Understanding Newton's Second Law of Motion

1. Chapter 4Newton’s Second Law of Motion How does an object move when a force acts on it? Physics 1 (Garcia) SJSU

2. Force & Acceleration Newton’s First Law of Motion, Zero Force Constant Velocity Definition of Acceleration, implies (same as uniform motion) (Change in Velocity) (Acceleration) = (Time interval) Physics 1 (Garcia) SJSU

3. Force Implies Acceleration From those two results we have that, Velocity not Constant Object Accelerates Net Force not Zero implies implies 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. Physics 1 (Garcia) SJSU

4. 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)

5. More Force, More Acceleration The greater the net force on an object, the greater the acceleration of that object. Physics 1 (Garcia) SJSU

6. implies implies implies Acceleration Goes As Force Larger the net force, greater the acceleration Double the Force Triple the Force Half the Force Double the Acceleration Triple the Acceleration Half the Acceleration Mathematically, we write Force ~ Acceleration. Acceleration “goes as” Force Force “goes as” Acceleration. Physics 1 (Garcia) SJSU

7. 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? Physics 1 (Garcia) SJSU

8. 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? Physics 1 (Garcia) SJSU

9. More Mass, Less Acceleration The greater the mass of an object, the less it accelerates when acted on by a force. Physics 1 (Garcia) SJSU

10. 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

11. implies implies implies Mass & Acceleration For a given force, greater mass, smaller the acceleration Double the Mass Triple the Mass Half the Mass Half the Acceleration Third of the Acceleration Double the Acceleration Acceleration goes as the inverse of mass. Mathematically, we write, Acceleration ~ 1/(Mass). Physics 1 (Garcia) SJSU

12. Check Yourself NO FRICTION ????? ????? ????? ????? Physics 1 (Garcia) SJSU

13. 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

14. Newton’s Second Law of Motion Acceleration goes as net Force. Acceleration goes as inverse of Mass. Acceleration only depends on Force and Mass. Acceleration is in the direction of the net Force. (Net Force) (Acceleration) = (Mass) Physics 1 (Garcia) SJSU

15. 1 kg 10 N 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 ( 10 Newtons ) = ( 1 kg ) X ( 10 m/s2 ) Physics 1 (Garcia) SJSU

16. 0 N 15 N Demo: Elevator Cable Tension in elevator cable depends on acceleration 5 m/s2 upward ( ½ g upward) Zero acceleration 5 m/s2 downward ( ½ g downward) 10 m/s2 downward (Free fall) 10 N 5 N 1 kg 1 kg 1 kg 1 kg Physics 1 (Garcia) SJSU

17. 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…). Physics 1 (Garcia) SJSU

18. 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 Physics 1 (Garcia) SJSU

19. Friction and Air Resistance Friction and air resistance are forces opposing motion. Physics 1 (Garcia) SJSU

20. 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. Physics 1 (Garcia) SJSU

21. 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. Physics 1 (Garcia) SJSU

22. 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) Physics 1 (Garcia) SJSU

23. Drag Weight Check Yourself Ping pong Ball Golf Ball 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)? Physics 1 (Garcia) SJSU

24. 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) Physics 1 (Garcia) SJSU

25. 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 Physics 1 (Garcia) SJSU

26. 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 (splay-legged), 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. Physics 1 (Garcia) SJSU

27. Mass & Weight Mass: Quantity of matter in an object Weight: Force of gravity on an object Mass is a universal property. Weight depends on gravity (different on 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) Weight Earth Moon Physics 1 (Garcia) SJSU