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Newton’s laws of motion, three statements describing the relations between the forces acting on a body and the motion of that body, became the foundation of classical mechanics. Newton's First Law Sometimes called the law of inertia, the first law states: If a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by an external force. We say it has 'inertia'. Friction is a force. This means that in an environment where there is little or no friction, such as in space where there is no air resistance, and far from any gravity sources so that gravity forces are negligible, an object given a push will continue to move forever! It also means that to send a spacecraft somewhere, you only have to fire the engine once and it will continue to move even though the engine has been turned off. This law of inertia was first formulated by Galileo for horizontal motion on Earth and was later generalized by Descartes. The law was not intuitively obvious to the naked eye. In ordinary experience, objects that are not being pushed tend to come to rest. The law of inertia was deduced by Galileo from his experiments with balls rolling down inclined planes; he was able to see that frictional forces were disguising the true nature of the movement. Newton was able to sort it all out and state the result in an unequivocal manner. Evidence of this law for moving objects is all around us. Imagine you're in a bus moving down the road at constant speed, and you're facing forward. If the seat is slippery (very little friction) there is no force there to stop you if the bus driver slams on the brakes. You will continue to move forwards and slide off the seat because no force was applied to stop you.  This is also why seatbelts and airbags are important in a car. Moving down the road at 50 km/h, you hit a post and crash to a stop. Without the force of seatbelt or airbag to hold you back, you will continue moving forward at 50 km/h until stopped by the windshield, where you die. "A body at rest or moving at a constant speed in a straight line will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by an external force". Newton's Second Law Newton’s second law describes quantitatively the changes that a force can produce on the motion of a body. The law says that the acceleration of an object depends on the mass of the object and the amount of force applied. Symbolically: a = F/m The bigger the force applied, the larger the acceleration will be. Conversely, the bigger the mass, the smaller the resultant acceleration. We are familiar with this mathematical relationship in its rearranged form: F = m·a A force applied to a body can change the magnitude of the acceleration, or its direction, or both. Acceleration and force are both vector quantities. The relation is only good for objects that have a constant mass. Newton’s second law is one of the most important in all of physics. If a body has a net force acting on it, it is accelerated in accordance with this equation. Conversely, if a body is not accelerated, there is no net force acting on it. This means that if a mass is moving at constant velocity in a straight line, there is no net force acting on it. However, an object can move at a constant speed in a curve (such as an elliptical orbit), and because it is continually changing direction, there must be a net force to hold it in orbit - gravity. An interesting fact is that Newton himself did not explicitly write formulae for his laws, but expressed them in words. The formula F= m·a did not even begin to be used until the 18th century, long after Newton's death, but it is implicit in his laws. Newton's Third Law This third law is the one that is most misunderstood. It says that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. Every force has an equal but opposite reaction. For example, when a plane flies, the air is pushed downward by the wing's curvature, and in reaction, the wing is pushed upward. Another example: the motion of a jet engine produces thrust, with hot exhaust gases flowing out the back of the engine. A reaction force is produced in the opposite direction, which propels the aircraft forwards. Consider a rocket in the near-vacuum of space. People used to claim that rockets wouldn't work in space because there was nothing for the exhaust gases to 'push agaist'. But that isn't necessary; it's the reactive force backwards on the rocket as the gases leave that causes it to move forwards. You can simulate this by holding a pile of bricks while on skates. Throwing a brick backwards will cause you to move forwards, because of the reactive force on your body as the brick leaves your hand. Relating this to Newton's second law, we can compare accelerations. The force F with which you throw the small brick will cause it to accelerate. But the same force F acting backwards on your body will cause you to accelerate forwards, but by a smaller amount because your body is so much more massive. For the same force (Law 3) a small mass will experience a large acceleration, but a large mass will experience a small acceleration (Law 2). A common problem students have when using this law is to answer questions like this: "A horse is pulling a wagon forwards. Newton's third law says that there is an equal and opposite force backwards. Won't these forces cancel each other? If so, why does the wagon move?" The answer is that the equal and opposite forces (Law 3) are acting on different things. Only one force acts on the wagon. The horse pulling, a force acting on the wagon, causes it to move forwards. The equal and opposite force is acting backwards on the horse, which means he will have to work harder to overcome it and keep moving. A Summary of Newton's Three Laws of Motion
Astronomers have put Newton's formulas and others to use in an amazing way. Find out how to calculate the mass of any celestial body that has a satellite. |