PHSX 114, Wednesday, PHSX 114, Wednesday, September 10, 2003September 10, 2003

• Reading for today:Reading for today: Chapter 4 (4-5 -- 4-6) Chapter 4 (4-5 -- 4-6)

• Reading for next lecture (Fri.): Reading for next lecture (Fri.): Chapter 4 Chapter 4 (4-7 -- 4-9)(4-7 -- 4-9)

• Homework for today's lecture:Homework for today's lecture: Chapter 4, Chapter 4, questions 12, 14; problems 5, 6, 17questions 12, 14; problems 5, 6, 17

Last time: Newton's first and Last time: Newton's first and second laws of motionsecond laws of motion

• First law: What happens when there is no First law: What happens when there is no net force?net force?

• Second law: What happens when there is a Second law: What happens when there is a net force?net force?

Your turnYour turn

Answer: 2.5 m/sAnswer: 2.5 m/s22 , 53.1 degrees from the , 53.1 degrees from the x x directiondirection

aaxx=( F=( F1x1x+ F+ F2x2x)/m=(3 + 0)/2 = 1.5 m/s)/m=(3 + 0)/2 = 1.5 m/s22 , ,

aayy=( F=( F1y1y+ F+ F2y2y)/m=(0 + 4)/2 = 2 m/s)/m=(0 + 4)/2 = 2 m/s22

An object has mass 2 kg and two forces An object has mass 2 kg and two forces act upon it. Fact upon it. F11= 3 N in the += 3 N in the +xx direction, direction,

FF22= 4 N in the += 4 N in the +yy direction. Find the direction. Find the

magnitude and direction of the magnitude and direction of the acceleration vector.acceleration vector.

A force is applied by another A force is applied by another object in the environmentobject in the environment

• Two basic types: 1) contact, 2) action-at-a Two basic types: 1) contact, 2) action-at-a distance (fundamental forces are of second distance (fundamental forces are of second type)type)

• Newton's 3Newton's 3rdrd law discusses the relation law discusses the relation between the object feeling the force and the between the object feeling the force and the object applying the forceobject applying the force

Here's a stupid question that the Here's a stupid question that the first two laws don't address:first two laws don't address:

• Why can't I push myself across the floor?Why can't I push myself across the floor?

Newton's Third Law of MotionNewton's Third Law of Motion

• Whenever one object exerts a force on a Whenever one object exerts a force on a second object, the second object exerts a second object, the second object exerts a force on the first object that is equal in force on the first object that is equal in magnitude and opposite in direction.magnitude and opposite in direction.

• Action-reactionAction-reaction

• Example: woman pulling sledExample: woman pulling sled

Introducing two forcesIntroducing two forces

• Force of Earth's gravity on an objectForce of Earth's gravity on an object

• Contact force from a surfaceContact force from a surface

Weight vs. massWeight vs. mass

• FFGG==mmgg

• Weight is a vector (units of Newtons or Weight is a vector (units of Newtons or pounds)pounds)

• Mass is a scalar (units of kilograms)Mass is a scalar (units of kilograms)

• An object with a mass of 1 kg has a weight An object with a mass of 1 kg has a weight of 9.8 N (downward)of 9.8 N (downward)

• Note: Note: mm here is "gravitational mass" here is "gravitational mass"

Projectile motion and Newton's Projectile motion and Newton's lawslaws

• ΣΣFF==mmaa

• For projectile motion, only force is For projectile motion, only force is FFGG==mmgg

• ΣΣFF==mmaa==mmgg

• a=g; aa=g; axx=0, a=0, ayy=-9.8 m/s=-9.8 m/s22

Contact forces from a surfaceContact forces from a surface

• Normal force, FNormal force, FNN, is perpendicular to the , is perpendicular to the

surfacesurface

• Frictional force, FFrictional force, Ffrfr, is along the surface, is along the surface

• For today, we ignore friction, focus on For today, we ignore friction, focus on normal forcenormal force

Consider a block on a Consider a block on a horizontal surfacehorizontal surface

• ExamplesExamples

Your turnYour turn

• A 20-kg block is sitting on the table. You A 20-kg block is sitting on the table. You push down on the block with a force of 30 push down on the block with a force of 30 N. What is the normal force exerted by the N. What is the normal force exerted by the table on the block?table on the block?

• Answer: 226 NAnswer: 226 N

• FFNN= 30 N + (20 kg) (9.8 m/s= 30 N + (20 kg) (9.8 m/s22) = ) =

30 N + 196 N = 226 N30 N + 196 N = 226 N

Object on a vertical ropeObject on a vertical rope

• ΣF=ΣF=mma= Fa= FTT – F – FGG

• Elevator exampleElevator example

• FFGG==mmg doesn't change with elevator's accelerationg doesn't change with elevator's acceleration

• Tension in rope, FTension in rope, FTT, determines elevator's , determines elevator's

accelerationacceleration

• If a=0 (elevator has constant speed), FIf a=0 (elevator has constant speed), FTT = F = FGG

• If a>0 (elevator accelerating upward), FIf a>0 (elevator accelerating upward), FTT > F > FGG

• If a<0 (elevator accelerating downward), FIf a<0 (elevator accelerating downward), FTT < F < FGG