ForcesForces

Chapter 4Chapter 4

ForcesForces

A push or a pullA push or a pull

GravitationalGravitational ElectromagneticElectromagnetic WeakWeak StrongStrong

Sir Isaac NewtonSir Isaac Newton

Newton’s First LawNewton’s First Law An object in motion remains in motion An object in motion remains in motion

and an object at rest remains at rest and an object at rest remains at rest unless acted on by an outside force.unless acted on by an outside force.

Sometimes called the Law of InertiaSometimes called the Law of Inertia ExamplesExamples

Sudden brakingSudden braking Flooring itFlooring it Seeing starsSeeing stars

InertiaInertia

A body’s tendency to keep doing what it’s A body’s tendency to keep doing what it’s already doingalready doing

Measured by massMeasured by mass Does not need gravitational force.Does not need gravitational force.

Newton’s Second LawNewton’s Second Law

The acceleration of an object is directly The acceleration of an object is directly proportional to the force on the object proportional to the force on the object and inversely proportional to the mass.and inversely proportional to the mass.

maF

UnitsUnits

Ns

mkgmaF

2

NewtonsNewtons English equivalent is English equivalent is

poundspounds 4.45N=1lb4.45N=1lb

PracticePractice A 2988kg elephant accelerates on a A 2988kg elephant accelerates on a

skateboard at a rate of 2.7m/sskateboard at a rate of 2.7m/s22. If the . If the elephant is being pushed with a 10,000N elephant is being pushed with a 10,000N force, what is the force of friction?force, what is the force of friction?

A 58.7N force is applied to a go kart to get it A 58.7N force is applied to a go kart to get it started. If the car starts from rest and started. If the car starts from rest and accelerates for 4.0s covering a distance of accelerates for 4.0s covering a distance of 7.8m, what is the mass of the kart?7.8m, what is the mass of the kart?

Newton’s Third LawNewton’s Third Law When one object exerts a force on a When one object exerts a force on a

second object, the second object exerts second object, the second object exerts a force on the first of equal magnitude a force on the first of equal magnitude and opposite directionand opposite direction

Action-reaction pairsAction-reaction pairs Switch the nounsSwitch the nouns

WeightWeight Weight and gravitational force are the same Weight and gravitational force are the same

thing.thing. Since acceleration due to gravity (g) is known, Since acceleration due to gravity (g) is known,

we can define weight as:we can define weight as:

mgFg In general, we will take care of directional In general, we will take care of directional

information (positives and negatives) in the information (positives and negatives) in the problem itself, so we will use +9.8m/sproblem itself, so we will use +9.8m/s22 instead instead of -9.8m/sof -9.8m/s22

Skydiving and Terminal Skydiving and Terminal VelocityVelocity

Practice ProblemsPractice Problems A skydiver reaches a terminal velocity A skydiver reaches a terminal velocity

of 55m/s when in free fall. If the of 55m/s when in free fall. If the skydiver has a mass of 78kg, how much skydiver has a mass of 78kg, how much force is air resistance providing?force is air resistance providing?

When starting up the elevator, a rider When starting up the elevator, a rider experiences an acceleration of 1.2m/sexperiences an acceleration of 1.2m/s22. . If the force from the elevator floor is If the force from the elevator floor is 650N, what is the mass of the rider?650N, what is the mass of the rider?

Normal ForceNormal Force Force pushing up from a surfaceForce pushing up from a surface When vertical acceleration is zero and the When vertical acceleration is zero and the

only two vertical forces are gravity and normal only two vertical forces are gravity and normal force, normal force and gravity are equal.force, normal force and gravity are equal.

Scales read normal forceScales read normal force ElevatorsElevators Weightlessness (Weightlessness (Newton’s MountainNewton’s Mountain))

FrictionFriction

Depends only on the surfaces, not on velocityDepends only on the surfaces, not on velocity Kinetic and static frictionKinetic and static friction Depends on two things, normal force of the object Depends on two things, normal force of the object

and the combination of surfacesand the combination of surfaces Coefficient of friction, Coefficient of friction, µ equals the ratio of frictional µ equals the ratio of frictional

force to normal force.force to normal force.

Nfr FF

PracticePractice

A 16.8 kg crate is pushed horizontally A 16.8 kg crate is pushed horizontally along the floor with a force of 207N. If along the floor with a force of 207N. If the coefficient of friction is 0.62, what is the coefficient of friction is 0.62, what is the acceleration of the crate?the acceleration of the crate?

A sled is pulled across the snow with a A sled is pulled across the snow with a constant velocity. If the sled has a constant velocity. If the sled has a mass of 32.1kg and the coefficient of mass of 32.1kg and the coefficient of kinetic friction is 0.14, what is the kinetic friction is 0.14, what is the magnitude of the pull?magnitude of the pull?

A bunch of guys try to push a car out of A bunch of guys try to push a car out of the mud. They push harder and harder the mud. They push harder and harder until it becomes unstuck and then push until it becomes unstuck and then push with a constant force. If the coefficient with a constant force. If the coefficient of static friction is 0.54 and the of static friction is 0.54 and the coefficient of kinetic friction is 0.40, what coefficient of kinetic friction is 0.40, what is the acceleration of the car once it is the acceleration of the car once it starts moving? starts moving?

A crate of chickens is pulled with 145N A crate of chickens is pulled with 145N of force with a rope that is inclined 30of force with a rope that is inclined 30° ° up from the horizontal. If the crate has up from the horizontal. If the crate has a mass of 35kg and the coefficient of a mass of 35kg and the coefficient of friction between the floor and the crate friction between the floor and the crate is 0.43, what is:is 0.43, what is: The normal force on the crate?The normal force on the crate? The acceleration of the crate, assuming it The acceleration of the crate, assuming it

accelerates horizontally.accelerates horizontally.

TensionTension

Upward force coming from a string or Upward force coming from a string or rope. rope.

All vertical ropes supporting an object All vertical ropes supporting an object account for an equal amount of force account for an equal amount of force unless specified otherwise.unless specified otherwise.

Atwood Machine ProblemsAtwood Machine Problems AssumptionsAssumptions

• aa11= a= a22

• FFT1T1= F= FT2T2

Pulley switches which Pulley switches which direction is positive.direction is positive.

Consider the direction Consider the direction of motion of the box to of motion of the box to be the positive be the positive direction.direction.

m1

m2

•If mass 1 is 5kg and mass 2 is 7kg, what is the acceleration of the system?

Box 1Box 1

amFF gT 1

maF

Fg

FT

a

amgmFT 11

Box 2Box 2

amFF Tg 2 maF

Fg

FT

a amFgm T 22

Putting it togetherPutting it together

amgmFT 11 amFgm T 22

amgmFT 11 TFamgm 22

amgmamgm 2211

gmgmamam 1212

Putting it together cont.Putting it together cont.

gmgmamm 1212 )(

gmgmamam 1212

2

21

12 63.1s

mmm

gmgma

Practice ProblemPractice Problem

mm11=8kg=8kg

mm22=4kg=4kg

Find FFind FTT

m1

m2

Sign ProblemsSign Problems

Equilibrium-the state where all forces are Equilibrium-the state where all forces are balanced and acceleration is zero.balanced and acceleration is zero.

Includes both stationary and constant Includes both stationary and constant velocity cases.velocity cases.

11stst Example Example

If the sign has a mass of If the sign has a mass of 15kg, what is the tension in 15kg, what is the tension in the string? What is the the string? What is the force the beam exerts on force the beam exerts on the sign?the sign?

Assume equilibrium.Assume equilibrium. One component at a time.One component at a time.

Set up equilibrium caseSet up equilibrium case

0

0

vertical

horizontal

F

F

cos

sin

Tx

Ty

FF

FF

Fy

Fx

FT

23

Fg

Fbeam

Equilibrium case for Equilibrium case for verticalvertical

0sin mgFT

0 gy FF

Nmg

FT 2.376sin

0verticalF

Equilibrium case for Equilibrium case for horizontalhorizontal

0horizontalF

0 Beamx FF

0cos BeamT FF

BeamT FF cos

N3.34623cos2.376

Practice Problem 2Practice Problem 2

Find the tension in Find the tension in each rope.each rope.

T1T2

Break up ComponentsBreak up Components

111 sinFFy

222 sinFFy

111 cosFFx

222 cosFFx

F1 F2

Fx1 Fx2

Fy1 Fy2

Fg

Horizontal PiecesHorizontal Pieces Since the sign isn’t Since the sign isn’t

accelerating accelerating horizontally, we can horizontally, we can use:use: 021 xx FF

0coscos 2211 FF

2211 coscos FF

0 xF

Fx1 Fx2

Fy1 Fy2

Fg

Vertical PiecesVertical Pieces Since the sign isn’t Since the sign isn’t

accelerating accelerating vertically, we can vertically, we can use:use: 021 gyy FFF

0sinsin 2211 mgFF

0 F

Fx1 Fx2

Fy1 Fy2

Fg

Putting the two togetherPutting the two together

0sinsincos

cos221

1

22

mgF

F

0sinsin 2211 mgFF 2211 coscos FF

1

221 cos

cos

F

F

Putting the two together Putting the two together cont.cont.

mgFF

221

1

22 sinsincos

cos

mgF

21

1

22 sinsincos

cos

211

2

2

sinsincoscos

mgF

Putting the two together Putting the two together cont.cont.

NF 383

62sin34sin34cos62cos

8.9472

NF

F 6.214cos

cos

1

221

Ramp ProblemsRamp Problems

Practice ProblemsPractice Problems

A box slides down a frictionless ramp. If the A box slides down a frictionless ramp. If the box has a mass of 12kg and the ramp is box has a mass of 12kg and the ramp is inclined at an angle of 32 degrees, what is the inclined at an angle of 32 degrees, what is the acceleration of the box?acceleration of the box?

A 76kg box slides down a ramp inclined at 21 A 76kg box slides down a ramp inclined at 21 degrees. If the acceleration of the box is degrees. If the acceleration of the box is 1.2m/s1.2m/s22, what is the coefficient of friction , what is the coefficient of friction between the box and the ramp?between the box and the ramp?

Random Practice Random Practice ProblemsProblems

A 28kg box is pulled at an angle of 18A 28kg box is pulled at an angle of 18oo up up from the horizontal with a force of 145N. from the horizontal with a force of 145N. If the coefficient of friction between the If the coefficient of friction between the floor and the box is .32, what is the floor and the box is .32, what is the acceleration of the box?acceleration of the box?

A dead pig has a A dead pig has a µµkk of .21 and a µ of .21 and a µss

of .43 when sitting on a book cover, how of .43 when sitting on a book cover, how far will the book cover need to be tilted far will the book cover need to be tilted to start the pig carcass moving? Once to start the pig carcass moving? Once it starts moving, how quickly will it it starts moving, how quickly will it accelerate?accelerate?

mm11=13kg=13kg

mm22=9kg=9kg

μμkk=.11=.11

What is a?What is a?