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Chapter 4 The Laws of Motion. 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

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Chapter 4 The Laws of Motion

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Chapter 4 the laws of motion

Chapter 4

The Laws of Motion


Chapter 4 the laws of motion

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


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

  • Newton’s First Law

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


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

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.


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

  • Forces of different origins

  • Gravitational force

  • Normal force

  • Tension force

  • Frictional force (friction)

  • Drag force

  • Spring force


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

Gravity force at the surface of the Earth

g = 9.8 m/s2


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

Free-body diagrams


Chapter 4 the laws of motion

  • 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


Chapter 4 the laws of motion

  • Normal force

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


Chapter 4 the laws of motion

Free-body diagrams


Chapter 4 the laws of motion

Free-body diagrams


Chapter 4 the laws of motion

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.


Chapter 4 the laws of motion

  • 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)


Chapter 4 the laws of motion

  • Static friction and kinetic friction

  • Moving an object: static friction vs. kinetic


Chapter 4 the laws of motion

  • 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)


Chapter 4 the laws of motion

Free-body diagrams


Chapter 4 the laws of motion

Free-body diagrams


Chapter 4 the laws of motion

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.


Chapter 4 the laws of motion

Answers to the even-numbered problems

Chapter 4

Problem 2

25 N


Chapter 4 the laws of motion

Answers to the even-numbered problems

Chapter 4

Problem 6

7.4 min


Chapter 4 the laws of motion

Answers to the even-numbered problems

Chapter 4

Problem 26

4.43 m/s2 up the incline, 53.7 N


Chapter 4 the laws of motion

  • Answers to the even-numbered problems

  • Chapter 4

  • Problem 40

  • 55.2°;

  • (b) 167 N


Chapter 4 the laws of motion

  • Answers to the even-numbered problems

  • Chapter 4

  • Problem 50

  • 18.5 N;

  • (b) 25.8 N


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