1. 18-Aug-15 Physics 1 (Garcia) SJSU Chapter 4 Newton’s Second Law of Motion How does an object move when a force acts on it?

2. 18-Aug-15 Physics 1 (Garcia) SJSU Force & Acceleration Newton’s First Law of Motion, Zero ForceConstant Velocity Definition of Acceleration, (Acceleration) = (Change in Velocity) (Time interval) implies (same as uniform motion)

3. 18-Aug-15 Physics 1 (Garcia) SJSU Force Implies Acceleration From those two results we have that, Net Force not Zero Object Accelerates implies Velocity not Constant 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.

4. 18-Aug-15 Physics 1 (Garcia) SJSU More Force, More Acceleration The greater the net force on an object, the greater the acceleration of that object.

5. 18-Aug-15 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 Double the Acceleration Triple the Acceleration Half the Acceleration implies Acceleration “goes as” Force Force “goes as” Acceleration. Mathematically, we write Force ~ Acceleration.

6. 18-Aug-15 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?

7. 18-Aug-15 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?

8. 18-Aug-15 Physics 1 (Garcia) SJSU 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) Mass & Weight Earth Moon Weight

9. 18-Aug-15 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.

10. 18-Aug-15 Physics 1 (Garcia) SJSU Demo: Hammer Head Hammer a nail into a piece of wood placed on top of massive object (gold brick or huge book). Inertia of massive object keeps it from moving; can place on top of head and not feel it.

11. 18-Aug-15 Physics 1 (Garcia) SJSU Mass & Acceleration For a given force, greater mass, smaller the acceleration Double the Mass Triple the Mass Half the Mass implies Half the Acceleration Third of the Acceleration Double the Acceleration implies Acceleration goes as the inverse of mass. Mathematically, we write, Acceleration ~ 1/(Mass).

12. 18-Aug-15 Physics 1 (Garcia) SJSU Check Yourself ????? NO FRICTION

13. 18-Aug-15 Physics 1 (Garcia) SJSU 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. (Acceleration) = (Net Force) (Mass)

14. 18-Aug-15 Physics 1 (Garcia) SJSU Demo: Spool Pull on string wrapped around a spool. Force is to the right. In what direction does the spool move? Spool moves? Pull

15. 18-Aug-15 Physics 1 (Garcia) SJSU Demo: Tricycle Pull on tricycle pedal with a string. Which direction does the tricycle move? Bike moves? Pull Pedal in top position Pedal in bottom position

16. 18-Aug-15 Physics 1 (Garcia) SJSU Weight on Earth From the Chapter 3, acceleration of gravity on Earth is 10 meters per second per second. (Notation: g = 10 m/s 2 ) 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/s 2 ) 1 kg 10 N

17. 18-Aug-15 Physics 1 (Garcia) SJSU Demo: Bowling Ball in a Bag Carry 6 kg bowling ball in a grocery bag. How much weight does the bag support? If I quick yank upwards, accelerating by 5 m/s 2, how much additional force is required?

18. 18-Aug-15 Physics 1 (Garcia) SJSU Demo: Elevator Cable Tension in elevator cable depends on acceleration 10 N 1 kg Zero acceleration 15 N 1 kg 5 m/s 2 upward ( ½ g upward) 5 N 1 kg 0 N 1 kg 5 m/s 2 downward ( ½ g downward) 10 m/s 2 downward (Free fall)

19. 18-Aug-15 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…).

20. 18-Aug-15 Physics 1 (Garcia) SJSU Demo: Falling in a Vacuum Feather falls slowly due to air resistance force. If we remove the air (create a vacuum) then feather and coin fall with same acceleration.

21. 18-Aug-15 Physics 1 (Garcia) SJSU Movie: Falling on the Moon

22. 18-Aug-15 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

23. 18-Aug-15 Physics 1 (Garcia) SJSU Friction and Air Resistance Friction and air resistance are forces opposing motion.

24. 18-Aug-15 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.

25. 18-Aug-15 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.

26. 18-Aug-15 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)

27. 18-Aug-15 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)? Golf Ball Ping pong Ball Drag Weight

28. 18-Aug-15 Physics 1 (Garcia) SJSU 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)

29. 18-Aug-15 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. From: www.animalhealthcare.ca 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!

30. 18-Aug-15 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 (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.