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4. Newton's Laws

4. Newton's Laws. The Wrong Question Newton’s 1 st & 2 nd laws Forces The Force of Gravity Using Newton’s 2 nd Law Newton’s 3 rd Law. Ans: Human body: contact force Wind & water: fluid pressure Gravity: action-at-a-distance. What forces govern the motion of the sailboard?.

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4. Newton's Laws

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  1. 4. Newton's Laws The Wrong Question Newton’s 1st & 2nd laws Forces The Force of Gravity Using Newton’s 2nd Law Newton’s 3rd Law

  2. Ans: • Human body: contact force • Wind & water: fluid pressure • Gravity: action-at-a-distance What forces govern the motion of the sailboard?

  3. 4.1. The Wrong Question Q: Why do things move? Aristotle (~350BC) : Because some forces are acting on them. Galileo (~1600) : Wrong question ( things move until stopped ). … it always rises to its starting height … If a ball is released here … The right question: Why do moving things change direction? Newton: Because some forces are acting on them. … so this ball should roll forever.

  4. 4.2. Newton’s 1st & 2nd laws Fnet 0  v  Net force determines motion. Newton’s 1st law of motion: A body at rest or in uniform motion remains so unless acted on by a nonzero net force. Fnet= 0  v =const

  5. GOT IT? 4.1. On a horizontal tabletop is a curved barrier that exerts a force on a ball, guiding its motion in a circular path. After the ball leaves the barrier, which of the dashed paths shown does it follow?

  6. Newton’s 2nd Law (quantity of motion) Momentum: Newton’s 2nd law of motion: The rate of change of momentum is equal to the net force. For a constant mass:

  7. Mass, Inertia, & Force Inertia: resistance to changes in motion. 1st law = law of inertia Operational definition of mass  Loaded truck has greater mass, more inertia, less acceleration. 1 N (Newton)  force required to give a mass of 1 Kg an acceleration of 1 m / s2. 1 N = 1 Kg m / s2. 1 Dyne = 1 g cm / s2.

  8. Example 4.1. AcceleratingCar • A 1200 kg car accelerates constantly in a straight line from rest to 20 m/s in 7.8 s. • What is the net force on it? • What is the net force on it if it rounds a bend 85 m in radius at v = 20 m/s?

  9. Inertial Reference Frames Inertial Reference Frames: reference frame in which Newton’s 1st law works. • Examples of non-inertial reference frames: • Accelerating planes. • Car rounding a curve. • Merry-go-round. • Earth (rotating). • Examples of inertial reference frames: • Newton: Distant “fixed” stars. • Einstein: General relativity.

  10. 4.3. Forces Fc= Fg • Examples of forces: • Pushes & pulls. • Car collided with truck & stopped. • Moon circles Earth. • Person sitting on chair. • Climber on rope. (action-at-a distance) (contact force) (tension force) T = Fg

  11. The Fundamental Forces • The fundamental forces: • Gravity: large scale phenomena • Electroweak force • Electromagnetic force: everyday phenomena • Weak (nuclear) force • Strong (nuclear) force 1025 1036 1 1038

  12. 4.4. The Force of Gravity m in f = m a is the inertia mass (same everywhere). Weight = force of gravity on mass: For a mass of 65 kg, weight on Earth = (65 kg) (9.8 m/s2 ) = 640 N. weight on Moon = (65 kg) (1.6 m/s2 ) = 100 N. weight in outer-space = (65 kg) (0 m/s2 ) = 0 N. Caution: In daily use, weight is often measured in units of mass. E.g., a person “weights” 65 kg. Strictly speaking, m in w = m g is the gravitational mass. Galileo experiment: mI = mG(coincidence) Einstein: mI = mG(exact: gravity is geometry)

  13. Weightlessness These astonauts feel “weightless” because they are in freefall. Their weight is about 93% of that on surface. same a

  14. 4.5. Using Newton’s 2nd Law • Tactics 4.1. Free-Body Diagram • Identify object of interest & forces on it. • Object  dot. • Draw forces on object as vectors at dot.

  15. Example 4.3. Elevator A 740 kg elevator accelerates upward at 1.1 m/s2. Find the tension force on the cable (of negligible mass).

  16. GOT IT? 4.4. • How’s T compared to w = m g if the elevator • moves upward starting at rest. • decelerates to stop while moving upward. • starts moving downward, accelerating from rest. • slows to stop while moving downward. • moves upward with constant speed. greater less less greater equal

  17. Conceptual Example 4.1. At the Equator When you stand on a scale, the scale reading shows the force it pushes up to support you. If you stand on a scale at Earth’s equator, is the reading greater or less than your weight? Ans: You’re in uniform circular motion so that the net force on you is centripetal. m a W = m g Fscale

  18. Parabolic Flight

  19. 4.6. Newton’s 3rd Law Newton’s 3rd law: Action = Reaction Forces of 3rd law pair act on different objects. Hence, they don’t cancel each other out. Horse-Cart dilemma

  20. Example 4.4. Pushing Books 2 books lie on frictionless horizontal surface. You push with force F on books of mass m1. which in turn on book of mass m2. What force does the 2nd book exert on the 1st ? Acceleration of books: Net force on 2nd book: Force exerted by 2nd book on the 1st

  21. GOT IT? 4.5 Is the net force on the larger block (a) greater than 2 N , (b) equal to 2N or (c) less than 2 N ?

  22. Normal force n : contact force acting normal to contact surface. Not a 3rd law pair Normal force Fnet 0 3rd law also applies to non-contact forces such as gravity.

  23. Measuring Force Force can be measured using Newton’s 3rd law. Ideal spring (Hooke’s law): k = spring constant fsp= 0 fsp= fwall < 0 Works only in inertial frame. fsp= fwall > 0

  24. Example 4.5. Helicopter Ride • Helicopter rises vertically. • A 35 kg bag sits in it on a spring scale of k = 3.4 kN/m. • By how much the spring compresses • when helicopter is at rest • when it’s accelerating upward at 1.9 m/s2. (a) (b)

  25. GOT IT? 4.6 • Example 4.5: • Helicopter rises vertically. • A 35 kg bag sits in it on a spring scale of k = 3.4 kN/m. • By how much the spring compresses • when helicopter is at rest • when it’s accelerating upward at 1.9 m/s2. • Continued from Example 4.5: • Would the answer to (a) change if the helicopter were moving upward with constant speed? • Would the answer to (b) change if the helicopter were moving downward but still accelerating upward? No No

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