Chapter 4 Newton's First Law of Motion - Inertia

Transcription

1 1 Academic Physics Mechanics Chapter 4 Newton's First Law of Motion - Inertia The Mechanical Universe Inertia (Episode 4)

2 4.1: Aristotle on the Causes of Motion The idea that a force causes motion goes back to the fourth century B.C., when the Greeks were developing some of the ideas of science. Aristotle, the foremost Greek scientist, studied motion and divided it into two types: natural motion and violent motion. Natural motion on Earth was thought to be either straight up (puff of smoke) or straight down (falling rocks). Objects seek their natural resting places high in the sky or on the ground. 2

3 4.1: Aristotle on the Causes of Motion Natural motion in the heavens was circular, for Aristotle saw both circular motion and the heavens as without beginning or end, so the planets and stars moved in perfect circles around the Earth. 3 Violent motion was imposed motion. It was the result of an object being pushed or pulled. Carts moved because they were pulled by a horse, ships were pushed by the wind, etc. The important thing about violent motion is that it had an external cause.

4 4.1: Consequences of Aristotle's Views 4 Objects in their natural resting places could not move by themselves; they had to be pushed or pulled by some external cause. Objects not in their natural resting place would naturally move to their natural resting place with no external cause. If an object was moving against its nature, then a force of some kind was responsible.

5 4.1: Consequences of Aristotle's Views 5 Obviously, the Earth must be in its natural resting place as we can't feel it move up or down and a force large enough to move it is unthinkable, it is clear that the Earth does not move. Since objects in the heavens do move in natural circular motion, while the Earth does not, it is clear that the Earth is the center of creation.

6 4.2: Copernicus and the Moving Earth 6 The motion of planets was observed to go backwards at times (this is called retrograde motion) but the first-century astronomer, cartographer, and astrologer Ptolemy devised a system of crystal spheres which accurately accounted for this motion. Nicolaus Copernicus formulated his theory of the moving Earth. Copernicus reasoned that the simplest way to interpret astronomical observations was to assume the Earth and other planets move around the Sun.

7 4.2: Copernicus and the Moving Earth This idea as extremely controversial at the time. People preferred to believe that the Earth was the center of the universe. Copernicus worked on his ideas in secret to escape persecution. In the last days of his life, and at the urging of close friends, he sent his ideas to the printer. The first copy of his work, De Revolutionibus, reached him on the day of his death, May 24, It should be noted that Ptolemy's model matched observations of the planets' positions better than Copernicus' model. 7

8 4.3: Galileo 8 Galileo Galelei, the foremost scientist of late-renaissance Italy, was outspoken in his support of Copernicus. As a result he suffered a trial and house arrest. While under house arrest at his villa near Florence, he continued earlier work with the motion of objects on the Earth, and for this is often called the Father of Modern Physics.

9 4.3: Galileo on Motion 9 One of Galileo's great contributions to physics was demolishing the notion that a force is necessary to keep an object moving. Friction is the name given to the force that acts between materials that touch as they move past each other. Friction is caused by irregularities in the surfaces of objects that are touching. Galileo realized that if no friction was present, a moving object would need no force to keep moving. He tested his ideas by rolling balls along tilted smooth plane surfaces. Video

10 4.3: Inertia 10 Galileo stated that the tendency of a moving object to keep moving is natural and that every material object resists change to its state of motion. We call this property of a body to resist change inertia.

11 4.4: Newton's Law of Inertia 11 On Christmas day in the year Galileo died, Isaac Newton was born. By age 24, he had developed his famous laws of motion, which quickly replaced the Aristotelian ideas that dominated the thinking of the best minds for most of the previous 2000 years. Newton's First Law of Motion, usually called the Law of Inertia, is a restatement of Galileo's idea: Every object continues in a state of rest, or of motion in a straight line at constant speed, unless it is compelled to change that state by forces exerted upon it.

12 4.4: Comparison 12 Where the ancients thought continual forces were required to maintain motion, we now know that objects continue to move by themselves. Forces are needed to overcome friction that may be present and to set objects in motion initially. Once the object is moving in a force-free environment, it will move in a straight line indefinitely.

13 4.4: Inertia in Practice 13 Mythbusters: Motorcycle Tablecloth Pull

14 4.5: Mass What will happen if you kick a can that is empty, one that is full of sand, and one that is full of metal? The different reactions of the can (and your foot) happen because the empty can has very little inertia and the metal-filled can has a large inertia. Mass is a measure of how much inertia an object has. It is a measure of the laziness than an object exhibits in response to any effort to change its motion. It is related to the amount of matter in the object. The S.I. unit of mass is the kilogram The B.E. unit of mass is the slug (pounds measure weight) 14

15 4.5: What Mass is NOT Mass is NOT volume. 15 Volume is the amount of space occupied by the object. Mass is NOT weight. Weight is the force of gravity on the object. One kilogram of mass weighs 9.8 newtons Weight = mass acceleration due to gravity

16 4.5: Understanding Mass 16 Does a 2-kg brick have twice as much inertia as a 1-kg brick? Twice as much mass? Twice as much volume? Twice as much weight? Does a 2-kg bunch of bananas have twice as much inertia as a 1-kg loaf of bread? Twice as much mass? Twice as much volume? Twice as much weight?

17 4.6: What is a Force? A force is a push or pull that acts on an object. 17 Forces can cause objects to change their motion. The S.I. unit of force is the newton, N, which is the forced needed to accelerate a 1-kg object at a rate of 1 m/s 2. The newton is named after Sir Isaac Newton, who explained how force, mass, and acceleration are related. The B.E. unit of force is the pound, lb.

18 4.6: What is a Force? Forces are vectors, so the direction of the push or pull needs to be specified along with how strong the push or pull is. Forces are commonly represented by arrows pointing in the direction of the push or pull, with a length proportional to their strength. 18

19 4.6: Combining Forces 19 Since forces are vectors, we add forces using vector addition. Addition or subtraction if the forces are collinear Pythagorean Theorem and tan -1 if the forces are perpendicular. Vector components if the forces are neither collinear nor perpendicular.

20 4.6: Net Force and Balanced Forces 20 The net force, ΣF, is the result of adding several forces together vectorially. When the forces in an object are balanced, or in equilibrium, the net force is zero and there is no change to the object's motion. When the forces in an object are unbalanced, the net force is not zero, and the object accelerates. Unbalanced forces cause accelerations.

21 4.7: Equilibrium & Support Force What forces act on your book when it is sitting on the table? Its not just its weight (the pull of the Earth's gravity). If it were, then the book would be in free fall. The book is at rest, so the other force acting on it must exactly balance the books' weight in order to produce a net force of zero. This other force is a support force called the normal force ( normal as its used in math, meaning perpendicular to the surface). 21

22 4.7: The Support Force The support force is generated by the atoms in the table acting as tiny springs pushing up on the book. In fact, when you step on a bathroom scale, the downward force supplied by your feet and the upward force supplied by the floor compress a calibrated spring. The compression of the spring gives your weight. However, in reality, it is measuring the floor's support force. 22

23 4.7: Equilibrium & Tension Force What forces act on you when you hang from a rope? Again, its not just your weight (the pull of the Earth's gravity). If it were, then you would be in free fall. Instead, you are hanging at rest, so there is another force acting on you that must exactly balance your weight in order to produce a net force of zero. This other force is a support force, but the atoms in the rope are not being compressed, they are being stretched. This support force is called tension. 23

24 4.7: Equilibrium & Tension Force A spring scale can also be used to measure tension. When you weigh a bag of fruit or vegetables by suspending it on a spring, the scale tells us the weight. In reality, the scale is reading the upward support force provided by whatever is holding it. 24 If you were hanging from a trapeze supported by two ropes, the tension in each rope would be half of your weight.

25 4.7: Other Tension Forces The tension in the rope is equal to the force each team pulls with. 25 If one team is replaced with a knot around a tree, then the tension is still equal to the force the team pulls with, which is also equal to the tension the tree pulls back with.

26 4.7: Other Tension Forces If all four people pull against the tree, then the tension is now twice what it was before, as more people pull. Note that the tree is also pulling with more force. Eventually, as you add more people, the tension in the rope exceeds the rope's ability to hold itself together, and the rope breaks at its weakest point. 26

27 4.8: Vector Addition of Forces 27 Lets now consider objects supported by two wires. The weight of the object is supported by the two vertical components of tension. The horizontal components of tension cancel each other.

28 4.8: Hanging from a Line 28 For any pair of scales, ropes, or wires supporting a load, the greater their angle from the vertical, the larger the tension force is in them. This is why a clothesline can support your weight when vertical but can't when horizontal. The resultant of the tension forces must be equal and opposite to the load they are supporting. Is it possible for a wire to strung completely horizontal without any sag?

29 4.9: The Moving Earth Again 29 When Copernicus announced the idea of a moving Earth in the 16 th century, it sparked much debate and argument. One of the arguments against a moving Earth was as follows: Consider a bird sitting at rest in the top of a tall tree. On the ground below is a fat, juicy worm. The bird sees the worm, drops down vertically, and catches it. It was argued that this would not be possible if the Earth moved, because in order to orbit the sun in one year, Earth would have to travel at a speed of km/h or about 30 km/s. Even if the bird could reach the ground in 1 second, the worm would be 30 km away from where the bird was by the time the bird got there. Can you refute this argument? Galileo could.

30 4.9: Inertia and the Moving Earth 30 Four hundred years ago, people had difficulty with the idea of inertia because slow, bumpy rides in horse-drawn carriages over cobblestone or dirt roads don't lend themselves to experiments that reveal inertia. Today, you can take a ride in a high-speed bus or car on a smooth road, toss and object straight up, and have it still land in your hand rather than smack into the back window or the passenger behind you. In fact, to your point of view, the object moves exactly as if you were at rest. Relative Motion Gun

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