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Connection between force & Motion <ul><li>Aristotle </li></ul><ul><li>(384 B.C. – 322 B.C.) </li></ul><ul><li>Galileo </li></ul><ul><li>(1564-1642) </li></ul>1. Discuss Aristotle and Galileo’s differing views on the connection between force and motion
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Their ideas lead to what we know today as….newton’s laws of motion! <ul><li>Sir Isaac Newton </li></ul><ul><li>(1642-1727) </li></ul>Random fact 1…Newton was born on Christmas day! Not so random fact 2… You can also thank Newton for inventing CALCULUS! random fact 3… He was a member of the Parliament of England. Only recorded comments: to complain about a draught in the room and request for a window to be closed. random fact 4… A British psychologist now believes it “fairly certain” that Newton had asperger’s disease. random fact 5… He never married.
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<ul><li>Unit is the NEWTON(N) </li></ul><ul><li>Is by definition a push or a pull </li></ul><ul><li>Can exist during physical contact (Tension, Friction, Applied Force) </li></ul><ul><li>Can exist with NO physical contact, called FIELD FORCES ( gravitational, electric, etc) </li></ul><ul><li>We measure FORCE using a spring scale! </li></ul><ul><li>A force is a VECTOR </li></ul>Facts about Force
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2. What is Newton’s first law of motion? Provide 3 examples of this law in action.
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<ul><li>An object in motion remains in motion in a straight line and at a constant speed OR an object at rest remains at rest, UNLESS acted upon by an EXTERNAL (unbalanced) Force. </li></ul>There are TWO conditions here and one constraint. Condition #1 – The object CAN move but must be at a CONSTANT SPEED Condition #2 – The object is at REST Constraint – As long as the forces are BALANCED!!!!! And if all the forces are balanced the SUM of all the forces is ZERO. The bottom line: There is NO ACCELERATION in this case AND the object must be at EQILIBRIUM ( All the forces cancel out). Newton ’s First Law
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<ul><li>INERTIA –the resistance of any physical object to a change in its state of motion or rest. It is proportional to an object’s MASS . Italian for “ LAZY ” . Unit for MASS = kilogram . </li></ul>Newton ’s First Law – The Law of Inertia 3. Define inertia
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4. Define mass 5. What is the difference between mass and weight?
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<ul><li>Weight or Force due to Gravity is how your MASS is effected by gravity. </li></ul>NOTE: MASS and WEIGHT are NOT the same thing. MASS never changes When an object moves to a different planet. What is the weight of an 85.3-kg person on earth? On Mars (g=3.2 m/s/s)? Weight
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Units of mass & force English SI Mass Slug Kilogram (kg) Force Pounds (lb) = 1 slug foot/sec 2 Newton (N) = kg meters/sec 2
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Free body diagrams <ul><li>Steps: </li></ul><ul><li>Draw a picture of the object being analyzed (isolate the object) </li></ul><ul><li>Draw & label vector (that show magnitude and direction) arrows representing external forces acting on the object. </li></ul><ul><ul><li>Arrows should be drawn to original from the center of the car </li></ul></ul><ul><li>Draw & label vector arrows representing the internal forces acting on the object </li></ul><ul><li>Purpose : to analyze the forces acting on an object to determine which forces affect the object. </li></ul>1. Draw a free-body diagram of this book. 2. What would this FBD look like if someone were pushing the book from the left?
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<ul><li>There are four different force types </li></ul>W 1 ,Fg 1 or m 1 g <ul><li>Force due to gravity (F g ) aka Weight(mg) – Always drawn from the center, straight down </li></ul><ul><li>Force Normal(F N ) – A surface force always drawn perpendicular to a surface. </li></ul><ul><li>Tension(T or F T ) – force in ropes and always drawn AWAY from object. </li></ul><ul><li>Friction(Ff)- Always drawn opposing the motion. </li></ul>m 2 g T T F N F f Free Body Diagrams
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<ul><li>Since the F net = 0, a system moving at a constant speed or at rest MUST be at “ EQUILIBRIUM ” . </li></ul><ul><li>TIPS for solving problems </li></ul><ul><li>Draw a FBD </li></ul><ul><li>Resolve anything into COMPONENTS </li></ul><ul><li>Write equations of equilibrium </li></ul><ul><li>Solve for unknowns </li></ul>Newton ’s First Law – The Law of “EQUILIBRIUM”
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2. What is Newton’s second law of motion? Give 3 examples of this law in action.
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Newton’s second law <ul><li>The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. </li></ul>DIRECTLY = They do the same thing . If the force increases, the acceleration increases. If the force decreases, the acceleration decreases. Acceleration is inversely proportional to the mass. INVERSELY = They do the opposite. If the mass decreases, the acceleration will increase. If the mass increases, the acceleration will decrease.
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<ul><li>a = Σ F </li></ul><ul><li>m </li></ul><ul><li>We more commonly see this equation as </li></ul><ul><li>Σ F = m a </li></ul>Newton’s second law If we add a second dog pulling with 100N just like the first dog, we could pull the sled with twice the acceleration, provided the mass of the sled was constant. F(net)=ma 2F=m(2a) 3F=m(3a)
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Putting it all together 10 N 3 N Magnitude of F NET = Direction = Acceleration = 7 N RIGHT 10 kg 0.70 m/s/s
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N.S.L Tips <ul><li>Draw a free body diagram </li></ul><ul><li>Break vectors into components if needed </li></ul><ul><li>Find the NET force by adding and subtracting forces that are on the same axis as the acceleration . </li></ul><ul><li>Set net force equal to “ ma ” this is called writing an EQUATION OF MOTION. </li></ul><ul><li>NOTE: To avoid negative numbers, always subtract the smaller forces from the larger one. </li></ul>
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Example: applying newton’s 2nd <ul><li>A 1000 kg car traveling at 20.0 m/s hits a snow bank and comes to a complete stop within 2.0 seconds of impact. If we neglect friction, what is the net force applied to the car? </li></ul><ul><li>Draw a FBD </li></ul><ul><li>Break vector into components </li></ul><ul><li>Find the NET force by adding and subtracting forces that are on the same axis as the acceleration . </li></ul><ul><li>Set net force equal to “ma” this is called writing an EQUATION OF MOTION. </li></ul>
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<ul><li>A 10-kg box is being pulled across the table to the right at a constant speed with a force of 50N. </li></ul><ul><li>Calculate the Force of Friction </li></ul><ul><li>Calculate the Force Normal </li></ul>mg F N F a F f Example
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<ul><li>Suppose the same box is now pulled at an angle of 30 degrees above the horizontal. </li></ul><ul><li>Calculate the Force of Friction </li></ul><ul><li>Calculate the Force Normal </li></ul>mg F N F a F f 30 F ax F ay Example
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Example <ul><li>A cafe sign with a mass of 65.5 kg is being held up by 2 cables as shown in the picture to the left. Calculate the tension in each of the ropes. </li></ul>mg T 1 T 2 T 1 cos19 T 1 sin19 T 2 cos35 T 2 sin35 750 N T 1 = 650 N
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N.S.L. <ul><li>"The acceleration of an object is directly proportional to the NET FORCE AND inversely proportional to the mass." </li></ul>Acceleration is directly proportional to the NET Force. DIRECTLY = They do the same thing. If the force increases, the acceleration increases. If the force decreases, the acceleration decreases. Acceleration is inversely proportional to the mass. INVERSELY = They do the opposite. If the mass decreases, the acceleration will increase. If the mass increases, the acceleration will decrease.
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N.S.L. N.S.L. works based on these direct and inverse relationships. As 2 of the variable change, ONE of them must remain constant. If the force is constant, the acceleration and mass change as shown above. F(net)=ma 2F=m(2a) 3F=m(3a) If we add a second dog pulling with 100N just like the first dog, we could pull the sled with twice the acceleration, provided the mass of the sled was constant.
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Example <ul><li>An elevator with a mass of 2000 kg rises with an acceleration of 1.0 m/s/s. What is the tension in the supporting cable? </li></ul>mg T Equation of Motion 21,600 N
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Example <ul><li>A 50 N applied force drags an 8.16 kg log to the right across a horizontal surface. What is the acceleration of the log if the force of friction is 40.0 N? </li></ul>50 N 40 N mg F n a 1.23 m/s/s
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Example <ul><li>A sled is being accelerated to the right at a rate of 1.5 m/s/s by a rope at a 33 degree angle above the + x . Calculate the Frictional Force if the mass of the sled is 66 kg and the tension in the rope is 150 N. </li></ul>mg F N T F f Tcos Tsin 26.8 N
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