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Transcript
Forces and Newton’s Laws of Motion Chapter 4 Inertia All objects naturally tend to continue moving in the same direction at the same speed. All objects resist changing their velocity. (velocity is speed and direction) Resistance to changing velocity is inertia. The amount of inertia is the mass. Mass is measured in kilograms (kg). Forces External forces can change an object's velocity. Total external force is called net force F. Net force F determines how quickly and in what direction the velocity changes. When net force F is zero, the velocity remains unchanged. If the object is moving, it keeps moving in a straight line. Newton's first law When net force F 0 , the velocity stays the same. (same speed and same direction) The reverse is also true. When the velocity stays the same, the net force F 0 . Newton's first law is also called the law of inertia because an object's inertia keeps it moving in the same direction at the same speed if the net force is zero. Inertial reference frame An inertial reference frame is a coordinate system in which Newton’s law of inertia is valid. Inertial frames have a constant velocity. All accelerating reference frames are noninertial because Newton’s law of inertia is not valid in accelerated coordinate systems. Non-inertial frame: A car when speeding up, slowing down, or turning a corner. Net force F The net force F is the vector sum of all external forces acting on a single object. F F1 F2 F3 Individual Forces Net Force F 4N 10 N 6N The SI unit of force is the newton (N). Net force F Individual Forces F1 Net Force F 3N F2 37 4N F F1 F2 F F2 4N F1 3N 5N Newton's second law An object's acceleration vector is equal to the net force F acting on the object divided by the object's mass. a F m Acceleration direction is same direction as net force F . Newton's second law Use x and y components when you need more than + and - to specify directions. F ma F or x max Fy may SI unit of force a F F ma m newton N is the SI unit for force m kg m N = kg 2 2 s s Force diagram (also known as free-body diagram) ALWAYS draw a force diagram with a force vector for each individual, external force acting on a single object. mass 1850 kg F 275N 395N 560 N 110 N Net force F is in the +x direction. Example: What is the car's acceleration? Net force is +110 N and car's mass is 1850 kg F +110 N m a 0.059 m 1850 kg s The “+” sign indicates the +x direction. 2 Newton's third law Two objects always exert equal and opposite forces on each other. Forces always occur in pairs. Each object experiences the force equally, but the forces are in opposite directions. Example: You are pushing down on the chair with some force and the chair is pushing on you with the same amount of force but in the opposite direction (up). Example Astronaut pushes with 36 N on a spacecraft. What are their accelerations? 11,000 kg 92 kg The two objects exert 36 N of force on each other. a spacecraft F mspacecraft 36 N m 0.0033 2 11,000 kg s aastronaut F mastronaut 36 N m 0.39 2 92 kg s Example Find the tension in the trailer drawbar and the force D that propels the truck forward. Ignore the forces of friction and air resistance. Unbalanced horizontal force Unbalanced horizontal forces FN FN Fg Fg Equal and opposite forces on different objects Forces There are two general types of forces in nature, fundamental and non-fundamental. Fundamental Non-fundamental gravity electromagnetism weak nuclear strong nuclear push pull support friction tension ... Universal law of gravity Every two objects in the universe attract each other with the gravity force. centerline Equal attracting forces in exactly opposite directions. (Newton's 3rd law: equal and opposite forces on two objects) magnitude universal gravity constant m1m2 F G 2 r G 6.673 1011 N m2 kg 2 Weight is the gravity force on an object ME MEm Fg G m G 2 mg 2 RE RE Fg mg where ME N m g G 2 9.8 9.8 2 r kg s Example: a 5 kg mass "weighs" 49 N N Fg mg 5kg 9.8 49 N kg Fg Fg Contact forces Support FN Perpendicular to the contact surfaces Friction f Tangent to the contact surfaces Sliding friction (kinetic) f k Non-sliding (static) f s Normal means perpendicular so the support force is often called the normal force. Examples: Forces on the block F ma 0 15 N block F FN Fhand Fg 15 N F FN 11 N 15 N 0 FN 26 N F ma 0 F FN Frope Fg F FN 11 N 15 N 0 FN 4 N 15 N Apparent weight Apparent weight is the reading of the scale. It is equal to the support force the scale exerts on the person and the person exerts on the scale. forces on the person F ma FN (by scale ) Fg Static friction Static means the two surfaces are not sliding across each another. Friction force direction opposes the impending relative motion between two objects. Static friction magnitude is just enough to prevent motion. 0 f static f MAX static s FN 0 s 1 static friction coefficient Kinetic friction Kinetic friction opposes sliding motion f k k FN 0 k 1 kinetic friction coefficient Friction forces do not depend on contact area. Friction depends on contact force FN . Example: Find sliding distance Kinetic friction force causes the sled to slow down. a F ma Fg FN f k 0° k 0.05 f k FN k ma180 Fg 90 FN 90 f k 180 Fx 40kg ax f k FN k force diagram get the directions analyze the x and y components N Fy 40kg 0 Fg FN 40kg 9.8 FN kg 0 392 N FN FN 392 N f k 392 N 0.05 19.6 N m 40kg ax 19.6 N ax 0.49 2 x 32.65m s Tension force Flexible things like rope, string, cables exert tension forces. Force direction is always tangent to the rope, etc. Tension force has the same magnitude at each end. Tension force Pulleys change the direction of a tension force, but not the magnitude of the force. man FN Ftension force of the rope on the block Ftension Fg Fg Newton's third law tells us that the rope exerts the same amount of force on the man as the man exerts on the rope. force of the man on the rope To simplify things, physics ropes and cables are usually massless and pulleys are usually frictionless. The rope has no weight that needs to be considered. Equilibrium Equilibrium mean balanced. For equilibrium the forces are balanced and the net force F 0 . Velocity magnitude & direction stay the same. F 0 or F Fx 0 y 0 Equilibrium Reasoning Strategy Select an object to analyze. Draw a force diagram showing only the forces acting on the object, but not forces that the object exerts on other things. Choose a set of x and y axes. Set up balanced force equations The sum of the x force components add up to zero. The sum of the y force components add up to zero. Solve for any unknown quantities. Example find F Object is the pulley, but first find the tension in the rope Ftension 2.2 kg First, select the block as the object. If the block stays at rest, then the forces acting on it are balanced. Therefore, the tension and gravity forces are balanced. ( Second law: F 0 ) m Fg mg 2.2kg 9.8 2 21.56 N s Second, select the pulley as the object 0 0 21.56 N 180 If the pulley stays at rest, then the forces on the pulley are balanced. (Second law: F 0 ) F F T1 T2 0 F F 180 21.56 N 35 21.56 N 35 0 F F 180 21.56 N 35 21.56 N 35 0 F 35.32 N Fx=F cos θ Fy=F sin θ -F 0 F180 17.66 N 12.37 N 21.56N35 17.66 N -12.37 N 21.56N 35 0 0 F 0 Example Engine weighs 3150 N 100 10 90 F T1100 T2 10 3150 N 90 0 The End