Ballistic Cart Demo Discuss law of cosines for planeinwindb

problem Other HW problems?

Chapter 4Chapter 4

Forces and Mass

Classical MechanicsClassical Mechanics

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

Newton’s First LawNewton’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!

ForcesForces

Usually a push or pull Vector Either contact or field force

Contact and Field ForcesContact and Field Forces

Fundamental (Field) ForcesFundamental (Field) Forces

Types Strong nuclear force Electromagnetic force Weak nuclear force Gravity

Strong Nuclear ForceStrong Nuclear Force

QCD (Quantum chromodynamics) confines quarksby exchaning gluons

Nuclear force: binds protons and neutronsby exchanging pions

Electromagnetic ForcesElectromagnetic Forces

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

Weak Nuclear ForceWeak Nuclear Force

Involves exchange of heavy W or Z particle

Responsible for decay of neutrons

GravityGravity

Attractive force between any two bodies Proportional to both masses Inversely proportional to square of

distance

2

1 2

r

mmGF

Inertia (Newton’s First Law)Inertia (Newton’s First Law)

Tendency of an object to continue in its original motion

MassMass

A measure of the resistance of an object to changes in its motion due to a force

Scalar SI units are kg

Newton’s Second LawNewton’s Second Law

Acceleration is proportional to net force and inversely proportional to mass.

amF

Units of ForceUnits of Force

SI unit is Newton (N)

US Customary unit is pound (lb) 1 N = 0.225 lb

2s

mkg1N 1

maF

WeightWeight

Weight is magnitude of gravitational force

2

2

earthR

GMg

r

mMGw

mgw

earth

earth

weight

mass

Weight vs. MassWeight vs. Mass

Mass is an inherent property Weight depends on location

Newton’s Third LawNewton’s Third Law

Single isolated force cannot exist For every action there is an equal and

opposite reaction

2112 FF

Force on “1” due to “2”

Newton’s Third Law cont.Newton’s Third Law cont.

F12 is action force F21 is reaction force You can switch

action <-> reaction

Action & reaction forces act on different objects

Action-Reaction PairsAction-Reaction Pairs

'gg FF

nn

Define the Define the OBJECT OBJECT (free body)(free body)

Newton’s Law uses the forces acting ON object

n and Fg act on object

n’ and Fg’ act on other objects

Assumptions for F=maAssumptions for F=ma

Objects behave as particles ignore rotational motion (for now)

Consider only forces acting ON object neglect reaction forces

Problem Solving StrategyProblem 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!

Mechanical ForcesMechanical Forces

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

Some Rules for Ropes and PulleysSome 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)

EquilibriumEquilibrium

0F

Cable Pull DemoCable Pull Demo

Example 4.1Example 4.1

Given that Mlight = 25 kg, find all three tensions

T3 = 245.3 N, T1 = 147.4 N, T2 = 195.7 N

Example 4.2Example 4.2

2) Which statements are correct?Assume the objects are static.

A) T1 must = T2

B) T2 must = T3

C) T1 must be < MgD) T1+T2 must be > Mg

cos(10o)=0.985 sin(10o)=0.173

A) TB) TC) TD) T

Example 4.3Example 4.3

a) Find accelerationb) Find T, the tension above the bowling ballc) Find T3, the tension in the rope between the pailsd) Find force ceiling must exert on pulley

a) a = g/6 = 1.635 m/s2

b) T = 57.2 Nc) T3=24.5 Nd) Fpulley=2T = 114.5 N

Inclined PlanesInclined Planes

Choose x along the incline and y perpendicular to incline

Replace force of gravity with its components

cossin

,

,mgFmgF

yg

xg

Example 4.4Example 4.4

Find the acceleration and the tension

a = 4.43 m/s2, T= 53.7 N

Example 4.5Example 4.5

Find M such that the box slides at constant v

M=15.6 kg

M

Forces of FrictionForces of Friction

Resistive force between object and neighbors or the medium

Examples: Sliding a box Air resistance Rolling resistance

Sliding FrictionSliding Friction

Direction parallel to surface, opposite toother forces

Nearly independent of the area of contact

The coefficient of friction (µ) depends on the surfaces in contact

ks

k

sNfNf

Coefficients Coefficients of Frictionof Friction

ks

k

sNfNf

Static Friction, ƒStatic Friction, ƒss

s is coefficient of static friction

n is the normal force

FfnF ss

,If

f

F

Kinetic Kinetic Friction, ƒFriction, ƒkk

k is coefficient of kinetic friction

Friction force opposes F n is the normal force

nf

nF

k

s

,If

F

f

Friction DemoFriction Demo

Example 4.6Example 4.6

The man pushes/pulls with a force of 200 N. Thechild 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/s2 / f=29.1 N, a=4.8 m/s2

Example 4.7Example 4.7

Given m1 = 10 kg and m2 = 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/s2 c) 39.25 N

Example 4.8Example 4.8

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

s = 0.577

Other kinds of frictionOther kinds of friction

Air resistance, F ~ Area v2

Rolling resistance, F ~ v

Terminal velocity:

velocitylat termina

2resistance

mgCAvF

Coffee Filter DemoCoffee Filter Demo

Accelerating Reference FramesAccelerating Reference Frames

Equivalent to “Fictitious” gravitational force

framefictitious ag

Fictitious Force: DerivationFictitious Force: Derivation

200

20

)(

21

)(

21

)(

tm

maFtvtxx

tatx

f

f

20

20

2121

tmF

tv

attvx

Eq. of motion in fixed frame

F-maf looks like force in new frame, maf acts like fake gravitational force!

Example 4.9Example 4.9

An elevator falls with acceleration a = 8.0 m/s2. If a 200-lb person stood on a bathroom scale during the fall, what would the scale read?

36.9 lbs

Example 4.10Example 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/s2:a) At what angle does the ball swing backwards?b) What is the tension in the string?

=17 degT= 25.6 N