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Transcript
Chapter 4 Newton’s Second Law of Motion How does an object move when a force acts on it? 22-May-17 Physics 1 (Garcia) SJSU Force & Acceleration Newton’s First Law of Motion, Zero Force implies Constant Velocity (same as uniform motion) Definition of Acceleration, (Change in Velocity) (Acceleration) = 22-May-17 (Time interval) Physics 1 (Garcia) SJSU Force Implies Acceleration From those two results we have that, Net Force not Zero implies Velocity not Constant implies Object Accelerates So if there’s a net force on an object, that implies that the object accelerates. Also have that if an object accelerates, that implies that there’s a net force. 22-May-17 Physics 1 (Garcia) SJSU Force Causes Acceleration • Net Force-The combination of all forces that act on an object • The acceleration of an object is directly related to the net force on an object (force and acceleration change in the same direction) More Force, More Acceleration The greater the net force on an object, the greater the acceleration of that object. 22-May-17 Physics 1 (Garcia) SJSU Acceleration Goes As Force Larger the net force, greater the acceleration Double the Force Triple the Force Half the Force implies implies implies Acceleration “goes as” Force Force “goes as” Acceleration. 22-May-17 Double the Acceleration Triple the Acceleration Half the Acceleration Mathematically, we write Force ~ Acceleration. Physics 1 (Garcia) SJSU Check Yourself You push on a crate with 100 Newtons of force. If the friction force is 100 Newtons, does the crate accelerate? Does that mean that the crate is not moving? 22-May-17 Physics 1 (Garcia) SJSU Check Yourself (cont.) Now push with 150 N; friction is still 100 N. Does the crate accelerate? A friend helps push with an additional 150 N. By how much does acceleration increase? 22-May-17 Physics 1 (Garcia) SJSU More Mass, Less Acceleration The greater the mass of an object, the less it accelerates when acted on by a force. 22-May-17 Physics 1 (Garcia) SJSU Mass Resists Acceleration • Acceleration is inversely proportional to mass – Inversely-the 2 values change in opposite directions • As mass increases, acceleration decreases for a given force • As mass decreases, acceleration increases for a given force Mass & Acceleration For a given force, greater mass, smaller the acceleration Double the Mass Triple the Mass Half the Mass Acceleration goes as the inverse of mass. 22-May-17 implies implies implies Half the Acceleration Third of the Acceleration Double the Acceleration Mathematically, we write, Acceleration ~ 1/(Mass). Physics 1 (Garcia) SJSU Check Yourself NO FRICTION ????? ????? ????? ????? 22-May-17 Physics 1 (Garcia) SJSU Newton’s Second Law • Also called the Law of Acceleration • The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction of the net force, and is inversely proportional to the mass of the body. or A=F/M Newton’s Second Law of Motion Acceleration goes as net Force. Acceleration goes as inverse of Mass. Acceleration only depends on Force and Mass. (Net Force) (Acceleration) = (Mass) Acceleration is in the direction of the net Force. 22-May-17 Physics 1 (Garcia) SJSU Weight on Earth From the Chapter 2, acceleration of gravity on Earth is 10 meters per second per second. (Notation: g = 10 m/s2 ) From Newton’s Second Law, (Force) = (Mass) X (Acceleration) For example, weight (force of gravity) for 1 kg is 1 kg ( 10 Newtons ) = ( 1 kg ) X ( 10 m/s2 ) 10 N 22-May-17 Physics 1 (Garcia) SJSU Demo: Elevator Cable Tension in elevator cable depends on acceleration Zero acceleration 5 m/s2 upward ( ½ g upward) 5 m/s2 downward ( ½ g downward) 10 m/s2 downward (Free fall) 0N 15 N 10 N 5N 1 kg 1 kg 1 kg 1 kg 22-May-17 Physics 1 (Garcia) SJSU Free Fall Acceleration Newton’s Second Law explains why all objects fall with same acceleration. Ratio of weight/mass always the same since weight depends on mass. Analogy with ratio of circumference / diameter always equals pi (3.1415…). 22-May-17 Physics 1 (Garcia) SJSU Demo: Drop the Sheet A flat sheet of paper falls slowly because of air resistance. What happens if we place it on top of a book, blocking the air from reaching it? Air Resistance Weight 22-May-17 Physics 1 (Garcia) SJSU Friction and Air Resistance Friction and air resistance are forces opposing motion. 22-May-17 Physics 1 (Garcia) SJSU Friction Origin of friction is molecular interaction between solid surfaces. Friction is complicated. Friction depends on support force and on properties of the surface. Basic properties of friction first established by Leonardo da Vinci. 22-May-17 Physics 1 (Garcia) SJSU Air Resistance (Drag) Origin of drag is molecules of gas (or liquid) striking a moving object. Drag force depends on: •Size (area) of the object •Speed of the object Larger the size or speed, larger the drag. Also depends on shape of object, density of gas or liquid, etc. 22-May-17 Physics 1 (Garcia) SJSU Air Resistance on a Falling Object Gravity force on an object (i.e., weight) is constant but air resistance depends on an object’s speed. As a falling object gains speed, the resistance force gets larger so the net force decreases. Net force is sum of: Weight (downward) Resistance (upward) 22-May-17 Physics 1 (Garcia) SJSU Check Yourself Golf ball has more mass than a ping-pong ball. Force of gravity is greater on: golf ball, ping-pong ball, or the same? The two balls are the same size; when speeds are equal, drag force is greater on which ball? Which ball falls faster (which has greater acceleration)? 22-May-17 Physics 1 (Garcia) SJSU Ping pong Ball Golf Ball Drag Weight Terminal Speed Speed of falling objects increases until drag force balances weight. When forces balance, zero acceleration so constant velocity. Speed for which air resistance balances weight called terminal speed. High terminal speed (better open the chute!) Low terminal speed (large area of chute) 22-May-17 Physics 1 (Garcia) SJSU Demo: Drop the Cat Cats seem to have an uncanny ability to survive falls from high places. For example, cats have been known to survive falls of up to 32 stories. By contrast, dogs rarely survive falls of more than six stories. Humans usually die when they fall from such heights. In a study of cats that had fallen from up to 32 stories, an interesting finding emerged: while the rate of injury in cats seemed to increase linearly depending on the length of the fall, after seven stories, the rate of injury seemed to level off! In other words, the survival rate and severity of injuries were no more severe in a cat that fell seven stories than in one that fell 32 and in some cases, injuries were even less! From: www.animalhealthcare.ca 22-May-17 Physics 1 (Garcia) SJSU Demo: Drop the Cat (cont.) After further study, the reasons for this discrepancy became clear. When a person falls from a building, maximum speed or "terminal velocity" (120 mph) is reached after 32 stories. Cats, on the other hand, achieve terminal velocity at 60 mph after falling only five stories! Until a cat reaches terminal velocity, it will experience acceleration and tend to reflexively extend its limbs, making it more susceptible to injuries. However, when a cat reaches terminal velocity, its vestibular system (i.e. the organs of balance) become less stimulated, causing the cat to relax. It will then orient its limbs more horizontally (splaylegged), thereby increasing air drag in much the same way a parachute does. In this posture, the force of impact also appears to become more evenly distributed. 22-May-17 Physics 1 (Garcia) SJSU Mass & Weight Mass: Quantity of matter in an object Weight: Force of gravity on an object Weight Mass is a universal property. Weight depends on gravity (different on Moon). Earth Moon Mass is the measure of inertia. Metric unit for mass is the kilogram. Metric unit for weight is Newton (since it’s a force) 22-May-17 Physics 1 (Garcia) SJSU