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Ch. 4
Laws of Motion
I. First two laws of motion
“If I have seen far, it is because I have stood
on the shoulders of giants.”
- Sir Isaac Newton
(referring to Galileo)
Forces

Forces can change motion.
 Start movement, stop movement, or change the direction of
movement
 Cause an object in motion to speed up or slow down
Newton’s First Law

Experimentation led Galileo to the idea that
objects maintain their state of motion or rest.

Newton developed the idea further, in what is
now known as Newton’s first law of motion:
B. Newton’s First Law

Newton’s First Law of Motion
 “Law of Inertia”

Inertia
 tendency of an object to resist any
change in its motion
 increases as mass increases
Newton’s First Law
 Which
object in each pair has more
inertia?
 A baseball at rest or a tennis ball
at rest
• Answer: the baseball
 A tennis ball moving at 125 mi/h
or a baseball at rest
• Answer: the baseball
What do you think?
• Imagine
the following
two situations:
• Imagine
the following
two situations:
– Pushing
a puckaacross
air hockey
table
– Pushing
puckan
across
an air
hockey table
– Pushing
a bookaacross
lab tablea lab table
– Pushing
bookaacross
• What should your finger do in each case to maintain a constant
• What
should
fingeracross
do inthe
each
case
to maintain a
speed
for the
objectyour
as it moves
table
or desk?
constant
(Choose
from speed
below.)for the object as it moves across the
table
(Choose
from
below.)
– A
quick or
pushdesk?
or force,
then release
the object
– Maintain
a constant
as youthen
pushrelease
the object
– A quick
pushforce
or force,
the object
– Increase
or decrease
the forceforce
as youaspush
object
– Maintain
a constant
youthepush
the object
• Explain
your choice
for the the
puckforce
and as
theyou
book.
– Increase
or decrease
push the object
• Explain your choice for the puck and the book.
A. Newton’s Second Law
F
a
m
The acceleration of an object
is directly proportional to the
net force acting on it and
inversely proportional to its
mass
F = ma
F: force (N)
m: mass (kg)
a: accel (m/s2)
1 N = 1 kg ·m/s2
Newton’s Second Law
 Which produces a greater acceleration on a 3-kg model airplane, a force
of 5 N or a force of 7 N?
• Answer: the 7 N force
 A force of 5 N is exerted on two model airplanes, one with a mass of 3 kg
and one with a mass of 4 kg. Which has a greater acceleration?
• Answer: the 3 kg airplane
Classroom Practice
Problem
 Space-shuttle
astronauts
experience accelerations of about
35 m/s2 during takeoff. What
force does a 75 kg astronaut
experience during an acceleration
of this magnitude?
 Answer: 2625 kg•m/s2 or 2625 N
Practice
1. What is the force of an object with a
mass of 12 kg and an acceleration of
4 m/s2?
2. Calculate the acceleration of a 25 kg
object that is moved with a force of
300 N
3. What is the mass of an object that is
accelerating at 15 m/s2 when a force
of 3000 N is exerted?
Gravity
Chapter 4 Section 2
B. Gravity

Gravity
 force of attraction between any two
objects in the universe
 increases as...
• mass increases
• distance decreases
B. Gravity
Who experiences more gravity - the
astronaut or the politician?
 Which exerts more gravity the Earth or the moon?

less
distance
more
mass
B. Gravity

Weight
 the force of gravity on an object
W = mg
W: weight (N)
m: mass (kg)
g: acceleration due
to gravity (m/s2)
MASS
WEIGHT
always the same
(kg)
depends on gravity
(N)
B. Gravity

Would you weigh more on Earth
or Jupiter?
 Jupiter because...
greater mass
greater gravity
greater weight
B. Gravity

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
W
g
m
elephant
g
W
m
feather
Animation from “Multimedia Physics Studios.”
B. Gravity
 What
happens when
you include air
resistance?
Bell Work
 The
attractive force between
objects is called?
 Weight is measured in units
called ____ while mass is
in____?
 An object transported from the
surface of the Earth to the Moon
would have a smaller weight or
mass?
A. 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 velocities
PROJECTILE MINI-LAB
A. Projectile Motion

Projectile Velocities

Horizontal and vertical velocities are
independent of each other!
A. Projectile Motion

Horizontal Velocity
 depends on inertia
 remains constant

Vertical Velocity
 depends on gravity
 accelerates
downward at
9.8 m/s2
ConcepTest


A moving truck launches a ball vertically
(relative to the truck). If the truck maintains a
constant horizontal velocity after the launch,
where will the ball land (ignore air resistance)?
A) In front of the truck
B) Behind the truck
C) In the truck
C) In the truck. The
horizontal velocity of the
ball remains constant
and is unaffected by its
vertical motion.
Animation from “Multimedia Physics Studios.”
B. Circular Motion

Centripetal Acceleration
 acceleration toward the center of a
circular path
 caused by centripetal force
B. Circular Motion

On the ground...
 friction provides centripetal force
B. Circular Motion

In orbit...
 gravity provides centripetal force
ROUND LAB
C. 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
C. Free-Fall

Weightlessness
 surroundings are falling at the same
rate so they don’t exert a force on
the object
ConcepTest 1
TRUE or FALSE:
An astronaut on the Space Shuttle
feels weightless because there is no
gravity in space.
FALSE!
There is gravity which is causing the
Shuttle to free-fall towards the Earth.
She feels weightless because she’s
free-falling at the same rate.
ConcepTest 2
Describe the path of a marble as it
leaves the spiral tube shown below.
It will travel in a straight line since the
tube is no longer exerting a net force
on it.
The 3rd Law of Motion
Chapter 4 Section 3
C. 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.
A. 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.
A. Newton’s Third Law

Problem:
 How can a horse
pull a cart if the cart
is pulling back on
the horse with an equal but
opposite force?
 Aren’t these “balanced forces”
resulting in no acceleration?
NO!!!
A. Newton’s Third Law

Explanation:
 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
A. Newton’s Third Law

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.
A. Newton’s Third Law

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
A. Newton’s Third Law

Action-Reaction Pairs

Both objects accelerate.

The amount of acceleration
depends on the mass of the object.
F
a 
m

Small mass  more acceleration

Large mass  less acceleration
JET CAR CHALLENGE
CHALLENGE:
Construct a car that will travel as far as
possible (at least 3 meters) using only
the following materials.
scissors
 tape
 4 plastic lids
 2 skewers

2 straws
 1 balloon
 1 tray

How do each of Newton’s Laws apply?
B. Momentum

Momentum
 quantity of motion
p = mv
p
m v
p:
m:
v:
momentum (kg ·m/s)
mass (kg)
velocity (m/s)
B. Momentum
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:
WORK:
p=?
p = mv
m = 280 kg
p = (280 kg)(3.2 m/s)
v = 3.2 m/s
p = 896 kg·m/s
p

m v
B. Momentum
The momentum of a second bumper car
is 675 kg·m/s. What is its velocity if its
total mass is 300 kg?
GIVEN:
WORK:
p = 675 kg·m/s
v=p÷m
m = 300 kg
v = (675 kg·m/s)÷(300 kg)
v=?
v = 2.25 m/s
p

m v
C. 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
C. Conservation of Momentum

Elastic Collision
 KE is conserved

Inelastic Collision
 KE is not conserved
C. Conservation of Momentum

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.
BEFORE
Cart 1:
p = 21 kg·m/s
m = 5 kg
v = 4.2 m/s
Cart 2 :
m = 2 kg
v = 0 m/s
p=0
pbefore = 21 kg·m/s
AFTER
Cart 1 + 2:
m = 7 kg
v=?
p
m v
v=p÷m
v = (21 kg·m/s) ÷ (7 kg)
v = 3 m/s
pafter = 21 kg·m/s
C. 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?
BEFORE
AFTER
Clown:
m = 50 kg
v = 0 m/s
p=0
Clown:
p = 1000 kg·m/s
m = 50 kg
v = 20 m/s
Cannon:
m = 250 kg
v = 0 m/s
p=0
Cannon: p = -1000 kg·m/s
m = 250 kg
v = ? m/s
pbefore = 0
pafter = 0
C. Conservation of Momentum

So…now we can solve for velocity.
GIVEN:
WORK:
p = -1000 kg·m/s v = p ÷ m
m = 250 kg
v = (-1000 kg·m/s)÷(250 kg)
v=?
v = - 4 m/s
p
(4 m/s backwards)
m v
Do Now
TRUE or FALSE?
The object shown in the diagram must
be at rest since there is no net force
acting on it.
FALSE! A net force does not
cause motion. A net force
causes a change in motion,
or acceleration.
Taken from “The Physics Classroom” © Tom Henderson, 1996-2001.
ConcepTest 2
You are a passenger in a car and not
wearing your seat belt.
Without increasing or decreasing its
speed, the car makes a sharp left turn,
and you find yourself colliding with the
right-hand door.
Which is the correct analysis of the
situation? ...
ConcepTest 2
1. Before and after the collision, there
is a rightward force pushing you
into the door.
2. Starting at the time of collision, the
door exerts a leftward force on you.
3. both of the above
4. neither of the above