravity. In fact, the book's weight is a measurement of Earth's gravitational attraction. So, if we say the book weighs 10 N, what we're really saying is that Earth is applying a force of 10 N on the book. The force is directed straight down, toward the center of the planet. Despite this force, the book remains motionless, which can only mean one thing: There must be another force, equal to 10 N, pushing upward. That force is coming from the table. If you're catching on to Newton's third law, you should have noticed another force pair described in the paragraph above. Earth is applying a force on the book, so the book must be applying a force on Earth. Is that possible? Yes, it is, but the book is so small that it cannot appreciably accelerate something as large as a planet. Newton’s Laws – Intro to Dynamics You see something similar, although on a much smaller scale, when a baseball bat strikes a ball. There's no doubt the bat applies a force to the ball: It accelerates rapidly after being struck. But the ball must also be applying a force to the bat. The mass of the ball, however, is small compared to the mass of the bat, which includes the batter attached to the end of it. Still, if you've ever seen a wooden baseball bat break into pieces as it strikes a ball, then you've seen firsthand evidence of the ball's force. These examples don't show a practical application of Newton's third law. Is there a way to put force pairs to good use? Jet propulsion is one application. Used by animals such as squid and octopi, as well as by certain airplanes and rockets, jet propulsion involves forcing a substance through an opening at high speed. In squid and octopi, the substance is seawater, which is sucked in through the mantle and ejected through a siphon. Because the animal exerts a force on the water jet, the water jet exerts a force on the animal, causing it to move. A similar principle is at work in turbine-equipped jet planes and rockets in space. Speaking of outer space, Newton's other laws apply there, too. By using his laws to analyze the motion of planets in space, Newton was able to come up with a universal law of gravitation. We'll explore this further in the next section The famous (un)true apple story Could a falling apple be related to a revolving planet or moon? Newton believed so. This was his thought process to prove it: 1. An apple falling to the ground must be under the influence of a force, according to his second law. That force is gravity, which causes the apple to accelerate toward Earth’s center. 2. Newton reasoned that the moon might be under the influence of Earth's gravity, as well, but he had to explain why the moon didn't fall into Earth. Unlike the falling apple, it moved parallel to Earth's surface. 3. What if, he wondered, the moon moved about the Earth in the same way as a stone whirled around at the end of a string? If the holder of the string let go -- and therefore stopped applying a force -- the stone would obey the law of inertia and continue traveling in a straight line, like a tangent extending from the circumference of the circle. 4. But if the holder of the string didn't let go, the stone would travel in a circular path, like the face of a clock. In one instant, the stone would be at 12 o'clock. In the next, it would be at 3 o'clock. A force is required to pull the stone inward so it continues its circular path or orbit. The force comes from the holder of the string. 5. Next, Newton reasoned that the moon orbiting Earth was the same as the stone whirling around on its string. Earth behaved as the holder of the string, exerting an inward-directed force on the moon. This force was balanced by the moon's inertia, which tried to keep the moon moving in a straight-line tangent to the circular path. 6. Finally, Newton extended this line of reasoning to any of the planets revolving around the sun. Each planet has inertial motion balanced by a gravitational attraction coming from the center of the sun. It was a stunning insight -- one that eventually led to the universal law of gravitation. According to this law, any two objects in the universe attract each other with a force that depends on two things: the masses of the interacting objects and the distance between them. More massive objects have bigger gravitational attractions. Distance diminishes this attraction. Newton expressed this mathematically in this equation: F = G(m1m2/r2) where F is the force of gravity between masses m1 and m2, G is a universal constant and r is the distance between the centers of both masses. Over the years, scientists in just about every discipline have tested Newton's laws of motion and found them to be amazingly predictive and reliable. But there are two instances where Newtonian physics break down. The first involves objects traveling at or near the speed of light. The second problem comes when Newton's laws are applied to very small objects, such as atoms or subatomic particles that fall in the realm of quantum mechanics.