Newtonian Mechanics
Newtonian mechanics encompasses the study of motion and the forces that change motion. Because of the understanding of Newton's laws of motion developed in the 17 th century, scientists have been able to successfully explain and predict many important phenomena including sending astronauts into Earth's orbit and to the Moon. Newton's ideas about motion was based on observation of how the planets moved around the Sun and on the previous work done by Galileo and Kepler. Isaac Newton concluded his study of motion with a set of fundamental principles that describe how all objects move. The relationships he developed describe the motion of a ball rolling down a hill as well as how the stars and planets move in the heavens.
Newton's Laws of Motion
Newton's first law states; a body remains at rest, or moves in a straight line at a constant speed, unless acted upon by a net outside force. By force Newton means a push or pull on an object. An outside force is one that exists from outside the body or object. For example if you try to lift yourself out of a chair by pulling up on your knees you will not move, you will remain at rest in the chair. This is because the force is not outside the body. The second part of Newton first law of motion is the counterintuitive portion and it is very difficult for my students to grasp this concept. To make an object such as a block move across the floor in a straight line at a constant speed you must push on the block and if you stop pushing the block will slow to a stop. While pushing on the object you might think there is a net force, you pushing on the block, but there is a resistive force from friction that resists your push and these two forces cancel each other out and as a result there is NO net force on the object. My students want to believe for an object to move there must be a net force acting on the object, but Newton showed that this is not true. Objects will continue in motion without change with no outside forces acting and to change an object's motion, either speed or direction, there must be a net outside force.
Newton's second law explains how the motion of an object changes when there is a net outside force acting on it. To understand Newton's second law I must first explain the three quantities that describe motion. The first and most basic quantity of motion is the speed which is a measure of how fast an object is moving. The second is velocity which is the speed of an object and the direction that the object is moving. An object can have the same speed but different velocities because of the inclusion of direction. Acceleration is the rate at which the velocity changes. This means that an object can be accelerated if either the speed or the direction changes. Turning or rotating an object results in the object being accelerated even if the speed is constant, due to the change in direction.
Newton's second law states; the acceleration of an object is proportional to the net outside force acting on the object. In other words, the greater the net force or push the greater the acceleration. Newton's second law can be written in an equation form as;
F n e t = ma
where m is the mass or the inertia of the object and a is the acceleration. The inertia is the resistance to a change in motion and is measured as the mass or amount of matter in kilograms. We can use mass and the acceleration due to gravity to determine the weight or the force due to gravity of an object not only on the Earth but any place in the Universe. Newton referred to inertia as the innate force of matter. One can pull a table cloth out from under the dishes because of the inertia of the dishes. Prior to Newton, Aristotle (and others) had believed that the natural tendency of object was to come to a stop. Many of my students also believe this because this is what they observe. Galileo was the first to recognize that motion is the natural state of matter. What my students fail to realize about the implication of Newton's law of inertia is that it takes as much energy to bring something to a stop as it does to get it going. Space probes visiting distant planets not only have to carry enough fuel to get them there but must bring along enough energy to slow to a stop for a soft landing. In the absence of friction, objects keep right on going until something stops them or turn them around. This natural stubbornness to stay in motion is what Newton called inertia. (Cole, 1999)
Newton's third law of motion describes action and reaction of multiple objects. It states; wherever one body exerts a force on a second body, the second body exerts an equal in magnitude and opposite in direction force on the first body. For example, a book resting on the desk exerts a force equal to its weight because the book is pressing down on the desk. Newton's third law tells us that the desk must push up on the book with an equal amount of force. If the desk did not push up on the book, the book would accelerate to the floor due to the weight (force due to gravity).
Newton realized that the Sun is exerting a force on the Earth to keep it in orbit and the Earth is exerting an equal and opposite force on the Sun. However the Earth is much less massive than the Sun. Therefore, even though the Sun's force on the Earth is the same as the Earth's pull on the Sun, the Earth has a much greater acceleration due to the Earth's much smaller mass. The greater acceleration of the Earth is why the revolution of the Earth around the Sun is more pronounced and the Sun accelerates to the Earth but because of its mass the acceleration is very small. Newton's Laws of motion reveal the reasoning for our heliocentric solar system. (Cole, 1999)
Newton's Gravitational Law
Newton observed the force that keeps a planet in orbit around the Sun as a pulling force that always acts towards the center of the Sun. Newton described that pull as gravity or the gravitational force. Newton's discovery of the force that acts on the planets led him to suspect the force of gravity as the reason for an apple falling toward the ground and these two forces are fundamentally the same as the force on the planets. Newton used his own third law and Kepler's laws of planetary motion to formulate a mathematical model that describes the nature of the gravitational force. The model that Newton described is called Newton's Law of Universal Gravitation and is as follows. Two bodies attract each other with a force that is directly proportional to the product of the mass of each body and inversely proportional to the square of the distance between them. In fact there is a gravitational attraction between any and all bodies or objects. In the equation form Newton's Gravitational Law states:
F g = Gm 1m 2 / r 2
Where G is the Universal Gravitational constant and experimentally determined to equal 6.67 x 10 - 1 1Nm 2/kg 2, m 1 is the mass of one object and m 2 is the mass of the other object and r is the radial distance between the objects.
Using Newton's laws of motion and the Universal Gravitational Law my students will have the ability to determine the speed needed for stable satellite orbits, and the escape speeds to leave the Earth's gravitational pull as part of the application to space science. The curriculum unit will include problem set that require student to complete these calculation for various Earth, Moon and Mars orbits.
Momentum and Energy
Momentum is defined as the product of the mass and the velocity of an object and applying Newton's first law, the momentum of an object remains constant unless acted upon by an outside force. The conservation of momentum states that the total momentum of a system does not change unless it is acted upon by an outside force. When the water in a pressurized bottle representing a rocket exits the bottle, the momentum of the water, it's mass times its' velocity, is equal to the momentum of the bottle rising above the Earth's surface. The conservation of momentum is the same concept used to launch any object into space. The greater the mass of the rocket the smaller the speed or the more momentum needed to fuel the rocket.
The conservation of mechanical energy states that the total energy of a system is a constant. As applied to the rocket, the sum of the kinetic energy and potential energy of the rocket is a constant in the absence of air resistance. Kinetic energy is the energy of an object due to motion. In other words, if an object is moving it has Kinetic energy. The equation for Kinetic energy, KE, is
KE = 1/2*mv 2
Where m is the mass and v is the velocity of the object. The gravitational potential energy, PE g, of an object is;
Pe g = mgh
Where m is the mass, g is the acceleration due to gravity and h is the height above a reference point such as the Earth's surface. In both these relationships the energy is directly proportional to the mass, the greater the mass the greater the energy. As applied to rocket science the heavier the rocket the greater the energy needed to launch it, but to get that energy more fuel is need which increases the mass and therefore requires even more energy.
The students will complete their study of mechanics with the design cycle inquiry lab. Students will be required to apply their knowledge of the conservation of momentum and energy to construct a water and air-pressure rocket. They will have to design their rockets to reduce air friction upon leaving the Earth's surface to reach the maximum possible altitude. In addition they will have to design their rocket to increase air-friction on the return flight to the Earth because they will be required to take a payload of a raw egg safely back to Earth.
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