Motion & ForcesMotion & ForcesLesson 1Lesson 1

Force & AccelerationForce & Acceleration Newton’s Second LawNewton’s Second Law Air ResistanceAir Resistance CalculationsCalculations

Newton’s Second LawNewton’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

Force and Acceleration Force and Acceleration

What’s different about What’s different about throwing a ball throwing a ball horizontally as hard horizontally as hard as you can and as you can and tossing it gently?tossing it gently?

When you throw hard, When you throw hard, you exert a much you exert a much greater greater forceforce on the on the ball.ball.

Force and Acceleration Force and Acceleration

The hard-thrown ball has a greater The hard-thrown ball has a greater change in change in velocityvelocity, and the change , and the change occurs over a shorter period of time.occurs over a shorter period of time.

Recall that acceleration is the change Recall that acceleration is the change in velocity divided by the in velocity divided by the timetime it it takes for the change to occur. takes for the change to occur.

So, a hard-thrown ball has a greater So, a hard-thrown ball has a greater accelerationacceleration than a gently thrown than a gently thrown ball. ball.

Mass and AccelerationMass and Acceleration

• If you throw a softball and a baseball If you throw a softball and a baseball as hard as you can, why don’t they as hard as you can, why don’t they have the same speed?have the same speed?

• The difference is due to their The difference is due to their massesmasses. .

• If it takes the same amount of time If it takes the same amount of time to throw both balls, the softball to throw both balls, the softball would have less.would have less.

• ForceForce, mass, acceleration and , mass, acceleration and acceleration are related. acceleration are related.

Newton’s Second LawNewton’s Second Law

• The acceleration of an object The acceleration of an object depends ondepends on its mass as well as the its mass as well as the forceforce exerted on it. exerted on it.

• Newton’s second law also can be Newton’s second law also can be used to calculate the net force if used to calculate the net force if massmass and acceleration are known. and acceleration are known.

• To do this, the equation for Newton’s To do this, the equation for Newton’s second law must be solved for the second law must be solved for the net force, net force, FF..

Newton’s Second LawNewton’s Second Law

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

1 N = 1 kg ·m/s2

aa

F

m

Fm

FrictionFriction

Suppose you give a skateboard a Suppose you give a skateboard a pushpush with your hand. with your hand.

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

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

FrictionFriction

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

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

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

FrictionFriction

Friction is the force that Friction is the force that opposesopposes motion between surfaces that touch motion between surfaces that touch each other.each other. Depends on two factors: The kinds of Depends on two factors: The kinds of

surfaces and the force pressing the surfaces and the force pressing the surfaces together. surfaces together.

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

• These microwelds are the source of These microwelds are the source of frictionfriction..

FrictionFriction• The larger the force pushing the two The larger the force pushing the two

surfaces together is, the stronger surfaces together is, the stronger these these microweldsmicrowelds will be, because will be, because more of the surface bumps will come more of the surface bumps will come into contact.into contact.

To move one surface over the other, To move one surface over the other, a force must be applied to a force must be applied to breakbreak the the microweldsmicrowelds

Static FrictionStatic Friction

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

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

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

Static Friction Static Friction

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

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

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

Static FrictionStatic Friction

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

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

Static FrictionStatic Friction

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

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

Sliding FrictionSliding Friction

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

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

Sliding FrictionSliding Friction

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

• This is because as the box slides This is because as the box slides across the floor, another across the floor, another forceforcesliding frictionsliding frictionopposesopposes the the motion of the box.motion of the box.

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

Rolling Friction

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

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

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

Air ResistanceAir Resistance• When an object falls toward Earth, it is When an object falls toward Earth, it is

pulled downward by the force of pulled downward by the force of gravitygravity.. • However, a friction-like force called However, a friction-like force called air

resistance opposes the motion of opposes the motion of objects that move through the air. It is objects that move through the air. It is the upward force on an object falling the upward force on an object falling through air. through air.

Air resistance causes objects to Air resistance causes objects to fallfall with with different accelerations and different different accelerations and different speedsspeeds

Air ResistanceAir Resistance

Air Resistance a.k.a. “fluid friction” or “a.k.a. “fluid friction” or “dragdrag”” forceforce that air exerts on a moving that air exerts on a moving

object to oppose its motion object to oppose its motion depends on:depends on:

speedspeed surface areasurface area shapeshape density of fluiddensity of fluid

Air ResistanceAir Resistance Falling with air resistance

Fgrav = Fair

Animation from “Multimedia Physics Studios.”

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

larger Flarger Fgravgrav

need larger Fneed larger Fairair

need higher speedneed higher speed

Air ResistanceAir Resistance

Terminal Velocity maximummaximum velocity reached by a velocity reached by a

falling objectfalling object

reached when…reached when…

FFgravgrav = F = Fairair

Fair

Fgrav

no net forceno net force no accelerationno acceleration constant velocityconstant velocity

Air ResistanceAir Resistance

Terminal Velocity

increasing speed increasing speed increasing air resistance increasing air resistance until…until…

FFairair = F = Fgravgrav

Animation from “Multimedia Physics Studios.”

CalculationsCalculations What force would be required to accelerate What force would be required to accelerate

a 40 kg mass by 4 m/sa 40 kg mass by 4 m/s22??

GIVEN:

F = ?m = 40 kga = 4 m/s2

WORK:F = ma

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

F = 160 N

m

F

a

CalculationsCalculations A 4.0 kg shotput is thrown with 30 N of A 4.0 kg shotput is thrown with 30 N of

force. What is its acceleration?force. What is its acceleration?

GIVEN:

m = 4.0 kgF = 30 Na = ?

WORK:a = F ÷ m

a = (30 N) ÷ (4.0 kg)

a = 7.5 m/s2

m

F

a

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

GIVEN:

F(W) = 557 Nm = ?a(g) = 9.8 m/s2

WORK:m = F ÷ a

m = (557 N) ÷ (9.8 m/s2)

m = 56.8 kgm

F

a