Chapter 3Chapter 3ForcesForces

I. Force & Acceleration Newton’s Second Law Friction Air Resistance Calculations

A. Newton’s Second LawA. Newton’s Second Law

Newton’s Second Law of Motion The acceleration of an object is

directly proportional to the net force acting on it and inversely proportional to its mass.

F = ma

F = maF: force (N)m: mass (kg)a: accel (m/s2)

1 N = 1 kg ·m/s2

am

F

a

Fm

B. CalculationsB. CalculationsWhat force would be required to

accelerate a 40 kg mass by 4 m/s2?

GIVEN:

F = ?

m = 40 kg

a = 4 m/s2

WORK:

F = ma

F = (40 kg)(4 m/s2)

F = 160 N

m

F

a

A 4.0 kg shotput is thrown with 30 N of force. What is its acceleration?

GIVEN:

m = 4.0 kg

F = 30 N

a = ?

WORK:

a = F ÷ m

a = (30 N) ÷ (4.0 kg)

a = 7.5 m/s2

m

F

a

• Suppose you give a skateboard a push with your hand.

• According to Newton’s first law of motion, if the net force acting on a moving object is zero, it will continue to move in a straight line with constant speed.

• Does the skateboard keep moving with constant speed after it leaves your hand?

C. FrictionC. Friction

• Recall that when an object slows down it is accelerating.

• By Newton’s second law, if the skateboard is accelerating, there must be a net force acting on it.

• The force that slows the skateboard and brings it to a stop is friction.

• Friction is the force that opposes the sliding motion of two surfaces that are touching each other.

• The amount of friction between two surfaces depends on two factorsthe kinds of surfaces and the force pressing the surfaces together.

• If two surfaces are in contact, welding or sticking occurs where the bumps touch each other.

• These microwelds are the source of friction.

• The larger the force pushing the two surfaces together is, the stronger these microwelds will be, because more of the surface bumps will come into contact.

Sticking Together

• To move one surface over the other, a force must be applied to break the microwelds.

• Suppose you have filled a cardboard box with books and want to move it.

Static Friction

• It’s too heavy to lift, so you start pushing on it, but it doesn’t budge.

• If the box doesn’t move, then it has zero acceleration.

• According to Newton’s second law, if the acceleration is zero, then the net force on the box is zero.

• Another force that cancels your push must be acting on the box.

• That force is the friction due to the microwelds that have formed between the bottom of the box and the floor.

• Static friction is the frictional force that prevents two surfaces from moving past each other.

• You ask a friend to help you move the box.

Sliding Friction

• Pushing together, the box moves. Together you and your friend have exerted enough force to break the microwelds between the floor and the bottom of the box.

• If you stop pushing, the box quickly comes to a stop.

• This is because as the box slides across the floor, another forcesliding frictionopposes the motion of the box.

• Sliding friction is the force that opposes the motion of two surfaces sliding past each other.

Rolling Friction

• As a wheel rolls over a surface, the wheel digs into the surface, causing both the wheel and the surface to be deformed.

• Static friction acts over the deformed area where the wheel and surface are in contact, producing a frictional force called rolling fiction.

• Rolling friction is the frictional force between a rolling object and the surface it rolls on.

D. Air ResistanceD. Air Resistance

Air Resistance a.k.a. “fluid friction” or “drag” force that air exerts on a moving

object to oppose its motion depends on:

• speed• surface area• shape• density of fluid

Terminal Velocity

maximum velocity reached by a falling object

reached when…

Fgrav = Fair

Fair

Fgrav

no net force no acceleration constant velocity

Falling with air resistance

Fgrav = Fair

heavier objects fall faster because they accelerate to higher speeds before reaching terminal velocity

larger Fgrav

need larger Fair

need higher speed

MythBusters!http://www.youtube.com/watch?v

=1Vjd_FhrohE

Chapter 3Chapter 3ForcesForces

II. Gravity Gravitational Force Projectile Motion Free fall and Weightlessness Calculations

A. GravityA. GravityGravity

Any two objects in the universe exert an attractive force on each other

increases as...

• mass increases

• distance between them decreases

• Force and mass are directly related

• All objects exert a pull on each other

Who experiences more gravity - the astronaut or the politician?

less distance

more mass

Which exerts more gravity -

the Earth or the moon?All matter accelerates toward Earth

at 9.8m/s2

Would you weigh more on Earth or Jupiter?

greater gravity

greater weight

greater mass

Jupiter because...

Accel. due to gravity (g) In the absence of air

resistance, all falling objects have the same acceleration!

On Earth: g = 9.8 m/s2

mW

g

Bowling ball

m

Wg

Feather

Weight The measure of the force of gravity

on an object

MASSalways the same (kg)

The amount of matter an object possesses (constant)

WEIGHTdepends on gravity (N)

On the moon: you’d weigh 1/6 of what you weigh on

Earth

W = mgW: weight (N)m: mass (kg)g: acceleration due

to gravity (m/s2)

Mrs. J. weighs 557 N. What is her mass?

GIVEN:

W = 557 N

m = ?

g = 9.8 m/s2

WORK:

m = W ÷ g

m = (557 N) ÷ (9.8 m/s2)

m = 56.8 kg

m

W

g

B. Projectile MotionB. Projectile Motion

Projectile any object thrown in

the air acted upon only by

gravity

follows a parabolic path called a trajectory

has horizontal and vertical velocitiesPROJECTILE MINI-LAB

Horizontal Velocity depends on inertia remains constant

Vertical Velocity depends on gravity accelerates downward

at 9.8 m/s2

Gravity is an unbalanced force

C. Circular MotionC. Circular Motion

Centripetal Acceleration acceleration toward the center of a

circular path caused by centripetal force

B-BALL DEMOPLATE DEMO

On the ground... friction provides centripetal force

Centripetal Force: friction between the tires and the road surface

• Car wants to keep moving in a straight line• Ice

In orbit... gravity provides centripetal force

ROUND LAB

• The Earth and the moon in orbit

D. Free-FallD. Free-Fall

Free-Fall when an object is influenced only

by the force of gravity

Weightlessness sensation produced when an object

and its surroundings are in free-fall object is not weightless!

CUP DEMO

Weightlessness surroundings are falling at the same

rate so they don’t exert a force on the object

Chapter 3Chapter 3ForcesForces

III. The Third Law of Motion Newton’s Third Law Momentum Conservation of Momentum

A. Newton’s Third LawA. Newton’s Third Law

Newton’s Third Law of Motion When one object exerts a

force on a second object, the second object exerts an equal but opposite force on the first.

Problem:

How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force?

NO!!!

Aren’t these “balanced forces” resulting in no acceleration?

forces are equal and opposite but act on different objects

they are not “balanced forces” the movement of the horse

depends on the forces acting on the horse

Explanation:

Action-reaction pairs

• Trampoline

• Row boat

• Sitting in a chair

• Billiards

• Jumping off a dock

Action-Reaction Pairs

The hammer exerts a force on the nail to the right.

The nail exerts an equal but opposite force on the hammer to the left.

Action-Reaction Pairs

The rocket exerts a downward force on the exhaust gases.

The gases exert an equal but opposite upward force on the rocket.

FG

FR

Action-Reaction PairsBoth objects accelerate.The amount of acceleration

depends on the mass of the object.

a Fm

Small mass more accelerationLarge mass less acceleration

p = mv

B. MomentumB. MomentumMomentum

A property that is due to mass and velocity (how much force is needed to change motion)

p: momentum (kg ·m/s)m: mass (kg)v: velocity (m/s)m

p

v

Find the momentum of a bumper car if it has a total mass of 280 kg and a velocity of 3.2 m/s.

GIVEN:

p = ?

m = 280 kg

v = 3.2 m/s

WORK:

p = mv

p = (280 kg)(3.2 m/s)

p = 896 kg·m/s

m

p

v

The momentum of a second bumper car is 675 kg·m/s. What is its velocity if its total mass is 300 kg?

GIVEN:

p = 675 kg·m/s

m = 300 kg

v = ?

WORK:

v = p ÷ m

v = (675 kg·m/s)÷(300 kg)

v = 2.25 m/s

m

p

v

C. Conservation of MomentumC. Conservation of Momentum

Law of Conservation of Momentum The total momentum in a group of

objects doesn’t change unless outside forces act on the objects.

pbefore = pafter

Elastic Collision KE is conserved

Inelastic Collision KE is not conserved

Momentum doesn’t change unless the object’s mass, velocity or both change When objects collide,

momentum is transferred

• Billiards, bowling

A 5-kg cart traveling at 1.2 m/s strikes a stationary 2-kg cart and they connect. Find their speed after the collision.

BEFORECart 1:m = 5 kgv = 4.2 m/s

Cart 2 :m = 2 kgv = 0 m/s

AFTERCart 1 + 2:m = 7 kgv = ?

p = 21 kg·m/s

p = 0

pbefore = 21 kg·m/s pafter = 21 kg·m/s

m

p

vv = p ÷ mv = (21 kg·m/s) ÷ (7 kg)v = 3 m/s

Some math to prove the Law of Conservation of Momentum

A 50-kg clown is shot out of a 250-kg cannon at a speed of 20 m/s. What is the recoil speed of the cannon?

BEFOREClown:m = 50 kgv = 0 m/s

Cannon:m = 250 kgv = 0 m/s

AFTERClown:m = 50 kgv = 20 m/s

Cannon:m = 250 kgv = ? m/s

p = 0

p = 0

pbefore = 0

p = 1000 kg·m/s

pafter = 0

p = -1000 kg·m/s