# Chapter 4 The Laws of Motion - PowerPoint PPT Presentation

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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

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

• 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/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

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*m2/kg2 = 6.67*10 –11 m3/(kg*s2) – universal constant

Gravity force at the surface of the Earth

g = 9.8 m/s2

• 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 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.

• 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 frictionμs

• Coefficient of kinetic frictionμk

• 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.

Chapter 4

Problem 2

25 N

Chapter 4

Problem 6

7.4 min

Chapter 4

Problem 26

4.43 m/s2 up the incline, 53.7 N

• Answers to the even-numbered problems

• Chapter 4

• Problem 40

• 55.2°;

• (b) 167 N

• Answers to the even-numbered problems

• Chapter 4

• Problem 50

• 18.5 N;

• (b) 25.8 N