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Chapter 4 The Laws of Motion

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**Newtonian mechanics Describes motion and interaction of objects**

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

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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

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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

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

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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

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**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

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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 kg, what acceleration does it have? Ignore friction.

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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

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**Forces of different origins**

Gravitational force Normal force Tension force Frictional force (friction) Drag force Spring force

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**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

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**Gravity force at the surface of the Earth**

g = 9.8 m/s2

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**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

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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

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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

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Free-body diagrams

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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

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

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Free-body diagrams

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Free-body diagrams

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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.

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**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)

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**Static friction and kinetic friction**

Moving an object: static friction vs. kinetic

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**Friction coefficient Coefficient of kinetic friction μk**

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)

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Free-body diagrams

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Free-body diagrams

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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

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**Answers to the even-numbered problems**

Chapter 4 Problem 2 25 N

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**Answers to the even-numbered problems**

Chapter 4 Problem 6 7.4 min

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**Answers to the even-numbered problems**

Chapter 4 Problem 26 4.43 m/s2 up the incline, 53.7 N

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**Answers to the even-numbered problems**

Chapter 4 Problem 40 55.2°; (b) 167 N

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**Answers to the even-numbered problems**

Chapter 4 Problem 50 18.5 N; (b) 25.8 N

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University Physics: Mechanics

University Physics: Mechanics

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