Understanding Newton’s Laws of Motion

1. Chapter 5 – Force and Motion I • Newton’s first law. • Newton’s second law. • Particular forces: • - Gravitational • - Weight • - Normal • - Friction • - Tension • IV. Newton’s third law.

2. Force • Forces are what cause any change in the velocity of an object • A force is that which causes an acceleration • The net force is the vector sum of all the forces acting on an object • Also called total force, resultant force, or unbalanced force

3. Zero Net Force • When the net force is equal to zero: • The acceleration is equal to zero • The velocity is constant • Equilibrium occurs when the net force is equal to zero • The object, if at rest, will remain at rest • If the object is moving, it will continue to move at a constant velocity

4. Classes of Forces • Contact forces involve physical contact between two objects • Field forces act through empty space • No physical contact is required

5. Fundamental Forces • Gravitational force • Between two objects • Electromagnetic forces • Between two charges • Nuclear (strong) force • Between subatomic particles • Weak forces • Arise in certain radioactive decay processes

6. A spring can be used to calibrate the magnitude of a force • Forces are vectors, so you must use the rules for vector addition to find the net force acting on an object

7. Newton mechanics laws cannot be applied when: 1) The speed of the interacting bodies are a fraction of the speed of light Einstein’s special theory of relativity. 2) The interacting bodies are on the scale of the atomic structure Quantum mechanics

8. I.Newton’s first law:If no net force acts on a body, then the body’s velocity cannot change; the body cannot accelerate  v = constant in magnitude and direction. Principle of superposition:when two or more forces act on a body, the net force can be obtained by adding the individual forces as vectors.

9. Newton’s First Law • If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration • This is also called the law of inertia • It defines a special set of reference frames called inertial frames, • We call this an inertial frame of reference Inertial reference frame:where Newton’s laws hold.

10. Inertial Frames • Any reference frame that moves with constant velocity relative to an inertial frame is itself an inertial frame • A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame • We can consider the Earth to be such an inertial frame although it has a small centripetal acceleration associated with its motion

11. Newton’s First Law – Alternative Statement • In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity • Newton’s First Law describes what happens in the absence of a force • Also tells us that when no force acts on an object, the acceleration of the object is zero

12. Inertia and Mass • The tendency of an object to resist any attempt to change its velocity is called inertia • Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity

13. Mass and Weight The weight of an object is the force of gravity on the object and may be defined as the mass times the acceleration of gravity, W = mg. Since the weight is a force, its SI unit is the newton. Density is mass/volume.

14. Mass and Weight The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object. Definitions of mass often seem circular because it is such a fundamental quantity that it is hard to define in terms of something else. All mechanical quantities can be defined in terms of mass, length, and time. The usual symbol for mass is m and its SI unit is the kilogram. While the mass is normally considered to be an unchanging property of an object, at speeds approaching the speed of light one must consider the increase in the relativistic mass.

15. Mass is an inherent property of an object • Mass is independent of the object’s surroundings • Mass is independent of the method used to measure it • Mass is a scalar quantity • The SI unit of mass is kg

16. Mass vs. Weight • Mass and weight are two different quantities • Weight is equal to the magnitude of the gravitational force exerted on the object • Weight will vary with location

17. Newton’s Second Law • When viewed from an inertial frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass • Force is the cause of change in motion, as measured by the acceleration • Algebraically, SF = m a

18. II. Newton’s second law: The net force on a body is equal to the product of the body’s mass and its acceleration. The acceleration component along a given axis is caused only by the sum of the force components along the same axis, and not by force components along any other axis.

19. Units of Force

20. System:collection of bodies. External force:any force on the bodies inside the system. III. Particular forces: Gravitational: pull directed towards a second body, normally the Earth  Weight: magnitude of the upward force needed to balance the gravitational force on the body due to an astronomical body 

21. Normal force: perpendicular force on a body from a surface against which the body presses. Frictional force:force on a body when the body attempts to slide along a surface. It is parallel to the surface and opposite to the motion.

22. Tension: pull on a body directed away from the body along a massless cord.

23. Newton’s Third Law • If two objects interact, the force F12exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2on object 1 • F12 = - F21 • Note on notation: FAB is the force exerted by Aon B

24. Newton’s Third Law, Alternative Statements • Forces always occur in pairs • A single isolated force cannot exist • The action force is equal in magnitude to the reaction force and opposite in direction • One of the forces is the action force, the other is the reaction force • It doesn’t matter which is considered the action and which the reaction • The action and reaction forces must act on different objects and be of the same type

25. Action-Reaction Examples • The force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to F21 exerted by object 2 on object 1 • F12 = - F21

26. Newton’s third law: When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction.

27. Q. A body suspended by a rope has a weigh Wof 75N. Is Tequal to, greater than, or less than 75N when the body is moving downward at (a) increasing speed and (b) decreasing speed? Fg

28. 5.There are two forces on the 2 kg box in the overhead view of the figure below but only one is shown. The figure also shows the acceleration of the box. Find the second force (a) in unit-vector notation and as (b) magnitude and (c) direction. F2

29. Rules to solve Dynamic problems • Select a reference system. • Make a drawing of the particle system. • Isolate the particles within the system. • Draw the forces that act on each of the isolated bodies. • Find the components of the forces present. • Apply Newton’s second law (F=ma) to each isolated particle.

30. 23. An electron with a speed of 1.2x107m/s moves horizontally into a region where a constant vertical force of 4.5x10-16N acts on it. The mass of the electron is m=9.11x10-31kg. Determine the vertical distance the electron is deflected during the time it has moved 30 mm horizontally. F dy v0 Fg dx=0.03m

31. 13. In the figure below, mblock=8.5kg and θ=30º, and the surface of incline is frictionless. Find (a) Tension in the cord. (b) Normal force acting on the block. (c) If the cord is cut, find the magnitude of the block’s acceleration. y x Fg N T

32. Friction • Related to microscopic interactions of surfaces • Friction is related to force holding surfaces together • Frictional forces are different depending on whether surfaces are static or moving

33. Kinetic Friction • When a body slides over a surface there is a force exerted by the surface on the body in the opposite direction to the motion of the body • This force is called kinetic friction • The magnitude of the force depends on the nature of the two touching surfaces • For a given pair of surfaces, the magnitude of the kinetic frictional force is proportional to the normal force exerted by the surface on the body.

34. + + Kinetic Friction The kinetic frictional force can be written as Where mk is a constant called the coefficient of kinetic friction The value of mkdepends on the surfaces involved FN = mg Fp m = 20.0 kg Ffr = mFN Fg = -mg

35. FN = -mg m Fg = mg Static Friction A frictional force can arise even if the body remains stationary • A block on the floor - no frictional force

36. FN = -mg Fp m Ffr = mFN Fg = mg Static Friction • If someone pushes the desk (but it does not move) then a static frictional force is exerted by the floor on the desk to balance the force of the person on the desk

37. FN = -mg m Fg = mg Static Friction • If the person pushes with a greater force and still does not manage to move the block, the static frictional force still balances it Fp Ffr = mFN

38. FN = -mg m Fg = mg Static Friction • If the person pushes hard enough, the block will move. • The maximum force of static friction has been exceeded Fp Ffr = mFN

39. Static Friction • The maximum force of static friction is given by • Static friction can take any value from zero to msFN • In other words

40. Forces on an incline • Often when solving problems involving Newton’s laws we will need to deal with resolving acceleration due to gravity on an inclined surface

41. q q Forces on an incline y What normal force does the surface exert? mgsinq mgcosq W = mg x

42. Forces on an incline

43. Forces on an incline

44. Equilibrium Forces on an incline

45. Forces on an incline • If the car is just stationary on the incline what is the (max) coefficient of static friction?

46. ‘Equilibrium’ problems (F = 0)

47. ‘Equilibrium’ problems (F = 0)

48. Connected Object problems • One problem often posed is how to work out acceleration of a system of masses connected via strings and/or pulleys • for example - Two blocks are fastened to the ceiling of an elevator.

49. Connected masses • Two 10 kg blocks are strung from an elevator roof, which is accelerating up at 2 m/s2. • Find T1 and T2 T1 a 2 m/s2 m1=10kg T2 m2=10kg

50. m1=1000kg T* T m2=10kg Connected masses • What is the acceleration of the system below, if T is 1000 N? • What is T*? a