Let’s More Clearly Define the Relationship between

Acceleration and Force!

What is the relationship between acceleration and force?

1.

2.

3.

4.

Parabolic

Linear

Proportional

ExponentialNet Force (N)

Acce

lera

tion

(m/s

2 )

What is the slope of the graph?

Proposition: The slope of the graph is 1/mass

Net Force (N)

Acce

lera

tion

(m/s

2 )

Do you agree???

You Discovered Another Law of Motion!

Newton’s 2nd Law of Motion

Does That Make Sense?

Mator’s force causes an acceleration in the opposite direction.

Fmator

a

v

Mator’s force causes Lightning McQueen to slow down!

Let’s Summarize It!

ΣF = Fnet = 0 N

Constant Velocity

Balanced Forces

ΣF = Fnet = ma

Constant Acceleration

Unbalanced Forces

Newton’s 1st and 2nd Law are basically the same law!

ΣF = m(0 m/s2)Constant v a = 0 m/s2

ΣF = ma ΣF = 0 N

Now We Can Understand…

ΣF = Fnet = ma

Newtons = kg • m/s2

What a NEWTON is!

A Newton is about a quarter of a pound!

ΣF = Fnet = ma

The magnitude of the Earth’s gravitational field is equal to the magnitude of the

acceleration due to gravity!

FgΣF = -Fg

-Fg = m(-a)

-Fg = m(-g)mg = mg

g = g

Now We Can Understand…

Why g and g are the same!

a

What will happen if…You apply the same force F to the following objects?

Sumo Wrestler Smurf

The Smurf will experience a greater acceleration than the Sumo Wrestler!

Why?

Objects have inertia!

Inertia of rest is an object’s want to stay where it is.

You have to FORCE them to change!

Sumo Wrestler

Smurf

What will happen if…A sumo wrestler and a smurf are running at you, and you apply

the same force on them to stop them from tackling you.

The Smurf will experience a greater acceleration than the Sumo Wrestler!

Sumo Wrestler Smurf

Why?Objects have inertia!

Inertia of motion is an object’s want to continue moving at the same speed it was already moving.

You have to FORCE them to change!

Sumo Wrestler

Smurf

What Makes Them Different?

Mass is a way for us to quantify inertia.

Sumo Wrestler

Smurf

The greater the mass…

1. The greater the inertia!

2. The less inertia!

m is really called the inertial mass!!

Defining BoundariesBefore we can use Newton’s laws of motion, we need to know the assumptions under which these laws operate.

1. The objects that these laws are being applied to are large compared to the diameter of an atom.

At this level, motion is governed by quantum mechanic theory.

Defining Boundaries

2. Objects are moving significantly slower than the speed of light.

At higher speeds, motion is governed by the theory of relativity.

Object must stay at around 20% of the speed of light or slower!

Defining Boundaries

3. Observations must be made in an inertial reference frame.

A reference frame is defined as a set of coordinates that can be used to determine positions and velocities of objects.

According to the person on the train, the velocity of the box is 0 m/s.

According to the person at the train station, the velocity of the box is v m/s.

Remember Sally and Bob??

Reference FramesAn inertial reference frame is one that is not

accelerating.

Physics

Observe one of the physics books sitting on my front table.

Are you observing it from an inertial reference frame?

Are you moving?

Earth as a Reference Frame

Technically, the Earth’s surface is not an inertial reference frame.

The Earth’s rotation and precession cause us to

accelerate.

So why do Newton’s laws work so well?

Because the objects we are observing are so small compared to the Earth, the effects of the acceleration is so small that we can assume that we are in an inertial reference frame.

Calvin and Hobbes Meet Newton

Hobbes is pulling Calvin on his sled. Calvin and the sled have a total mass of 20 kilograms and Hobbes can pull with a force of 8.5 N. In addition, there is a frictional force that acts in the opposite direction of Hobbes with a magnitude of 2.0 N. What will Calvin’s acceleration be?

Draw a free-body diagram. Make an information list.

Select a Newton’s law.

Derive an expression for the unknown.

Calculate the value of the unknown.

Calvin and Hobbes Meet Newton

Hobbes is pulling Calvin on his sled. Calvin and the sled have a total mass of 20 kilograms and Hobbes can pull with a force of 8.5 N. In addition, there is a frictional force that acts in the opposite direction of Hobbes with a magnitude of 2.0 N. What will Calvin’s acceleration be?

FHobbes = 8.5 N

FFriction = 2.0 N

m = 20 kg

FHobbes = 8.5 NFfriction = 2.0 N

Fground

Fgravity

a

Calvin and Hobbes Meet Newton

FHobbes = 8.5 N

FFriction = 2.0 N

m = 20 kgFHobbes = 8.5 NFfriction = 2.0 N

Fground

FgravityFnetx = max

Fnety = 0FHobbes + (-Ffriction)= max

FHobbes - Ffriction = max

ax = (FHobbes - Ffriction)/m

ax = 0.325 m/s2

ay = 0 m/s2

a

Fnetx = FHobbes + (-Ffriction)

Calvin and Hobbes Meet Newton

FHobbes = 8.5 N

What if Hobbes pulled at a 45°??

FHobbesx = 8.5 N cos 45°

There is still an acceleration in the x-direction!

FHobbesx = 6.0 N

FHobbesy = 8.5 N sin 45°

FHobbesy = 6.0 N

There is still no acceleration in the y-direction!

Calvin and Hobbes Meet Newton

FHobbesxFfriction

Fground

Fgravity

a

FHobbesy

Fnetx = max

FHobbesx + (-Ffriction)= max

FHobbesx - Ffriction = max

ax = (FHobbesx - Ffriction)/max = 0.25 m/s2

Fnety = 0

ay = 0 m/s2

FHobbesx = 6.0 N

Ffriction = 2.0 N

FHobbesy = 6.0 N

m = 20 kg

Does this make sense?

The sled won’t accelerate as much in the x-direction because some of the force is now in the y-direction.

Now It’s Your Turn!!Free-body Diagram Component Free-body Diagram

(if applicable)

Derive an expression Calculate the unknown(s)