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Chapter 5 NEWTON's LAWS of MOTION

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Chapter 5 NEWTON's LAWS of MOTION Nerd Bling UNIVERSITY PHYSICS Chapter 5 NEWTON’S LAWS OF MOTION Monday: • Newton’s Three Laws of Motion • FREE BODY DIAGRAMS • Inclined planes Wednesday: • Action-Reaction forces • Pulleys and Ropes Man of the Millennium Sir Issac Newton 1687 Published Principia •Invented Calculus (1642 -1727) •3 Laws of Motion •Universal Law of Gravity What Is a Force? . A force is a push or a pull. A force acts on an object. Pushes and pulls are applied to something. From the object’s perspective, it has a force exerted on it. Contact forces are forces that act on an object by touching it at a point of contact. Long-range forces are forces that act on an object without physical contact. (gravity, electricity,etc) Slide 5-18 Forces are Interactions FFEarth on Rock Rock on Earth Thinking About Force . Every force has an agent which causes the force. Forces exist at the point of contact between the agent and the object (except for the few special cases of long-range forces). Forces exist due to interactions happening now, not due to what happened in the past. Consider a flying arrow. A pushing force was required to accelerate the arrow as it was shot. However, no force is needed to keep the arrow moving forward as it flies. It continues to move because of inertia. Slide 5-75 Galileo Challenged The Dogma Of Aristotle’s Natural Motion (Forces are needed for any motion) The natural motion of a body is to remain in whatever state of motion it is in unless acted upon by net external forces. Newton’s First Law (Law of Inertia) An object will remain at rest or in a constant state of motion unless acted upon by external net forces. Net Force Direction of applied forces matters!!! Opposite forces cancel! Inertia The resistance of an object to change its state of motion. A measure of mass or how much stuff an object has. QuickCheck 5.10 A hollow tube lies flat on a table. A ball is shot through the tube. As the ball emerges from the other end, which path does it follow? Slide 5-76 QuickCheck 5.10 A hollow tube lies flat on a table. C A ball is shot through the tube. As the ball emerges from the other end, which path does it follow? Slide 5-77 Mass & Weight F ma W mg g 9.8 m / s2 (g is a scalar!) Calculate your weight in N. 1 lb = 4.45 N Calculate your mass in Kg. Moon Mass The acceleration due to gravity on the surface of the moon is only 1/6 as it is on the Earth. What is the weight of a 10-kg object on the moon and on the Earth? What is its mass on each? Mass is the same everywhere in the universe! 10 kg! 2 WEE mg 10 kg 9.8 m / s 98 N 11 WM mg m g 98 N 16.3 N EME66 Perception of Weight The perception of weight comes from the support force acting back on you. If you are in free fall you feel weightless. Galileo Challenged Aristotle Physics In a vacuum, all objects fall with the same acceleration due to gravity: 9.80 m/s2, independent of their weight. The Weight to Mass Ratio of ALL objects always equals g! The force of gravity – the weight of an object – is greater for a larger mass, but the larger mass has greater INERTIA and resists a change in motion more so that the ratio of weight to mass is a universal constant. Finding little g Calculate the acceleration of gravity acting on you at the surface of the Earth. What is g? Gmyou M E F myou a F 2 RE GM Source of the Force E Reaction to the Force a 2 RE 6.673x 1011 Nm 2 / kg 2 5.98 x 10 24 kg a 2 6.38xm 106 a 9.81 m/ s2 = g! Rock & Feather A rock and feather fall with the same acceleration due to gravity in a vacuum. Is the force of gravity acting on them the same? Newton’s First Law (Law of Inertia) IF an object remains at rest or in a constant state of motion the net external forces are zero! EQUILIBRIUM!! Newton’s First Law If F 0 => No Change in Motion Dynamic Equilibrium Static Equilibrium Static Equilibrium Forces up equal the forces down. Forces sideways cancel too. Fy 0 Fx 0 Newton’s 2nd Law F ma F a net m The acceleration of object is directly related to the net forces acting on it and inversely proportional to its mass. Newton’s 2nd Law UnitsF ma m kg N s2 Acceleration is in the direction of the net Force but not necessarily in the direction of velocity. F a net m Newton’s 3rd Law FFhand on wall wall on hand To every force there is an equal but opposite reaction force. Newton’s 3 Laws of Motion 1. If F 0 No change in motion 2. Fnet ma Change in motion More on N3 Wednesday 3. FF1 on 2 2 on 1 Force Components F ma Fx ma x F y ma y Newton’s Second Law is a Vector equation that can be broken down into scalar components. Since x and y directions are independent, Newton’s Second Law can be expressed as independent x and y equations. Force Vector Diagrams Align axes to simplify the problem! Show all the External forces acting ON the body only. Force Vector Diagrams Draw free-body diagrams for every object! Solving Force Problems 1. State the knowns and desired unknowns. 2. Draw a force vector diagram, label everything and define direction. 3. Solve for the components of each force. 4. Use Fnet = ma on each direction to generate equations. 5. Derive a solution in terms of the given knowns. 6. Enter the numbers and solve for the desired unknown. Problem Starting from rest, Sally pulls Billy on the sled (total mass = 60kg) with a total force of 100 N at an angle of 40 degrees above the horizontal, as shown. After 5 seconds, how fast is the sled moving and how far has it traveled from where it started? Fxx ma Fcos max F cos a = vf v0 at x m FNcos 100 cos40 v v at t 5 s 6.38 m / s f 0 m60 kg Problem The magnitude of F1 is 75.0N and F2 is 50.0N. Ignore friction. What is the acceleration of the block? The Inclined Plane Orient your axes relative to the plane!!! Why is the angle of the incline here? Prove it. FIGURE 5.22 FIGURE 5.23 Incline Plane Problem Draw a free-body diagram of a block which slides down a frictionless plane having an inclination of = 15.0°. If the block starts from rest at the top and the length of the incline is 2.00 m, find (a) the acceleration of the block and (b) its speed when it reaches the bottom of the incline. Prelab Problem Statics Problem +y Find the tensions in the wires. +x T T1 2 43 55 W Show all the External forces acting ON the body only. Newton’s 3 Laws of Motion 1. If F 0 No change in motion 2. Fnet ma Change in motion More on N3 Wednesday 3. FF1 on 2 2 on 1 At an instant when a 4.0-kg object has an acceleration equal to (5i + 3j) m/s2, one of the two forces acting on the object is known to be (12i + 22j) N. Determine the magnitude of the other force acting on the object. a. 2.0 N b. 13 N c. 18 N d. 1.7 N e. 20 N Newton’s 3rd Law FFhand on wall wall on hand To every force there is an equal but opposite reaction force. Newton’s 3rd Law FFhand on wall wall on hand You can’t TOUCH without being TOUCHED back!! Newton’s 3rd Law FFhand on wall wall on hand To every force there is an equal but opposite reaction force. Newton’s 3rd Law FFhand on wall wall on hand This is an INTERACTIVE Universe. Gravity is an Interaction FFEarth on Rock Rock on Earth Gravity is an Interaction The Earth pulls on you, you pull on the Earth. You fall to the Earth, the Earth Falls to you. You accelerate towards the Earth with g =9.8m/s2. With what acceleration is the Earth falling towards you? FFEarth on You You on Earth This is your weight: mg MEE a mg aE M E (65kg )(9.8 m / s2 ) a1.1 x 1022 m / s 2 E 5.98x 1024 kg Force is not Acceleration Force is the Same! Acceleration is NOT! FFEarth on You You on Earth aaEarth to You You to Earth An interaction requires a pair of forces acting on two objects. kick Gun Pushes Bullet out. Bullet Pushes back on Gun (& Man) Action Reaction Pairs kick Gun Pushes Bullet out. Bullet Pushes back on Gun (& Man) Rocket Thrust Rocket Pushes Gas Out. Gas Pushes Back on Rocket. Newton’s 3rd Law Newton’s 3rd Law In order to get an object moving, you must push harder on it than it pushes back on you. A) True B) False Question You push a heavy car by hand. The car, in turn, pushes back with an opposite but equal force on you. Doesn’t this mean the forces cancel one another, making acceleration impossible? How is it that the car moves? The System Action-Reaction forces act on different objects.
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