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1. Chapter 4 The Laws of Motion

2. Sir Isaac Newton (1643 – 1727) • Newtonian mechanics • Describes motion and interaction of objects • Applicable for speeds much slower than the speed of light • Applicable on scales much greater than the atomic scale • Applicable for inertial reference frames – frames that don’t accelerate themselves

3. Force • What is a force? • Colloquial understanding of a force – a push or a pull • Forces can have different nature • Forces are vectors • Several forces can act on a single object at a time – they will add as vectors

4. Force superposition • Forces applied to the same object are adding as vectors – superposition • The net force – a vector sum of all the forces applied to the same object

5. Newton’s First Law • If the net force on the body is zero, the body’s acceleration is zero

6. Newton’s Second Law • If the net force on the body is not zero, the body’s acceleration is not zero • Acceleration of the body is directly proportional to the net force on the body • The coefficient of proportionality is equal to the mass (the amount of substance) of the object

7. Newton’s Second Law • SI unit of force kg*m/s2 = N (Newton) • Newton’s Second Law can be applied to all the components separately • To solve problems with Newton’s Second Law we need to consider a free-body diagram • If the system consists of more than one body, only external forces acting on the system have to be considered • Forces acting between the bodies of the system are internal and are not considered

8. Chapter 4 Problem 12 Two forces are applied to a car in an effort to move it. (a) What is the resultant of these two forces? (b) If the car has a mass of 3 000 kg, what acceleration does it have? Ignore friction.

9. Newton’s Third Law • When two bodies interact with each other, they exert forces on each other • The forces that interacting bodies exert on each other, are equal in magnitude and opposite in direction

10. Forces of different origins • Gravitational force • Normal force • Tension force • Frictional force (friction) • Drag force • Spring force

11. Gravity force (a bit of Ch. 7) • Any two (or more) massive bodies attract each other • Gravitational force (Newton's law of gravitation) • Gravitational constant G = 6.67*10 –11 N*m2/kg2 = 6.67*10 –11 m3/(kg*s2) – universal constant

12. Gravity force at the surface of the Earth g = 9.8 m/s2

13. Gravity force at the surface of the Earth • The apple is attracted by the Earth • According to the Newton’s Third Law, the Earth should be attracted by the apple with the force of the same magnitude

14. Weight • Weight (W) of a body is a force that the body exerts on a support as a result of gravity pull from the Earth • Weight at the surface of the Earth: W = mg • While the mass of a body is a constant, the weight may change under different circumstances

15. Tension force • A weightless cord (string, rope, etc.) attached to the object can pull the object • The force of the pull is tension ( T ) • The tension is pointing away from the body

16. Free-body diagrams

17. Normal force • When the body presses against the surface (support), the surface deforms and pushes on the body with a normal force (n) that is perpendicular to the surface • The nature of the normal force – reaction of the molecules and atoms to the deformation of material

18. Normal force • The normal force is not always equal to the gravitational force of the object

19. Free-body diagrams

20. Free-body diagrams

21. Chapter 4 Problem 30 An object with mass m1 = 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 10.0 kg, as shown in the Figure. Find the acceleration of each object and the tension in the cable.

22. Frictional force • Friction ( f) - resistance to the sliding attempt • Direction of friction – opposite to the direction of attempted sliding (along the surface) • The origin of friction – bonding between the sliding surfaces (microscopic cold-welding)

23. Static friction and kinetic friction • Moving an object: static friction vs. kinetic

24. Friction coefficient • Experiments show that friction is related to the magnitude of the normal force • Coefficient of static frictionμs • Coefficient of kinetic frictionμk • Values of the friction coefficients depend on the combination of surfaces in contact and their conditions (experimentally determined)

25. Free-body diagrams

26. Free-body diagrams

27. Chapter 4 Problem 49 Find the acceleration reached by each of the two objects shown in the figure if the coefficient of kinetic friction between the 7.00-kg object and the plane is 0.250.

28. Answers to the even-numbered problems Chapter 4 Problem 2 25 N

29. Answers to the even-numbered problems Chapter 4 Problem 6 7.4 min

30. Answers to the even-numbered problems Chapter 4 Problem 26 4.43 m/s2 up the incline, 53.7 N

31. Answers to the even-numbered problems • Chapter 4 • Problem 40 • 55.2°; • (b) 167 N

32. Answers to the even-numbered problems • Chapter 4 • Problem 50 • 18.5 N; • (b) 25.8 N