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Chapter 4 Forces and Mass

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**Classical Mechanics Conditions when Classical Mechanics does not apply**

very tiny objects (< atomic sizes) objects moving near the speed of light

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Newton’s First Law If the net force SF exerted on an object is zerok the object continues in its original state of motion. That is, if SF = 0, an object at rest remains at rest and an object moving with some velocity continues with the same velocity. Contrast with Aristotle!

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**Forces Usually think of a force as a push or pull Vector quantity**

May be contact or field force

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**Contact and Field Forces**

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**Fundamental Forces Types Characteristics Strong nuclear force**

Electromagnetic force Weak nuclear force Gravity Characteristics All field forces Listed in order of decreasing strength Only gravity and electromagnetic in mechanics

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**Fundamental Forces Types Characteristics Strong nuclear force**

Electromagnetic force Weak nuclear force Gravity Characteristics All field forces Listed in order of decreasing strength Only gravity and electromagnetic in mechanics

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Strong Nuclear Force QCD (Quantum chromodynamics) confines quarks to interior of protons and neutrons Force between protons and neutrons responsible for formation of nuclei QCD: Exchange of gluons Nuclear Force: Exchange of pions

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**Electromagnetic Force**

Opposites attract, like-signs repel Electric force responsible for binding of electrons to atoms and atoms to each other Magnetic forces arise from moving charges and currents Electric motors exploit magnetic forces

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**Electromagnetic Force**

Opposites attract, like-signs repel Electric force responsible for binding of electrons to atoms and atoms to each other Magnetic forces arise from moving charges and currents Electric motors exploit magnetic forces

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**Weak Nuclear Force Involves exchange of heavy W or Z particle**

Responsible for decay of neutrons

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**Gravity Attractive force between any two bodies**

Proportional to both masses Inversely proportional to square of distance

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Inertia Tendency of an object to continue in its original motion

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Mass A measure of the resistance of an object to changes in its motion due to a force Scalar quantity SI units are kg

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Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. F and a are both vectors

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**Units of Force SI unit of force is a Newton (N)**

US Customary unit of force is a pound (lb) 1 N = lb See table 4.1

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Weight The magnitude of the gravitational force acting on an object of mass m near the Earth’s surface is called the weight w of the object

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**Weight and Mass Mass is an inherent property**

Weight is not an inherent property of an object Weight depends on location

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Newton’s Third Law If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1. Equivalent to saying a single isolated force cannot exist For every action there is an equal and opposite reaction

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**Newton’s Third Law cont.**

F12 may be called the action force and F21 the reaction force Either force can be the action or the reaction force The action and reaction forces act on different objects

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**Some Action-Reaction Pairs**

n and n’ n is the normal force, the force the table exerts on the TV n is always perpendicular to the surface n’ is the reaction – the TV on the table n = - n’

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**More Action-Reaction pairs**

Fg and Fg’ Fg is the force the Earth exerts on the object Fg’ is the force the object exerts on the earth Fg = -Fg’

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**Forces Acting on an Object**

Newton’s Law uses the forces acting on an object n and Fg are acting on the object n’ and Fg’ are acting on other objects

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**Applying Newton’s Laws**

Assumptions Objects behave as particles ignore rotational motion (for now) Masses of strings or ropes are negligible Interested only in the forces acting on the object neglect reaction forces

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**Problem Solving Strategy**

Make a free-body diagram Identify object (free body) Label all forces acting on object Resolve forces into x- and y-components, using convenient coordinate system Apply equations, keep track of signs!

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**Examples of Mechanical Forces**

Strings, ropes and Pulleys Gravity Normal forces Friction Springs (later in the book)

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**Some Rules for Ropes and Pulleys**

When a rope is attached to an object, the force of the rope on that object is away from that object The magnitude of the force is called the tension The tension does not change when going over a pulley (if frictionless)

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Equilibrium An object either at rest or moving with a constant velocity is said to be in equilibrium The net force acting on the object is zero

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Do Cable Pull Demo

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Example Given that Mlight = 25 kg, find all three tensions T3 = 245.3, T1 = kg, T2 = kg

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**Example a) Find acceleration b) Find T c) Find T3**

d) Find force ceiling must exert on pulley a) a=g/6, b) T = 57.2 N c) T3=24.5 N, d) Fpulley=2T = N

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Inclined Planes Choose x along the incline and y perpendicular to incline Replace force of gravity with its components

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Example Find the acceleration and the tension a = 4.43 m/s2, T= 53.7 N

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Forces of Friction Resistive force between object and neighbors or the medium Examples: Sliding a box Air resistance Rolling resistance

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**Sliding Friction Proportional to the normal force**

Direction is parallel to surface and opposite other forces Force of friction is nearly independent of the area of contact The coefficient of friction (µ) depends on the surfaces in contact

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**Coefficients of Friction**

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**Static Friction, ƒs f F ms is coefficient of static friction**

n is the normal force f F

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**Kinetic Friction, ƒk f F mk is coefficient of kinetic friction**

Friction force opposes F n is the normal force F

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Example The man pushes/pulls with a force of 200 N. The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is For each case: What is the frictional force opposing his efforts? What is the acceleration of the child? f=59 N, a=4.7 m/s / f=29.1 N, a=5.7 m/s2

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**Example Given m1 = 10 kg and m2 = 5 kg:**

a) What value of ms would stop the block from sliding? b) If the box is sliding and mk = 0.2, what is the acceleration? c) What is the tension of the rope? ms = 0.5, a=1.96 m/s2

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Example What is the minimum ms required to prevent the sled from slipping down a hill of slope 30 degrees? ms = 0.577

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Example You are calibrating an accelerometer so that you can measure the steady horizontal acceleration of a car by measuring the angle a ball swings backwards. If M = 2.5 kg and the acceleration, a = 3.0 m/s2: a) At what angle does the ball swing backwards? b) What is the tension in the string? q = 17 deg T= 25.6 N q

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Quiz, All Sections 1) What is your section number?

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**Quiz, Section 1 A only A and B only A, B and C only All statements**

2) Which statements are correct? Assume the objects are static. A) T1 must = T2 B) T2 must = T3 C) T1 must be < Mg D) T1+T2 must be > Mg A only A and B only A, B and C only All statements None of the statements cos(10o)= sin(10o)=0.173

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**Quiz, Section 2 A only A and B only A, B and C only All statements**

2) Which statements are correct? Assume the objects are static. A) T1 must = T2 B) T2 must = T3 C) T1 must be < Mg D) T1+T2 must be > Mg A only A and B only A, B and C only All statements None of the statements cos(10o)= sin(10o)=0.173

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**Quiz, Section 3 A only A and B only A, B and C only All statements**

2) Which statements are correct? Assume the objects are static. A) T1 must = T2 B) T2 must = T3 C) T1 must be < Mg D) T1+T2 must be > Mg A only A and B only A, B and C only All statements None of the statements cos(10o)= sin(10o)=0.173

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