# Newton

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```					Isaac Newton
(1643 – 1727)

Defining his
3 Laws

Newton at age 46
Scalar vs. Vector
• Speed is scalar – (how fast something
is going)

• Velocity is a vector so its direction
matters! – (speed and direction)

• Acceleration is also a vector it has
magnitude and direction
Speed and Direction

Speed is important
(100 km/hr)

But . . .

Direction can be even
more important!!!
Uniform circular motion
How Many Accelerators Does
Newton’s First Law of Motion

• Every object in a state of uniform motion
tends to remain in that state of motion
unless an external force is applied to it
Forces are Balanced
a = 0 m/s2

Object at rest                Object in Motion

V = 0 m/s                      V ≠ 0 m/s

Stay in motion same
Stay at rest             speed and direction in
straight line
Car in motion makes a left hand turn
Acceleration in a car

Car starts from rest    Moving car brakes to stop
Newton’s Second Law of Motion

• The relationship between an object’s
mass (m), its acceleration (a), and the
applied force (F) is F = ma

In terms of acceleration:
a = F/m
Forces are Unbalanced

There is an acceleration

a = F/m

The acceleration                The acceleration
depends directly               depends inversely
upon the                        upon the
“net force”                    object’s mass
Aristotle vs. Newton

• Aristotle  force maintains motion (s)
(F=ms)
 Common sense

• Newton  force causes change in velocity
•                 (F=ma)
 looks at all forces involved
Baseball and Tennis Ball
A. Drop in a vacuum from height of ~ 30 feet
B. Drop from the roof of DeLaRoche
Which hits the ground 1st?

Baseball
- mass 142 to 149 g
-circumference 22.9 to 23.5 cm

Tennis ball
- mass 57.7 to 58.5 g
-circumference 19.95 to 20.95 cm
Drop a baseball and tennis ball (in vacuum)
• _____________________

• Baseball 2.5 times mass of tennis ball – Earth
pulls 2.5 times as hard on baseball

But

• Baseball’s greater mass makes it 2.5 times as
hard to accelerate

• ___________________________________
Drop a baseball and tennis ball (off DeLaRoche)

• ________________ lands first

• must take into account air
resistance

• when air resistance = gravity
 terminal velocity

• ______________ reaches terminal velocity quicker
than ______________

• ___________ falls longer before air resistance
balances gravity – more time to fall more time to
accelerate
Terminal Velocity
[Don’t try to memorize]
Vt is the terminal velocity

m is the mass of the falling object

g is gravitational acceleration at
the Earth's surface

Cd is the drag coefficient

ρ is the density of the fluid the
object is falling through

A is the object's cross-sectional
area
Momentum
• Momentum – “mass in motion”

• All objects have mass so if moving object has
momentum

• Newton’s statement of his second law
involved the rate of change of “motion”
(=momentum)

• can be restated in terms of momentum

ρ=m•v
Stopping Momentum

• Any object with momentum is hard to stop

• Must apply a force against its motion over
time

• The greater the momentum the greater the
force or longer the time period to stop the
object
Impulse = Force • Time = Change in Momentum
Can be derived from Newton’s 2nd law

F = ma              a = Δ v/t

F = m(Δ v/t)        Ft = Δmv

To minimize the affect of the force on an object time
must be increased [Ft = Δmv]

To maximize the affect of the force on an object time
must be decreased [Ft = Δmv]
Combinations of Force and Time required
to produce 100 units of Impulse
Force         Time        Impulse
100            1           100
50             2           100
25             4           100
10            10           100
4            25           100
2            50           100
1            100          100
0.1          1000          100
Real Life Examples
Hitting the “Long Ball”
Hitting the “Long Ball”
• You want the ball to have the largest
possible velocity when it leaves the bat

• What does the impulse-momentum equation

• You want the largest possible momentum
for the ball as it leaves the bat. Ball has
essentially zero momentum when you hit it
(i.e., zero velocity)
Hitting the “Long Ball”

• You want the largest possible change in
momentum for the ball

• The change in momentum of the ball equals the
impulse that you apply (with the bat) to the ball

• To get the largest possible change in momentum,
apply the largest possible impulse to the ball
Hitting the “Long Ball”

• Impulse depends directly on force applied and
time the force is applied. (Impulse = (force)(time)

• To get the largest possible impulse you should
either:

 apply the largest possible force

 apply the force for the longest possible time

 or both
Hitting the “Long Ball”

• You want to apply maximum force by hitting the
ball hard. If you hit the ball with twice the force,
you will impart twice the impulse to the ball
• Impulse = change in momentum - this will double
the ball's change in momentum
• Momentum equals mass times velocity - doubling
the ball's momentum will double its velocity
• However, if you try to apply too much force your
coordination and timing will suffer, and your swing
will not be accurate - you may even miss the ball!
Hitting the “Long Ball”

• You can also increase the impulse on the ball
by increasing the time that the bat exerts its
force on the ball - "following through"

• If you hit the ball for twice as much time, you
will impart twice the impulse to the ball, which
means twice the change in momentum for the
ball. So, following through is important
Golf – Tennis - Soccer
• To get largest possible velocity for the ball:

 want the largest possible momentum for the ball

• To get the largest possible momentum for the ball:

 want to apply the largest possible impulse to the
ball

• To apply the largest possible impulse to the ball:
want to apply the largest possible force
apply a force for the longest possible time
or both
Newton’s Third
Law of Motion

• For every action
there is an equal
and opposite
reaction
Balanced Forces
The forces on the person are balanced

Gravity pulls
The floor pushes                downward on the
upward on the person                person
Conservation of Momentum

• Product of mass x velocity

• In isolated system momentum must
remain constant

• Adult pushing child away on ice

• Angular momentum and a spinning ice
skater
[Don’t try to memorize following slides!!]
Is the force the car exerts on the truck?
A. greater than the force the truck exerts on the car
B. less than the force the truck exerts on the car
C. equal to the force the truck exerts on the car
mass-car (m1) = 1500kg
mass-truck (m2) = 20,000kg

Velocity-car (u1) = 8m/s,
Velocity-truck (u2) = 5 m/s

solution for final velocity can be derived from
conservation of momentum
ρ 0 = ρf
ρ1 + ρ2 = (m1 + m2)*V
(m1u1) – (m2u2) = (m1 + m2)*V
V = (m1u1 – m2u2)/(m1 + m2)
V= [(1500 kg)(8 m/s) – (20,000 kg)(5 m/s)]/)1500 kg + 20,000 kg)
V = -4.09 m/s
We can find the forces acting on the driver in each
vehicle by noting that the change in velocity of the
car or truck is the same as the change in velocity of
the driver

Let's assume the crash takes place over a time
period of about 0.2 s. The acceleration of the truck
is a2 = vf - v0/tcrash = (V - u2)/ tcrash = (-4.09 m/s – (-5)
m/s)/0.2 s = +4.6 m/s2
The car driver experiences an acceleration of
(V - u1)/tcrash = (-4.09 m/s - 8 m/s)/0.2 s = -60.5
m/s2

The magnitude of the forces are equal since,
Ftruck = (20,000 kg)(4.6 m/s2) = 92,000 Nt and
Fcar = (1500 kg) (60.5 m/s2) = 91,000 Nt with the
difference being round off error

Since the accelerations of the car and truck are
opposite signed, the directions of the forces on
both are in opposite directions just as Newton's
Third Law demands
If the truck driver and car driver are about the
same mass, then the force on the car driver is
about 13 times as great as the force on the truck
driver!

F = ma if mass = 70 kg = 154 lbs
Ftruck driver = 70kg * 4.6 m/s2 = 322 Nt
Fcar driver = 70kg * 60.5 m/s2 = 4235 Nt

```
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 views: 14 posted: 8/8/2011 language: English pages: 37