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2. Chapter 4 Newton’s Laws

3. Main points of Chapter 4 Forces Newton's first law – inertia Newton’s second law – F = ma Newton’s third law – action-reaction forces Noninertial frames Identifying forces; free-body diagrams Finding the motion

4. 4-1 Forces and Newton’s First Law Force is a vector Forces are additive – vector sum of all forces acting on an object is the net force: (4-2)

5. When there is no net force acting on an object, that object maintains its motion with a constant velocity. Different Ways of Stating the Law of Inertia 4-1 Forces and Newton’s First Law

6. When an object moves with constant velocity, the net force acting on it must be zero. Different Ways of Stating the Law of Inertia 4-1 Forces and Newton’s First Law

7. When there is no net force on an object, it will be at rest in a reference frame that is one of a set of reference frames moving at constant velocity to one another. Different Ways of Stating the Law of Inertia 4-1 Forces and Newton’s First Law

8. Constant-velocity equations of motion: (4-3) (4-4) (4-5) Common forces: Gravity Tension (in rope, string, wire, etc) Normal force (exerted by one surface on another)

9. 4-1 Forces and Newton’s First Law Relative Motion – who is at rest? No correct answer – each point of view is as good as the other

10. 4-2 Newton’s Second Law of Motion An object acted upon by a net force accelerates. (4-6,7)

11. 4-2 Newton’s Second Law of Motion Second law is more than just a definition of force: can use it to measure forces and masses, and to predict motion

12. 4-2 Newton’s Second Law of Motion Units of force: newtons (4-10) Observers in different reference frames agree on forces but disagree on velocities – cannot tell who is moving and who at rest by measuring forces

13. 4-3 Newton’s Third Law of Motion When a force due to object B acts on object A, then an equal and opposite force due to object A acts on object B. (4-15)

14. 4-4 Noninertial Frames Are they both accelerating downward, acceleration g? Or, as man sees he is at rest with respect to woman, and believes she should be subject to gravitational force but doesn’t feel one himself, is there something counteracting gravity?

15. 4-4 Noninertial Frames Answer can be found by identifying forces; if there are none that can account for motion, then frame must be accelerating.

16. 4-5 Using Newton’s Laws: Identifying Forces and Free-Body Diagrams A good free-body diagram is essential in solving force problems.

17. External and Internal Forces 4-5 Using Newton’s Laws: Identifying Forces and Free-Body Diagrams Look at two-block system – internal forces are those exerted by one block on the other (or within a single block) External forces come from outside the two blocks; net force in Newton’s second law is net external force

18. Forces on a sled: A sled sliding down a hill has three forces acting on it – gravity, the normal force, and friction 4-5 Using Newton’s Laws: Identifying Forces and Free-Body Diagrams

19. 4-5 Using Newton’s Laws: Identifying Forces and Free-Body Diagrams We see that two of the forces are at right angles to each other: and choose those as our coordinate axes:

20. 4-5 Using Newton’s Laws: Identifying Forces and Free-Body Diagrams More on drawing free-body diagrams: Identify and isolate object; make sketch with clear labels Identify and draw all forces, with reasonably accurate directions and magnitudes, emanating from a single point on object

21. 4-5 Using Newton’s Laws: Identifying Forces and Free-Body Diagrams More on drawing free-body diagrams (cont): Draw coordinate axes so that as many forces as possible are along one or the other Separate forces into components if necessary Arrow showing acceleration, if you draw one, should be clearly distinguishable from forces; same with net force

22. 4-6 Using Newton’s Laws: Finding the Motion Have found net force, and can then find acceleration – now need to use kinematics laws to find motion For constant force, acceleration is constant – have already developed equations for this Variable forces need to be treated individually

23. 4-6 Using Newton’s Laws: Finding the Motion Example: spring force This last equation is the one that will need to be solved for x(t) – later.

24. Summary of Chapter 4 Newton’s first law: if net force on object is zero, object moves with constant velocity Newton’s second law: (4-6,7) Units of force: newtons Newton’s third law: interacting objects exert equal and opposite forces on each other: (4-15)

25. Summary of Chapter 4, cont. Observers in different reference frames moving at constant velocity with respect to each other measure different velocities but the same forces – not true for accelerating frames If forces are known, can find motion of object, or vice versa Internal forces do not affect object’s motion