Chapter 4: Forces & Newton s Laws of Motion. Newton s 3 Laws Types of Forces Solving 1D &2D Problems Force Vector Diagrams!!!
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1 Chapter 4: Forces & Newton s Laws of Motion Newton s 3 Laws Types of Forces Solving 1D &2D Problems Force Vector Diagrams!!!
2 Man of the Millennium Sir Issac Newton ( ) 1687 Published Principia Invented Calculus 3 Laws of Motion Universal Law of Gravity
3 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.
4 Newton s 2nd Law F ma a F net m The acceleration of an object is directly related to the net external forces acting on it and inversely proportional to its mass.
5 Net Force? Direction of applied forces matters!!! Opposite forces cancel!
6 Newton s 3rd Law F hand on wall F wall on hand To every force there is an equal but opposite reaction force.
7 What Is a Force? A force is a push or a pull. The Unit is the NEWTON: F ma m s kg 2 N 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 Pearson Education, Inc. Slide 5-18
8 What Is a Force? Contact forces are forces that act on an object by touching it at a point of contact. The bat must touch the ball to hit it. Long-range forces are forces that act on an object without physical contact. A coffee cup released from your hand is pulled to the earth by the long-range force of gravity Pearson Education, Inc. Slide 5-20
9 Types of Mechanical Forces 2013 Pearson Education, Inc. Slide 5-45
10 Forces are Interactions F Earth on Rock F Rock on Earth
11
12 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 Pearson Education, Inc. Slide 5-75
13 EXTERNAL Forces either Speed you up Slow you down Change your direction Cancel each other out!!! 2013 Pearson Education, Inc.
14 Galileo Challenged The Dogma Of Natural 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.
15 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.
16 Inertia The resistance of an object to change its state of motion. A measure of mass or how much stuff an object has.
17 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
18 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? C Slide 5-77
19 Mass & Weight F ma W mg g 9.8 m/ s 2 (g is a scalar!) Calculate your weight in N. 1 lb = 4.45 N Calculate your mass in Kg.
20 Galileo Challenged Aristotle Physics In a vacuum, all objects fall with the same acceleration due to gravity: 9.80 m/s 2, independent of their weight.
21 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?
22 Acceleration is not Force! MASS IS NOT WEIGHT!!!
23 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.
24 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.
25 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 WE mge 10kg 9.8 m/ s 98N 1 1 WEM mgm m ge 98 N 16.3 N 6 6
26 Newton s First Law If F 0 => No Change in Motion Dynamic Equilibrium Static Equilibrium
27 Static Equilibrium Forces up equal the forces down. Forces sideways cancel too. F y 0 F x 0
28 Force Vector Diagrams Show all the External forces acting ON the body only.
29 Dynamic Equilibrium F 0 If the Net Force is zero, then the object moves at a constant speed in dynamic equilibrium. W
30 Newton s 2nd Law F ma a F net m The acceleration of object is directly related to the net forces acting on it and inversely proportional to its mass.
31 Newton s 2nd Law Units F ma m kg 2 s N
32 Acceleration is in the direction of the net Force but not necessarily in the direction of velocity. a F net m
33 Force Components F ma F ma F ma x x y 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.
34 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 F net = 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.
35 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? F x ma x F cos ma x F cos ax = v f v0 at m Fcos 100Ncos 40 v f v0 at t 5 s 6.38 m / s m 60kg
36 Frictional Forces Friction always opposes the applied force and is in the opposite direction of motion. The greater the normal force the greater the frictional force. Frictional forces always SLOW DOWN the motion and NEVER speed it up!!! f s N s f k k N
37 Statice vs Kinetic Friction f s f k Fig. 5.16, p.131
38 Problem The magnitude of F 1 is 75.0N and F 2 is 50.0N. The coefficient of friction between the block and the floor is How do you know which direction to put the friction? What is the acceleration of the block?
39 Air Resistance Air resistance is proportional to the size and speed of an object. WHY? The greater the cross sectional area of an object, the greater amount of air pushed out of the way the air pushes back! The faster an object falls, the faster it has to push the air out of the way the air pushes back! This is air resistance.
40 a Terminal Velocity When the air resistance balances the weight, the object stops accelerating and it falls with constant velocity called F Terminal Velocity. Net + W m m R R W W m W 0
41 Problem What is the acceleration of a sky diver when the air resistance equals ½ the total weight? a F Net m W R m W W /2 m mg mg /2 g /2 m R + W
42 The Inclined Plane Orient your axes relative to the plane!!! Why is the angle of the incline here? Prove it.
43
44 Incline Plane Problem Draw a free-body diagram of a block which slides down a plane having a coeeficient of friction of 0.05 and an inclination of = 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.
45 A block is pushed up a frictionless 30 incline by an applied force as shown. If F = 25 N and M = 3.0 kg, what is the magnitude of the resulting acceleration of the block? a. 2.3 m/s 2 b. 4.6 m/s 2 c. 3.5 m/s 2 d. 2.9 m/s 2 e. 5.1 m/s 2
46 Tension Forces Tension forces are transmitted undiminished through the rope. Different T Same T
47 Force Vector Diagrams Continuous Rope has same T everywhere! What is T?
48 Force Vector Diagrams Align axes to simplify the problem!
49 Force Vector Diagrams Draw free-body diagrams for every object! Note: T and a are the same! Ropes connected by ideal pulleys have the same tension everywhere!
50 Pulleys, Masses, Strings What is the acceleration of the system? (If they are connected, it is the same for both masses!) What is the tension in the string? Compare to g and the weight of m2. 1. If it falls from rest 2. If it is dragged to the left 3. If the string is cut FIRST: Draw free-body diagrams for each mass!!!
51 Problem A force F = 40 N pulls the two masses. If the table is frictionless, find the tension in the string. m 3 kg, m 1.5kg a) 13 N b) 36 N c) 23 N d) 15 N e) 28 N 1 2
52 QuickCheck 5.8 An object on a rope is lowered at constant speed. Which is true? A. The rope tension is greater than the object s weight. B. The rope tension equals the object s weight. C. The rope tension is less than the object s weight. D. The rope tension can t be compared to the object s weight. Slide 5-68
53 QuickCheck 5.8 An object on a rope is lowered at constant speed. Which is true? Constant velocity Zero acceleration A. The rope tension is greater than the object s weight. B. The rope tension equals the object s weight. C. The rope tension is less than the object s weight. D. The rope tension can t be compared to the object s weight. Slide 5-69
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