Chapter 4 The Laws of Motion Newtonian mechanics

Chapter 4 The Laws of Motion

Newtonian mechanics Sir Isaac Newton (1643 – 1727) • 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

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

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

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

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

Newton’s Second Law • SI unit of force kg*m/s 2 = 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

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.

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

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

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*m 2/kg 2 = 6. 67*10 – 11 m 3/(kg*s 2) – universal constant

Gravity force at the surface of the Earth g = 9. 8 m/s 2

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

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

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

Free-body diagrams

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

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

Free-body diagrams

Free-body diagrams

Chapter 4 Problem 30 An object with mass m 1 = 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 m 2 = 10. 0 kg, as shown in the Figure. Find the acceleration of each object and the tension in the cable.

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)

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

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

Free-body diagrams

Free-body diagrams

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.

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

Answers to the even-numbered problems Chapter 4 Problem 6 7. 4 min

Answers to the even-numbered problems Chapter 4 Problem 26 4. 43 m/s 2 up the incline, 53. 7 N

Answers to the even-numbered problems Chapter 4 Problem 40 (a) 55. 2°; (b) 167 N

Answers to the even-numbered problems Chapter 4 Problem 50 (a) 18. 5 N; (b) 25. 8 N