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Ballistic Cart Demo Discuss law of cosines for planeinwindb problem Other HW problems?

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Chapter 4 Forces and Mass

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Classical Mechanics does not apply for very tiny objects (< atomic sizes) objects moving near the speed of light

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Newton’s First Law If the net force F exerted on an object is zero the object continues in its original state of motion. That is, if F = 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 a push or pull Vector Either contact or field force

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Contact and Field Forces

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Fundamental (Field) Forces Types Strong nuclear force Electromagnetic force Weak nuclear force Gravity

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Strong Nuclear Force QCD (Quantum chromodynamics) confines quarks by exchaning gluons Nuclear force: binds protons and neutrons by exchanging pions

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Electromagnetic Forces Opposites attract, like-signs repel Electric forces bind electrons in atoms Magnetic forces arise from moving charges

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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 (Newton’s First Law) 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 SI units are kg

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Newton’s Second Law Acceleration is proportional to net force and inversely proportional to mass.

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Units of Force SI unit is Newton (N) US Customary unit is pound (lb) 1 N = 0.225 lb

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Weight Weight is magnitude of gravitational force weight mass

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Weight vs. Mass Mass is an inherent property Weight depends on location

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Newton’s Third Law Single isolated force cannot exist For every action there is an equal and opposite reaction Force on “1” due to “2”

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Newton’s Third Law cont. F 12 is action force F 21 is reaction force You can switch action reaction Action & reaction forces act on different objects

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Action-Reaction Pairs

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Define the OBJECT (free body) Newton’s Law uses the forces acting ON object n and F g act on object n’ and F g ’ act on other objects

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Assumptions for F=ma Objects behave as particles ignore rotational motion (for now) Consider only forces acting ON object neglect reaction forces

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Problem Solving Strategy 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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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 Force from rope points AWAY from object Magnitude of the force is called tension Tension does not change when going over a pulley (if frictionless)

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Equilibrium

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Cable Pull Demo

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Example 4.1 Given that M light = 25 kg, find all three tensions T 3 = 245.3 N, T 1 = 147.4 N, T 2 = 195.7 N

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Example 4.2 2) Which statements are correct? Assume the objects are static. A) T 1 must = T 2 B) T 2 must = T 3 C) T 1 must be < Mg D) T 1 +T 2 must be > Mg cos(10 o )=0.985 sin(10 o )=0.173 A) T B) T C) T D) T

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Example 4.3 a) Find acceleration b) Find T, the tension above the bowling ball c) Find T 3, the tension in the rope between the pails d) Find force ceiling must exert on pulley a) a = g/6 = 1.635 m/s 2 b) T = 57.2 N c) T 3 =24.5 N d) F pulley =2T = 114.5 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 4.4 Find the acceleration and the tension a = 4.43 m/s 2, T= 53.7 N

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Example 4.5 Find M such that the box slides at constant v M=15.6 kg M

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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 Direction parallel to surface, opposite to other forces 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, ƒ s s is coefficient of static friction n is the normal force f F

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Kinetic Friction, ƒ k k is coefficient of kinetic friction Friction force opposes F n is the normal force F f

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Friction Demo

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Example 4.6 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 0.15. For each case: What is the frictional force opposing his efforts? What is the acceleration of the child? f=59 N, a=3.80 m/s 2 / f=29.1 N, a=4.8 m/s 2

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Example 4.7 Given m 1 = 10 kg and m 2 = 5 kg: a) What value of s would stop the block from sliding? b) If the box is sliding and k = 0.2, what is the acceleration? c) What is the tension of the rope? a) s = 0.5 b) a=1.96 m/s 2 c) 39.25 N

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Example 4.8 What is the minimum s required to prevent a sled from slipping down a hill of slope 30 degrees? s = 0.577

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Other kinds of friction Air resistance, F ~ Area v 2 Rolling resistance, F ~ v Terminal velocity:

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Coffee Filter Demo

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Accelerating Reference Frames Equivalent to “Fictitious” gravitational force

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Fictitious Force: Derivation Eq. of motion in fixed frame F-ma f looks like force in new frame, ma f acts like fake gravitational force!

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Example 4.9 An elevator falls with acceleration a = 8.0 m/s 2. If a 200-lb person stood on a bathroom scale during the fall, what would the scale read? 36.9 lbs

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Example 4.10 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/s 2 : a) At what angle does the ball swing backwards? b) What is the tension in the string? = 17 deg T= 25.6 N

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