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Motion 1: Projectiles and Forces
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Transcript of Motion 1: Projectiles and Forces
mg
x=0
x=0
x=0
x=0
walk
stop
run
stop
Motion
Physics:
Graphs: 2D motion
v
t
Describe the motion here.
Total distance? Total displacement?
Equations for
constant
acceleration
v = u + at
x = ut + at
x = vt  at
1
2
1
2
x = (u + v)t
v = u + 2ax
1
2
2
2
2
2
A golf ball rolls across the green. Rolling friction decelerates it at 1 m/s/s. The ball was hit 32 m from the hole and only just reaches it.
What was the ball's initial velocity?
Year 12 Motion
Example
Vector Addition
wind
V
V
H
V
Vector Subtraction
10 m/s
5 m/s
20 m/s
20 m/s
Vector components
Question 2:
A ball is thrown vertically in the air and takes 4 seconds to get to its highest point.
How fast is the ball travelling after 4 seconds?
How long does it take to get back to its original point?
Question 1:
If the total velocity of a projectile at A is 10m/s at an angle of 60 to the horizontal, what is the total velocity at point E?
A
B
C
D
E
o
Qualitative understanding of air resistance
Air resistance increases as the speed of the object increases
Direction opposite to the
total velocity
15 m/s
30
o
A bullet is shot from a gun horizontal to the ground.
At the same instant, another bullet is dropped
Which hits the ground first?
A motorcyclist rides off a cliff 30 m high at a horizontal velocity of 30 m/s.
The horizontal and vertical motions
are
independent
of each other
A
B
PROJECTILE MOTION
C
H
type 1 problems
type 2 problem
Example
Max height?
20 m/s
60
o
Time of the jump?
Range (horizontal displacement)?
Vertical velocity just before impact?
Total velocity just before impact?
Your projectiles SAC.
Not ignoring air resistance...
Vector Components
Example: Type 1 problem
A ball is thrown off a 20 m high platform at 30 m/s at an angle of 30 .
What is the ball's:
o
Example
Kinematics
Vectors
Projectiles
Which direction is the net force on the object as shown
(A, B, C, D or E):
if air resistance is ignored?
if air resistance is not ignored?
Forces
Inertia
Nothing starts moving, stops moving or changes direction without an
unbalanced
force
More mass = more inertia
Newton's laws
F= ma
What are the Newton 3rd Law reaction forces for for the following?
Why does the Moon go around the Earth?
Does the Moon exert a force on the Earth as well?
How big is this force compared to the size of the force the Earth exerts on the Moon?
Why?
Forces
a is in the same direction as F
If F =0 a=0
net
Action = reaction
For every force acting on an object there is an
equal
and
opposite
reaction force acting on the
other
object
N
Action reaction pair?
net
Arrow points in the direction of applied force.
The length of the arrow represents the strength of the force.
Field forces
begin at the objects center of mass.
Contact forces
begin at point of contact.
All forces should be labelled.
Drawing force diagrams
(have on screen while doing WS: freebody diagrams)
Connected bodies
Tension
Exerts an equal and opposite force at either end of a wire
Friction
Between solid surfaces:
opposes relative motion
http://phet.colorado.edu/en/simulation/forcesandmotion
Problem 1
A car with mass 1200 kg is rolling down a 15 slope. A 100 N frictional force acts on the car.
Forces on a slope
Course content
Unit 3 (16%)
Motion (kinetamics/forces/energy/momentum)
Photonics (electricity/optical devices)
Unit 4 (24%)
Electromagnetism (magnets/motors/generators)
DS Sound*
Light and Matter (waveparticle nature)
*if you want to do another DS you must convince me it is a good idea
You will need:
Checkpoints
Textbook downloaded from student share
Scientific calculator
Workbook for qs
Workbook for notes
3 differently coloured pens + a pencil
DOES NOT HAPPEN.
End of Year Exam 60%
You must:
Take
EXCELLENT
notes in class
Keep up to date with checkpoints
Hand in worksheets
DONT WAIT
to ask for help
You should:
Summarise each topic as you go
Read textbook & do questions
Do extra practice questions
General:
Show FSA
Use scinotation
Use 2 to 3 sigfigs
SI units
for everything always
g = 10 m/s/s
A ball is thrown straight up.
Ignoring airres...
Question
acceleration = ?
_
v = ?
v = ?
a = ?
t = 0 sec
t = 3 s
t=0
, t = 2 s
Multiple bodies WS/pracs
Vertical displacement?
Flight time?
Horizontal displacement?
A snowboarder jumps off the end of a ramp.
Draw all the forces acting on them.
Example 2
Forces on a driving wheel
Velocity
Fr = "static friction"
Fr = "rolling friction"
NOW: 2630, 5153
THEN: 3134, 4346, 4950
6468
(aka driving force/traction)
CPs
(2014)
:
(opposes velocity)
Here is a cute bunny in a
frontwheel drive
car.
Draw and label all the
friction forces
acting on each tyre of the car when it is
accelerating forwards
in a straight line.
Example 1
Now draw and label all the
friction forces
when it is
braking
in a straight line.
Forces equal > what does that mean?
Cps
(2015)
36, 4044, 72
Textbook
Forces: 611, 21
A 1200 kg car travels at constant speed towards a set of traffic lights. The car then decelerates as the lights turn red. A constant frictional force of 360 N acts against the motion of the car.
Example 2
N
mg
flat road
Forces on a slope
Year 12 Physics
Vector Addition
wind
2 m/s
5 m/s
Range
+ve
Example
H = 30m
type 1 problems
A motorcyclist rides off a cliff 30 m high at a horizontal velocity of 30 m/s.
Total velocity just before impact?
Example: Type 1 problem
u = 30m/s
+ve
PROJECTILE MOTION
type 2 problems
* assume no air resistance > symmetrical *
+ve
Important now
_
_
_
Draw xt, vt + at graphs
_
_
_
_
_
from the same height as the gun.
Time of the jump?
Range (horizontal displacement)?
Vertical velocity just before impact?
Range (horizontal displacement)?
Time of jump?
type 3 problems
Projectile motion
type 3 problems
+ve
Acceleration is
negative
Vertical displacement is
negative
u sin(2 )
g
:
acceleration is
negative
R =
Strategy for all projectile motion questions
Draw a picture
Chose a direction to be positive
Decide: horizontal or vertical components?
List known variables
Use equations of motion
s
Example 1
F = F
A on B
B on A
What are the N3 action reaction pairs to the following?
W
F
Earth on bird
bird on Earth
table on book
F
book on table
N
table
on book
W
Earth
on book
N and W act on the
same
object
so they are
not
an action reaction pair
N
Type 1
H comp
a = 0
u = v
v =
x
t
_
H
H
H
H
=
>
H
_
=
>
Both
V comp
a = g = 10
V
x = H
u = 0
V
V
t =

_
_
_
H
5
_
_
_
_
_
_
_
_
Type 2
H comp
a = 0
u = u cos
H
H
u =
x
t
_
H
H
_
=
>
Both
V comp
a = g = 10
V
x =
vmax
v = 0
V
t =

_
_
_
H
5
_
_
_
_
_
_
_
_
2
u = v
H
H
=
>
u = u sin
V
at max hight:
H
R =
u sin(2 )
2
g
_
_
_
_
_
_
_
_
Range formula
Type 3
H comp
a = 0
u = u cos
H
H
u =
x
t
_
H
H
_
=
>
u = v
H
H
=
>
V comp
a = g = 10
u = u sin
V
NB:
x is ve
V
NO SHORTCUTS
+ve
+ve
+ve
Strategy for all projectile motion questions
Draw a picture
Chose a direction to be positive
Decide: horizontal or vertical components?
List known variables
Use equations of motion
Summary: projectiles
=
=
>
>
http://phet.colorado.edu/en/simulation/forcesandmotion
Friction
Static vs sliding (dynamic) friction
Depends on type of surface and normal reaction force
Friction between solid surfaces opposes relative motion
http://phet.colorado.edu/en/simulation/forcesandmotion
Forces on a driving wheel
Velocity
F = "
static
friction"
F = "
rolling
friction"
(aka
driving force
)
Static
and
kinetic (sliding)
friction
Static:
prevents
any
motion up to some limit
Kinetic:
once moving, kinetic friction opposes the relative motion
3 types:
static
,
kinetic
and
rolling
friction
Rolling:
opposes
velocity
of a wheel
Static:
provides 'traction' to make wheel/foot move
Need friction to move wheels
Tension Force (T)
The force transmitted through a connecting
wire/chord
.
The tension force pulls
equally
on both objects at the opposite ends of the wire.
T
W=mg
T
W=mg
T
T = mg
2T = mg
2Tcos(30) = mg
Forces in equilibrium
H and V components must balance
T
W=mg
T
30
o
30
o
r
d
Mildly amusing video showing how things cant move without friction
Look at individually
Look at as a unit
m + m
1
2
m + m
1
2
Connected bodies have the
same acceleration
Ignore internal connecting forces
Weight force on m accelerates
both
masses
2
Pulleys
a =
m g
m + m
1
2
2
_
_
_
_
_
_
One SAC per topic plus EPI
sem 1: SAC SAC EPI
sem 2: SAC SAC SAC
SACs
(dates TBD)
Minimum requirements
Turn up to class
Hand in 80% of work
Do the tests
Do not copy
_
_
_
_
_
_
_
_
_
_
Range formula
NB: only works for type 2
W
1
W
2
N
2
N
1
N +N
1 2
W +W
1 2
m
1
m
2
T
1
T
1
T
2
T
T
m g
2
As a unit:
N
m g
2
m g
1
m
2
2
m
1
m + m
1
2
T accelerates
both
masses
2
= F
net
T
2
= F
net
mg sin( )
N
mg cos( )
...........................
N =
mg sin( )
F
mg cos( )
F =
net
(unbalanced forces only)
Example 3

A car jumps off the end of a ramp, engine roaring, wheels spinning...

Draw all the forces acting on it.

If the brakes exert a force of 600 N, what is the car's acceleration?
Draw and label the forces acting on the car before the breaks are applied
Forces on a block
Draw a diagram and calculate the forces acting on the car
Find the acceleration of the car
Newton's laws cont.
(warning: irritating music)
o
Must have
one double sided A4
page of notes
May bring books for
emergency use only
Moving >
Moving <
accel
const. v
decel
accel
const. v
decel
v=0
v=0
v=0
2
Checkpoints
(2015)
:
3739, 6062, 6871
Textbook:
3537, 4047, 5153
Checkpoints
(2015)
:
57, 7374
Textbook:
5664
(to find T or a)
1
(to find T or a)
2
T =
m g
m + m
1
2
2
_
_
_
_
_
_
_
m
1
NOW: 6768, 2731, 5054
THEN: 3235, 4447, 6366
6468
CPs
(2015)
:
r
One Exam in November
May bring
two double sided A4
pages
(unless stated otherwise)
(a) What force is applied on the block by the compressed spring?
(b) How much potential energy is stored in the compressed spring?
(c) How much work was done on the spring by the block?
(d) The block is released. What is its velocity when it leaves the spring?
A 1 kg block is pushed against a 30 cm spring until its length is reduced to 20 cm. The spring constant of the spring is 50 N/m.
Example
Hooke's law
F = k x
_
_
_
Work
W = F x = area under Fx graph
av
When F is constant
W = Fx
When F is linear
(area of square)
W = k( x)



2
1
2
_
(area of triangle)
eg friction, gravity, pushing
eg springs
F = kx
k = gradient
x is the
change
in length from its
natural length
k = force constant of spring
N/m



Natural length
Applied F
Restorative F



x
A force F can be applied to a spring to
change its length
by x
F = k x
_
_
_
Hooke's Law
NB: force is
not
constant!
can't
use in formula for work
k = force constant of spring
(can leave minus sign off tho)
+

displacement
+

velocity
+

velocity
+

velocity
+

velocity
A 50 kg block pulled by a 150 N force accelerates at 2 m/s/s
What is the frictional force?
What is the normal force?
30
o
Strategy
draw a force diagram
break any angled force into components
deal with H and V components separately (generally)
vector sum of the forces
Example
150 N
Cps
(2016)
36, 4044, 70
CPS Q74, 57 (2016)
(2016)
57, 74, 64, 65
Checkpoints to try now
(2015)
SORRY I CANT FIND MY COPY :(
Normal Force (N)
The force exerted on an object by a
surface
acting
perpendicular
to the surface preventing the object from falling
Sometimes friction is helpful
and provides the
driving force
Full transcriptx=0
x=0
x=0
x=0
walk
stop
run
stop
Motion
Physics:
Graphs: 2D motion
v
t
Describe the motion here.
Total distance? Total displacement?
Equations for
constant
acceleration
v = u + at
x = ut + at
x = vt  at
1
2
1
2
x = (u + v)t
v = u + 2ax
1
2
2
2
2
2
A golf ball rolls across the green. Rolling friction decelerates it at 1 m/s/s. The ball was hit 32 m from the hole and only just reaches it.
What was the ball's initial velocity?
Year 12 Motion
Example
Vector Addition
wind
V
V
H
V
Vector Subtraction
10 m/s
5 m/s
20 m/s
20 m/s
Vector components
Question 2:
A ball is thrown vertically in the air and takes 4 seconds to get to its highest point.
How fast is the ball travelling after 4 seconds?
How long does it take to get back to its original point?
Question 1:
If the total velocity of a projectile at A is 10m/s at an angle of 60 to the horizontal, what is the total velocity at point E?
A
B
C
D
E
o
Qualitative understanding of air resistance
Air resistance increases as the speed of the object increases
Direction opposite to the
total velocity
15 m/s
30
o
A bullet is shot from a gun horizontal to the ground.
At the same instant, another bullet is dropped
Which hits the ground first?
A motorcyclist rides off a cliff 30 m high at a horizontal velocity of 30 m/s.
The horizontal and vertical motions
are
independent
of each other
A
B
PROJECTILE MOTION
C
H
type 1 problems
type 2 problem
Example
Max height?
20 m/s
60
o
Time of the jump?
Range (horizontal displacement)?
Vertical velocity just before impact?
Total velocity just before impact?
Your projectiles SAC.
Not ignoring air resistance...
Vector Components
Example: Type 1 problem
A ball is thrown off a 20 m high platform at 30 m/s at an angle of 30 .
What is the ball's:
o
Example
Kinematics
Vectors
Projectiles
Which direction is the net force on the object as shown
(A, B, C, D or E):
if air resistance is ignored?
if air resistance is not ignored?
Forces
Inertia
Nothing starts moving, stops moving or changes direction without an
unbalanced
force
More mass = more inertia
Newton's laws
F= ma
What are the Newton 3rd Law reaction forces for for the following?
Why does the Moon go around the Earth?
Does the Moon exert a force on the Earth as well?
How big is this force compared to the size of the force the Earth exerts on the Moon?
Why?
Forces
a is in the same direction as F
If F =0 a=0
net
Action = reaction
For every force acting on an object there is an
equal
and
opposite
reaction force acting on the
other
object
N
Action reaction pair?
net
Arrow points in the direction of applied force.
The length of the arrow represents the strength of the force.
Field forces
begin at the objects center of mass.
Contact forces
begin at point of contact.
All forces should be labelled.
Drawing force diagrams
(have on screen while doing WS: freebody diagrams)
Connected bodies
Tension
Exerts an equal and opposite force at either end of a wire
Friction
Between solid surfaces:
opposes relative motion
http://phet.colorado.edu/en/simulation/forcesandmotion
Problem 1
A car with mass 1200 kg is rolling down a 15 slope. A 100 N frictional force acts on the car.
Forces on a slope
Course content
Unit 3 (16%)
Motion (kinetamics/forces/energy/momentum)
Photonics (electricity/optical devices)
Unit 4 (24%)
Electromagnetism (magnets/motors/generators)
DS Sound*
Light and Matter (waveparticle nature)
*if you want to do another DS you must convince me it is a good idea
You will need:
Checkpoints
Textbook downloaded from student share
Scientific calculator
Workbook for qs
Workbook for notes
3 differently coloured pens + a pencil
DOES NOT HAPPEN.
End of Year Exam 60%
You must:
Take
EXCELLENT
notes in class
Keep up to date with checkpoints
Hand in worksheets
DONT WAIT
to ask for help
You should:
Summarise each topic as you go
Read textbook & do questions
Do extra practice questions
General:
Show FSA
Use scinotation
Use 2 to 3 sigfigs
SI units
for everything always
g = 10 m/s/s
A ball is thrown straight up.
Ignoring airres...
Question
acceleration = ?
_
v = ?
v = ?
a = ?
t = 0 sec
t = 3 s
t=0
, t = 2 s
Multiple bodies WS/pracs
Vertical displacement?
Flight time?
Horizontal displacement?
A snowboarder jumps off the end of a ramp.
Draw all the forces acting on them.
Example 2
Forces on a driving wheel
Velocity
Fr = "static friction"
Fr = "rolling friction"
NOW: 2630, 5153
THEN: 3134, 4346, 4950
6468
(aka driving force/traction)
CPs
(2014)
:
(opposes velocity)
Here is a cute bunny in a
frontwheel drive
car.
Draw and label all the
friction forces
acting on each tyre of the car when it is
accelerating forwards
in a straight line.
Example 1
Now draw and label all the
friction forces
when it is
braking
in a straight line.
Forces equal > what does that mean?
Cps
(2015)
36, 4044, 72
Textbook
Forces: 611, 21
A 1200 kg car travels at constant speed towards a set of traffic lights. The car then decelerates as the lights turn red. A constant frictional force of 360 N acts against the motion of the car.
Example 2
N
mg
flat road
Forces on a slope
Year 12 Physics
Vector Addition
wind
2 m/s
5 m/s
Range
+ve
Example
H = 30m
type 1 problems
A motorcyclist rides off a cliff 30 m high at a horizontal velocity of 30 m/s.
Total velocity just before impact?
Example: Type 1 problem
u = 30m/s
+ve
PROJECTILE MOTION
type 2 problems
* assume no air resistance > symmetrical *
+ve
Important now
_
_
_
Draw xt, vt + at graphs
_
_
_
_
_
from the same height as the gun.
Time of the jump?
Range (horizontal displacement)?
Vertical velocity just before impact?
Range (horizontal displacement)?
Time of jump?
type 3 problems
Projectile motion
type 3 problems
+ve
Acceleration is
negative
Vertical displacement is
negative
u sin(2 )
g
:
acceleration is
negative
R =
Strategy for all projectile motion questions
Draw a picture
Chose a direction to be positive
Decide: horizontal or vertical components?
List known variables
Use equations of motion
s
Example 1
F = F
A on B
B on A
What are the N3 action reaction pairs to the following?
W
F
Earth on bird
bird on Earth
table on book
F
book on table
N
table
on book
W
Earth
on book
N and W act on the
same
object
so they are
not
an action reaction pair
N
Type 1
H comp
a = 0
u = v
v =
x
t
_
H
H
H
H
=
>
H
_
=
>
Both
V comp
a = g = 10
V
x = H
u = 0
V
V
t =

_
_
_
H
5
_
_
_
_
_
_
_
_
Type 2
H comp
a = 0
u = u cos
H
H
u =
x
t
_
H
H
_
=
>
Both
V comp
a = g = 10
V
x =
vmax
v = 0
V
t =

_
_
_
H
5
_
_
_
_
_
_
_
_
2
u = v
H
H
=
>
u = u sin
V
at max hight:
H
R =
u sin(2 )
2
g
_
_
_
_
_
_
_
_
Range formula
Type 3
H comp
a = 0
u = u cos
H
H
u =
x
t
_
H
H
_
=
>
u = v
H
H
=
>
V comp
a = g = 10
u = u sin
V
NB:
x is ve
V
NO SHORTCUTS
+ve
+ve
+ve
Strategy for all projectile motion questions
Draw a picture
Chose a direction to be positive
Decide: horizontal or vertical components?
List known variables
Use equations of motion
Summary: projectiles
=
=
>
>
http://phet.colorado.edu/en/simulation/forcesandmotion
Friction
Static vs sliding (dynamic) friction
Depends on type of surface and normal reaction force
Friction between solid surfaces opposes relative motion
http://phet.colorado.edu/en/simulation/forcesandmotion
Forces on a driving wheel
Velocity
F = "
static
friction"
F = "
rolling
friction"
(aka
driving force
)
Static
and
kinetic (sliding)
friction
Static:
prevents
any
motion up to some limit
Kinetic:
once moving, kinetic friction opposes the relative motion
3 types:
static
,
kinetic
and
rolling
friction
Rolling:
opposes
velocity
of a wheel
Static:
provides 'traction' to make wheel/foot move
Need friction to move wheels
Tension Force (T)
The force transmitted through a connecting
wire/chord
.
The tension force pulls
equally
on both objects at the opposite ends of the wire.
T
W=mg
T
W=mg
T
T = mg
2T = mg
2Tcos(30) = mg
Forces in equilibrium
H and V components must balance
T
W=mg
T
30
o
30
o
r
d
Mildly amusing video showing how things cant move without friction
Look at individually
Look at as a unit
m + m
1
2
m + m
1
2
Connected bodies have the
same acceleration
Ignore internal connecting forces
Weight force on m accelerates
both
masses
2
Pulleys
a =
m g
m + m
1
2
2
_
_
_
_
_
_
One SAC per topic plus EPI
sem 1: SAC SAC EPI
sem 2: SAC SAC SAC
SACs
(dates TBD)
Minimum requirements
Turn up to class
Hand in 80% of work
Do the tests
Do not copy
_
_
_
_
_
_
_
_
_
_
Range formula
NB: only works for type 2
W
1
W
2
N
2
N
1
N +N
1 2
W +W
1 2
m
1
m
2
T
1
T
1
T
2
T
T
m g
2
As a unit:
N
m g
2
m g
1
m
2
2
m
1
m + m
1
2
T accelerates
both
masses
2
= F
net
T
2
= F
net
mg sin( )
N
mg cos( )
...........................
N =
mg sin( )
F
mg cos( )
F =
net
(unbalanced forces only)
Example 3

A car jumps off the end of a ramp, engine roaring, wheels spinning...

Draw all the forces acting on it.

If the brakes exert a force of 600 N, what is the car's acceleration?
Draw and label the forces acting on the car before the breaks are applied
Forces on a block
Draw a diagram and calculate the forces acting on the car
Find the acceleration of the car
Newton's laws cont.
(warning: irritating music)
o
Must have
one double sided A4
page of notes
May bring books for
emergency use only
Moving >
Moving <
accel
const. v
decel
accel
const. v
decel
v=0
v=0
v=0
2
Checkpoints
(2015)
:
3739, 6062, 6871
Textbook:
3537, 4047, 5153
Checkpoints
(2015)
:
57, 7374
Textbook:
5664
(to find T or a)
1
(to find T or a)
2
T =
m g
m + m
1
2
2
_
_
_
_
_
_
_
m
1
NOW: 6768, 2731, 5054
THEN: 3235, 4447, 6366
6468
CPs
(2015)
:
r
One Exam in November
May bring
two double sided A4
pages
(unless stated otherwise)
(a) What force is applied on the block by the compressed spring?
(b) How much potential energy is stored in the compressed spring?
(c) How much work was done on the spring by the block?
(d) The block is released. What is its velocity when it leaves the spring?
A 1 kg block is pushed against a 30 cm spring until its length is reduced to 20 cm. The spring constant of the spring is 50 N/m.
Example
Hooke's law
F = k x
_
_
_
Work
W = F x = area under Fx graph
av
When F is constant
W = Fx
When F is linear
(area of square)
W = k( x)



2
1
2
_
(area of triangle)
eg friction, gravity, pushing
eg springs
F = kx
k = gradient
x is the
change
in length from its
natural length
k = force constant of spring
N/m



Natural length
Applied F
Restorative F



x
A force F can be applied to a spring to
change its length
by x
F = k x
_
_
_
Hooke's Law
NB: force is
not
constant!
can't
use in formula for work
k = force constant of spring
(can leave minus sign off tho)
+

displacement
+

velocity
+

velocity
+

velocity
+

velocity
A 50 kg block pulled by a 150 N force accelerates at 2 m/s/s
What is the frictional force?
What is the normal force?
30
o
Strategy
draw a force diagram
break any angled force into components
deal with H and V components separately (generally)
vector sum of the forces
Example
150 N
Cps
(2016)
36, 4044, 70
CPS Q74, 57 (2016)
(2016)
57, 74, 64, 65
Checkpoints to try now
(2015)
SORRY I CANT FIND MY COPY :(
Normal Force (N)
The force exerted on an object by a
surface
acting
perpendicular
to the surface preventing the object from falling
Sometimes friction is helpful
and provides the
driving force