Download Speed, Velocity and Acceleration

Work, Force, and Motion
SOL Standard
 PS.10 The student will investigate
and understand the scientific
principles of work, force and motion.
Key concepts include
 Speed, velocity and acceleration
 Newton’s laws of motion
 Work, force
Guiding Questions
 What is the difference between work, force and motion?
 How is the speed, velocity, and acceleration of an object
measured and calculated?
 How does speed, velocity, and acceleration describe
motion?
 What is the difference between mass and weight?
 What is an example of each of Newton’s three Laws of
Motion?
 What is the relationship between force, mass and
acceleration?
What is a force?
A force is a push or a pull on matter
Motion
 a change in position, or location of a
place or object, over a certain amount
of time
 relies on a frame of reference or
something assumed to be stationary
 Frame of reference is a stationary
location or object to which you
compare other locations or objects
How does Frame of Reference
relate to motion?
 Motion is relative to a frame of reference
 Something that is not moving in one point of
reference can be moving in a different point of
reference
Understanding frame of reference
 Nothing is truly stationary when relative to
all other objects
 If you sit perfectly still, are you moving?
What Is Work?
• Work is a transfer of energy
• In science, work is done when a force
causes an object to move in the
direction of the force.
• If there is no movement in the
direction of the force, no work is done
How to Calculate Work
We use the equation W = F x D
“Work equals Force times Distance”
Do forces always cause work?
Speed
 the rate at which an object moves
 a measure of how fast something moves, or the distance it
moves, in a given amount of time
 Formula: S = d
t
 typically expressed in units of m/s
 is considered average when taking into account the total
distance covered and the total time of travel
 is considered constant when it does not change
 is considered instantaneous when it represents a specific
instant in time
00:00. 0
5
4
3
12
6
What is the ball’s speed?
6 meters
Interesting Speeds
meters/second
miles/hour
Cockroach
1.25
2.8
Kangaroo
15
34
Cheetah
27
60
Sound
343
767
Space Shuttle
7,823
17,500
Light
300,000,000
671,080,888
(in
200C
air)
(getting into orbit)
Practice Problems - Speed
1.
If you walk for 1.5 hours and travel 7.5 km, what is
your average speed?
S=d
t
2.
S=
7.5 km =
1.5 hr
5 km
hr
Calculate the speed of a bee that flies 22 meters in
2 seconds.
S=d
t
S=
22 m
2 sec
=
11 m
sec
The Speed Triangle
S
t
=
=
d
d
d = S .t
St
d
S
.
t
Distance-Time Graph
Shows how speed relates to distance and time
C
This distance-time graph will
show a student’s speed as he
returns to class after lunch. What is the speed
Distance (meters)
120
100
from B-C ?
80
What is the speed
from A-B ?
60
A
40
What is the speed
from 0-A ?
20
0
10
20
30
40
B
What is the
student’s
average speed?
50
60
Time (seconds)
70
80
90
100
Can you figure this out?
Two birds perched directly
next to each other, leave the
same tree at the same time.
They both fly at 10 km/h for
one hour, 15 km/h for 30
minutes, and 5 km/h for one
hour. Why don’t they end up
at the same destination?
Velocity
 the rate of change of an object’s position
 speed in a given direction
 is considered constant when speed and direction do not
change
 changes as speed or direction changes
 is a vector
 can be combined (added if moving in the same direction
and subtracted if moving in the opposite direction)
 i.e. – If you are walking at a rate of 1.5 m/s up the aisle of
an airplane that is traveling north at a rate of 246 m/s,
your velocity would actually be 247.5 m/s
29 m/s east
25 m/s west
visuals taken from: http://www.amazing-animations.com/
What is the difference between
speed and velocity
Velocity includes a
direction…..Speed
does not include a
particular direction.
Both use the same equation:
Speed or Velocity = distance
time
Acceleration
 the rate at which velocity changes
 occurs when something is speeding up (+),
slowing down (-), or changing direction
 Formula: a = vf – vi
t
 typically expressed in units of m/s2
 is always changing, and considered
centripetal, when traveling in a circle
Explain how both cars are accelerating.
Velocity and Acceleration
Acceleration Formula
Practice Problems - Acceleration
1.
Tina starts riding her bike down a hill with a velocity of
2 m/s. After six seconds, her velocity is 14 m/s. What is
Tina’s acceleration?
a = vf – vi
t
2.
a = 14 m/s - 2m/s = 2 m
2
6s
s
A motorcyclist goes from 35 m/s to 20 m/s in five seconds.
What was his acceleration?
a = vf – vi
t
a = 20 m/s - 35 m/s = -3 m
5s
s2
SI (International System)
Units of Measurement
We measure speed in m/s.
We measure velocity in m/s.
We measure acceleration in m/s2.
(Or…meters per second per second.)
Velocity-Time Graph
Velocity (meters/second)
Shows how acceleration relates to velocity and time
12
This velocity-time graph will
show a student’s acceleration as
she returns to class after lunch.
10
8
Describe the student’s
acceleration as she
travels to class?
6
4
2
0
10
20
30
40
50
60
Time (seconds)
70
80
90
100
Momentum
 a measure of mass in motion
 the product of an object’s mass and velocity
 Formula: p = mv
 typically expressed in units of kg·m/s
 is in the same direction as the velocity
 makes an object harder to stop or change direction as it
increases
 can be transferred
20 kg
0.17 kg
Which
object
has
more momentum
Describe
the
scenario
where the–
thepuck
curling
rock
or more
the hockey
puck?
would
have
momentum
Explain
your
reasoning.
than the
curling
rock?
Practice Problems - Momentum
1.
What is the momentum of a 7.3 kg bowling ball moving at
8.9 m/s?
p = mv
2.
p = (7.3 kg)(8.9 m/s) = 65 kg·m/s
At a velocity of 8.5 m/s, Tim moves down a hill on an
inner tube. If his mass is 59 kg, how much momentum
does he have?
p = mv
p = (59 kg)(8.5 m/s) = 502 kg·m/s
Newton’s 1st Law of Motion
Newton’s 1st Law
 objects at rest remain at rest, and
objects in motion remain in motion with
the same velocity, unless acted upon by
an unbalanced force
 also considered the Law of Inertia
How is this illustrated when riding in a
car? Can you think of other
experiences where this is illustrated?
Inertia
 the resistance of an object to a change
in the speed or the direction of its
motion
 directly related to mass
Newton’s 2nd Law of Motion
Newton’s 2nd Law
 the acceleration of an object increases
with increased force and decreases with
increased mass
 the direction in which an object
accelerates is the same as the direction
of the force
 Formula: F = ma (or a = F/m)
Practice Problems - Force
1.
What net force is needed to accelerate a 24 kg dogsled
to a rate of 3 m/s2?
F = ma
2.
2
72
kg
·
m/s
F = (24 kg) (3 m/s2) =
or 72 N
A 1.5 kg object accelerates across a smooth table at a
rate of 0.5 m/s2? What is the unbalanced force applied
to it?
F = ma
F = (1.5 kg)(0.5 m/s2) = 0.75 kg·m/s2
or 0.75 N
More on the Law of Acceleration
Newton’s
nd
3
Law of Motion
Newton’s 3rd Law
 states that every time one object exerts
a force on another object, the second
object exerts a force that is equal in
size and opposite in direction back on
the first object.
According to Newton’s 3rd Law of Motion,
Forces Always Come In Pairs (or Twos)
What is a force?
Force




a push or pull acting on an object
typically measured in Newtons (kg•m/s2)
is a vector
can be combined to predict motion net force
Calculating Net Forces
A net force is the total amount of
all forces acting on an object.
Add forces moving in the same
direction.
Subtract forces moving in opposite
directions.
Net Force = 0 N
Net Force = 20 N
Net Force = 2 N
BALANCED FORCES vs.
UNBALANCED FORCES
 Balanced forces
are always equal
to ZERO and DO
NOT cause
motion.
 Unbalanced
forces ALWAYS
cause motion and
NEVER equal to
zero.
Vector
 a quantity that has both direction and
magnitude (size)
 drawn as an arrow which shows direction and
magnitude (length of arrow)
 consists of two parts: tail and head
Head
Tail
Consider the vectors above. Describe the direction and
relative magnitude (force) of each ball based on the vector.
Combining Vectors
 can be combined/added to help determine net force
What is the hockey
puck’s net force?
Gravity = 14 N
Gravity = 14 N
23 N
Applied Force = 25 N
Friction = 2 N
Applied Force = 25 N
Friction = 2 N
Normal Force = 14 N
Normal Force = 14 N
What’s the Net Force
Fnorm = 10 N
Fapp = 20 N
Ffric = 5 N
Fgrav = 10 N
You throw a baseball to your
friend who is to your left.
Ffric = 5 N
Fapp = 15 N
Fgrav = 10 N
Your dog pulls you down the
street on a skateboard in an
eastward direction.
What’s the Net Force
(An Interesting Case)
A skydiver is descending with a
constant velocity. Consider air
resistance.
Ffric
The same skydiver is
descending after 30 seconds.
Consider air resistance.
Ffric
Fgrav
Fgrav
What has the skydiver
reached in this scenario?
Types of Forces
 Contact Forces







Applied
Normal
Friction
Air Resistance
Tension
Spring
Centripetal
 Non-Contact Forces
 Gravity
 Electromagnetic
Applied Force
 any push or pull on an object created
from another source (person, animal,
another object, etc.)
Normal Force
 the support force exerted on an object directly
related to weight (gravity)
 consequence of Newton’s 3rd Law
 is always perpendicular to the surfaces in contact
Gravity
Box 900
Normal
Force
Gravity
Friction
 exerted by a surface as an object moves across it or
attempts to move across it
 opposes the motion of an object
 depends on the type of surfaces and the normal
force (weight)
In which direction
 Types
is the force (friction)
 Kinetic
vector pointing?
 Static
Motion
Friction
FRICTION is a force that works in the
opposite direction to motion.
Static Friction vs. Kinetic Friction
 Static friction is found
where there is NO
motion.
 Kinetic friction is
found where MOTION
occurs.
Air Resistance




friction due to air molecules
acts upon objects as they travel through the air
opposes the motion of an object
most noticeable for objects traveling at fast
speeds
 Terminal Velocity- velocity of a falling body occurs during
free fall when a falling body experiences zero
acceleration
 Air resistance exists because air molecules collide into a
falling body creating an upward force opposite gravity. This
upward force will eventually balance the falling body's
weight. It will continue to fall at constant velocity known as
the terminal velocity.
Tension
 force that is transmitted through a string, rope,
cable or wire when it is PULLED tight by forces
acting from opposite ends
 directed along the length of the wire and PULLS
equally on the objects on the opposite ends of the
wire
Spring
 force exerted by a compressed or stretched spring
upon any object that is attached to it
 for most springs, the magnitude of the force is
directly proportional to the amount of stretch or
compression of the spring
If both springs are the same
size when not compressed, which
spring will apply more force to
the ball when released? Explain
your reasoning.
Images taken from:
http://www.lesjoforsab.com/standard-springs/compression-springs.asp
Centripetal Force
 any force that keeps an object moving in
a circle
 directed toward the center of the circle
In this case, the force of the
ball as it accelerates around
the circle is pointing inward,
toward the center.
Gravity
 natural force of attraction
between any two objects
 factors:
 distance – increased
distance  less
gravitational pull or vice
versa
 mass – increased mass 
more gravitational pull or
vice versa
Why does the force of gravity
have more of an impact on
holding our solar system
together compared to holding
the parts of an atom together?
Gravitational Force
The force of Gravity acts between all
objects
If the Mass increases, the force of gravity increases. If
the mass decreases the force of gravity decreases.
If the distance decreases, the force of gravity increases, If
the distance increases, the force of gravity decreases.
The Force of Gravity and Mass
The Force of Gravity and Distance
Electromagnetic Force
 force that moving charges exert on one
another
 results from the repulsion of like
charges and the attraction of opposites
+ +
+
-
- -
Notice how the
particles with
the same charge
move apart and
the particles
with different
charges move
together.
SI (International System) Units of
Measurement
We measure forces in NEWTONS.
We measure weight in NEWTONS.
Weight is measurement of the
FORCE of GRAVITY.
Gravity is a major force in the universe!