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Transcript
Chapter 4 Forces and Newton's Laws of Motion Definition of Force That which changes the velocity or direction of an object. Direct (contact) Those forces which need to physically touch the object to change its velocity or direction. Examples are friction, tension in a rope, motion caused by a spring, etc. Noncontact Two types: Those forces which do not have a visible hold on the object. Examples are gravity, electric field, etc. More Definitions... Forces are Vectors you label a force as you would a vector and need both a magnitude and direction to fully describe them. Mass A scalar quantity which describes how much of the object you have. For instance, a car has more mass than a bicycle. Isaac Newton Born 1643 in Lincolnshire England Entered Cambridge University to study law but was attracted to the teachings of Galileo and Kepler. Eventually he produced the three laws we are about to learn. Newton's First Law An object at rest stays at rest unless acted upon by an outside net force. An object in motion stays in motion unless acted upon an outside net force. Net force is the vector sum of all forces acting on an object! Friction Air Resistance Engine 30 m/s 30 m/s Engine = Friction + Air Resistance Inertia vs. Mass Inertia is the reason an object at rest stays at rest or an object moving in a straight line continues to move with the same velocity along that line unless an external force causes it to do otherwise. If you have two objects with different masses, the one with more mass is said to have more inertia (a greater tendency to not change its current speed or direction). This then leads us to intepret the measure of inertia as the object's mass. Both inertia and mass are measured in SI units of kgs. Everyday Use of Inertia The pedulum is a heavy weight and is attached to the car but is free to swing back and forth. When the car rapidly slows down, the pendulum's inertia (tendency to not change it's speed) causes it to continue forward even though the car is slowing. This causes the locking bar to stop the rotation of the ratchet wheel and prevents the seatbelt from being extended thus holding the passenger close to the seat. A frame is the way you choose to view the problem. Example: You are given a problem of a boat accelerating in some direction on a lake. You could choose many different frames. Inertial vs. Non-Inertial Frames You could choose to view the water as the stationary object and see the boat accelerating in some direction. This frame includes the water, the boat, and anything in the boat. This is an inertial frame since it is not accelerating, only objects within it accelerate! You could also choose to move along with the boat as it accelerates. Now, the boat appears to be stationary and all motion is relative to the boat. The frame includes only the boat and anything in the boat. This is a non-inertial frame since the frame itself is accelerating! Newton's First Law and Non-Inertial Frames Newton's First Law (Law of Inertia) only applies in inertial frames. Good example from the book: A passenger is riding in a car which begins to accelerate. There are two frames of reference one can easily identify. You could reference all motion to the ground below the car. The first law would apply here since the ground is not accelerating! You could reference all motion to the accelerating car. The first law would not apply here since the car is accelerating. Newton's Second Law of Motion Simply stated: F = ma (only one force acting on the object = ma) F = ma SI unit for force is the Newton (I wonder why?) definition: 1N = 1 kg m/s2 (sum of all forces acting on an object = ma) Newton's Second Law You may (and should) consider forces in the xdirection to be completely separate from forces in the y-direction. The 2nd law states: As long as a force is acting on the object, there must be an acceleration (the equality demands this). This means the velocity must be changing as time changes. Remember, a change in velocity does not only mean a change in speed. It could also mean a change in direction. Free Body Diagrams Engine Friction y Friction Engine x These allow one to draw all the forces in one place and helps simplify the problem. If any force does not lie on either the x or y axis, it needs to be broken into its components. y Friction Engine x Comments on the Previous FBD Fx = max ; Fy = may There is no acceleration in the y direction since there are no forces in this direction (either positive nor negative). Since the force due to the engine is larger than the frictional force, the car will accelerate in the +x direction. Simply states: Newton's Third Law If one object pushes on another object, the object being pushed, pushes back with an equal but opposite force. The two objects do not usually have the same mass, so the less massive object will have a larger acceleration. Forces on the First Person on One Side of a Tug-of-War Friction force Normal force Tension from the other team Gravitational force Tension from your team Normal force = Gravitational Force (y direction) The war starts with everyone stationary, therefore, vox = 0. After the war starts, if the person does not start to move (∆vx = 0) then there is no acceleration in the x direction and the 2nd law tells us there is not a net force in the x direction. This means the tension(+) = tension(-) + friction force. Newton's Law of Gravitation Magnitude: F G m1 m 2 r 2 Direction: The line joining the two masses. Moon: m2 +F Earth: m1 -F r 7.35 1022 kg Mass of the Earth: 5.98 1024 kg Mass of the Moon: 6.67 10-11 N m2 / kg2 r: 3.85 108 m F: 1.98 1020 N G: Does the rotation of the moon about the earth affect the position of the earth in space? amoon = 1.98 1020 N / 7.35 1022 kg = 2.69 10-3 m/s2 # " aearth = 1.98 1020 N / 5.98 1024 kg = 3.31 10-5 m/s2 ! Newton's Law of Gravitation (2) No, mass is universal. I have the same mass whether I am on the earth, the moon, or simply floating in space. Mass is the measure of how much of something you have. Weight is a quantity which depends upon where you are and the force of acceleration there. Example: my mass is 80 kg my weight on earth is then 784 N my weight on the moon is 130 N ) ( * + ' % Isn't mass and weight the same thing? & $ Mass vs. Weight This is the force provided by one object to support another object. Example: A book rests on a table and has a weight of 18 N (1.8 kg. 9.8 m/s2). Newton's third law says the table must push back with an equal and opposite force since the book is not accelerating up or down. This force provided by the table is known as the normal force. / . - , Normal Force The word "normal" is a mathematical term which is defined as the vector perpendicular to the surface one is describing. Examples of a Normal Force N mg N mg