Transcript Laws of Motion and Vectors

Karry Queen, famous American novelist, was found slumped at
a desk next to an empty bottle of sleeping pills. His last
conversation was with the bellhop about how excited he was to
be visiting England for the first time. The detective read the
note and declared it a murder!
Note: I have lost my will to live. My writing was the centre of
my life, but now I realize they were just trashy novels. As the
colour fades from my eyes, I can only hope for a better life in the
next world.
 Why was the detective so sure the author was murdered?
 Finish Test?
 Notes 12.1 “Newton’s 1st and 2nd Laws” in “Laws of
Motion” unit online.
 Work on Conceptual Problems
Assignments:
1. Newton’s Laws Conceptual Problems - TBA
 To access notes and projects online:
 fths.ftusd.org
 Menu-> Staff Directory -> Olson
 Useful Links -> Int Sci
 Laws of Motion Unit
Ch 12 “Forces”
I don’t want to move and you can’t make me… unless there’s
enough force.
Mt. Graham
 Explain how to make objects speed up, slow down, or
change direction using forces.
 Describe what factors determine how much objects
change speed.
From your own experience, what will happen?
1. A marble is placed at the top of a smooth ramp. What will
happen to the marble? What force causes this?
2. A marble is rolling around in the back of a small toy
wagon. The wagon stops suddenly by when it hits a rock,
and the marble rolls toward the front of the wagon. Why
does the marble keep going?
Newton’s First Law
〉Things in motion stay in motion, things at rest
stay at rest UNLESS acted on by an outside force.
〉 speed up
〉 slow down
〉 change directions
Inertia
 Objects resist change unless there is an outside force
 Related to mass
 Bigger mass = more inertia
 Smaller mass = less
EX- Seat belts and cup holders.
 Seat belts and friction between you and the seat provide and
unbalanced backward force that stops you as the car stops.
 Cup holders stop your drink from sliding around as the car
accelerates or turns corners
〉 Newton’s 2nd Law
〉 Results of applying force depends on mass and acceleration.
〉 net force = mass × acceleration, or F = ma
〉 Force is measured in newtons (N): 1 N = 1 kg m/s2
 For equal forces, a larger mass accelerates less.
 For equal masses, a greater force produces a greater
acceleration.
Zookeepers lift a stretcher with a sedated lion. The
total mass of the lion and stretcher is 175 kg, and the
upward acceleration is 0.657 m/s2. What force is
needed to produce this acceleration?
1. Use F=ma.
Given:
mass, m = 175 kg
acceleration, a = 0.657 m/s2
Unknown: force, F = ? N
2. Insert the values into the equation, and solve.
F = 175 kg  0.657 m/s2
F = 115 kg  m/s2
F = 115 N
Newton’s second law can also be stated as follows:
 The acceleration is proportional to the net force and
inversely proportional to the mass.
force
acceleration =
mass
F
a=
m
a
F
a
m
1.
What is the equation for Newton’s 2nd Law?
2.
What force is needed to accelerate a 1,600 kg car forward at 2.0 m/s2?
3.
A baseball accelerates downward at 9.8 m/s2. If the gravitational force is
1.4 N, what is the ball’s mass?
4.
A sailboat and crew have a mass of 655 kg. If there is a 895 N force
pushing the boat forward, what is the boat’s acceleration?
Materials: 2 balls, ramp, stop watch
 How do you think mass will affect the speed of the
balls?
 Does the heavier ball roll faster, slower, or the same
speed as the lighter one?
 What factors probably affected the motion of the two
balls?
Which will reach the floor first? A. flat paper or B. ball
Why are the forces on these two pieces of paper
different?
Draw the force diagrams!
The “Soul-Ace Hotel” was holding its first birthday party and
all eight of the regular customers were invited. The owner
ordered the cake and cut it into 4 slices since she only
expected half of the people to attend. To her dismay,
everyone invited showed up.
 How can she make the cake into eight equal size pieces
with just one cut?
 Finish Test? Check Grades?
 Review Newton’s 1st and 2nd Laws
 Work on Conceptual Problems
Assignments:
1. Newton’s Laws Conceptual Problems - TBA
Materials: 2 balls, ramp
 How do you think mass will affect the speed of the
balls?
 Does the heavier ball roll faster, slower, or the same
speed as the lighter one?
 What factors probably affected the motion of the two
balls?
Which will reach the floor first? A. flat paper or B. ball
Why are the forces on these two pieces of paper
different?
Draw the force diagrams!
1.
What is the equation for Newton’s 2nd Law?
2.
What force is needed to accelerate a 1,600 kg car forward at 2.0 m/s2?
3.
A baseball accelerates downward at 9.8 m/s2. If the gravitational force is
1.4 N, what is the ball’s mass?
4.
A sailboat and crew have a mass of 655 kg. If there is a 895 N force
pushing the boat forward, what is the boat’s acceleration?
 Many people suffer neck injuries from rear-end car
collisions. How does inertia apply here? How do
headrests help?
 If you’re being chased by an elephant, it’s a good idea
to zigzag. Why is your smaller mass an advantage?
 A 100 N bag of nails is suspended from a rope. How
many N of tension are exerted on the strand? What if
there were 4 vertical strands?
Usually uses F = ma…
 Two forces are exerted on a 2 kg object, one is 50 N
east and the other is 30 N west. What is the object’s
acceleration?
 A cart is being moved by a certain net force. If its mass
suddenly doubles, how much does the acceleration
change?
 A rocket picks up speed and significantly increases
acceleration as it continues firing. Why?
 Please find your new seat.
Tori D.
Iversin N.
Jay A.
Tayton T.
Kevin N.
Tatianna M.
Crystal W.
Kobe T.
 Please find your new seat.
Brittany C.
Dawndreah
W.
Joy B.
Cassie B.
Mariah S.
Robyn O.
Cia N.
Kristen P.
Bash W.
Romeo M.
Tehya W.
Delilah L.
I can run, but not walk. Wherever I go, thought follows
close behind.
 What am I?
 Get textbooks and finish “Motion” test – 20 minutes
 Notes Ch 12.2 “Gravity”
 Work on Conceptual Problems
Quiz on Laws 1-2 and Gravity THURSDAY
Assignments:
1. Newton’s Laws Conceptual Problems - TBA
Objectives
〉Explain how mass and weight are related.
〉Describe gravity as attraction between objects.
〉Analyze why a projectiles’ path is curved.
Weight is a measure of the gravitational force exerted on an
object.
Elvis is a student whose mass is 70 kg. On Earth, he weighs about
690 N. Suppose Elvis could stand on the surface of the following
bodies in the solar system. Match Elvis’s weight with planet or
moon. (Hint: Earth has a mass of 6.0 x 1024 kg.)
Planet
Elvis’s weight
a. Jupiter (m = 1.9 x 1027 kg)
780 N _______
b. Venus (m = 4.9 x 1024 kg)
113 N _______
c. Neptune (m = 1.0 x 1026 kg)
260 N _______
d. Mercury (m = 3.3 x 1023 kg)
1800 N _______
e. Earth’s moon (m = 7.4 x 1022 kg)
620 N _______
Suppose Elvis is in orbit around Venus at a distance twice
as far from the planet’s center as the surface of Venus is.
Would you expect his weight to be greater than, less than,
or equal to his weight on the surface of the planet?
Weight is equal to mass times free-fall acceleration.
 weight = mass x free-fall acceleration
 w = mg
How much does a 17 kg crate of books weigh?
use g = 9.8 m/s2
Gravity!!
Weight is measured in newtons (N).
Weight is different from mass.
 mass = a measure of the amount of matter in an object
 weight = the gravitational force an object experiences
because of its mass
All objects in the universe attract each other through
the force of gravity.
Newton’s Law of Universal Gravitation gives the size
of the gravitational force between two objects.
Equation for universal gravitation…
m1m2
F =G 2
d
– m1 and m2 are the masses of the objects
– d is the distance between the objects
– G is a gravitational constant
Equation for universal gravitation…
m1m2
F =G 2
d
– Depends on mass and distance of objects
– Distance changes usually have more impact
than mass.
1st Law
 An object weighs 98 N on earth. How much would it
weigh on Planet X where gravitational acceleration is 6
m/s2? Use F=ma
2nd Law
 What force is acting on 10 kg object in free fall towards
Earth?
 What is the net force if it encounters 15 N of air
resistance?
All matter is affected by gravity.
 Two objects always have a gravitational force between
them.
 When something is very large, like Earth, the force is
easy to detect.
 Gravitational force increases as mass increases.
 Gravitational force decreases as distance increases.
free fall: acceleration due only to gravity
 Ignore air resistance for now.
 Works ideally close to Earth’s surface
 Accelerate at same rate REGARDLESS of mass.
What is the product of the following series?
(X-A) x (X-B) x (X-C) …. (X-X) x (X-Y) x (X-Z)
 Get textbooks?
 Quiz Newton’s Law 1-2 and Gravity
 Work on Conceptual Problems
Assignments:
1. Newton’s Laws Conceptual Problems - TBA
Two mothers and two daughters go shopping. They have 21 $1
bills which they split so each got $7.
 How is this possible?
 10-15 min to work on Conceptual Problems or finish
quiz
 Notes on Free Fall (Ch 12.2)
 Start Calculating Free Fall Lab
Assignments:
1. Newton’s Laws Conceptual Problems - TBA
Air resistance can balance weight.
–terminal velocity: the velocity
of a falling object when the force
of air resistance is equal in
magnitude and opposite in
direction to the force of gravity
 Astronauts in orbit are in free
fall.
 What force keeps the ball on my hand?
 How is the motion different if I shove it off my hand?
2 Components – horizontal and vertical
 Result is a curved path.
 Thrown, launched, fired, etc objects
 Near Earth’s surface
Horizontal component… ignore air resistance
 After thrown, no horizontal forces are acting on the ball. So, the
horizontal component of velocity of the ball is constant.
Vertical component…ignore air resistance
 When you throw a ball, gravity pulls it downward, giving the ball
vertical motion with an acceleration of 9.8 m/s2 on Earth.
 Orbiting is projectile motion.
If you saw your mirror image holding a letter “d” in your
left hand, what would you actually be doing?
 Notes on Circular Motion
 Finish “Calculating Free Fall Lab”
 Work Time
 Circular Motion Wksht due THURSDAY
 Conceptual Problems
Assignments:
1. Newton’s Laws Conceptual Problems - TBA
Object is traveling at a
constant (uniform) speed on a
circular path
 Period (T) – Time it takes
to make one trip around the
circle
Distance =>
Circumference = 2r
 Speed (v) – distance / time
1.2 m
Find v
 v = 3.77 m/s
T=2s
 Speed is constant, but velocity is always changing
 This acceleration is “centripetal” acceleration
Object moves in circle.
 At time t0 it is at O with
a velocity tangent to the
circle.
 At time t, it is at P with
a velocity tangent to the
circle
 The radius has moved
angle 
 Draw the velocity
vectors so that they
have the same tail.
 The vector connecting
the heads is v
 Draw the triangle
made by the position
change (b)
These are similar
triangles.
Equations get rearranged…
Know this and
this!
 At any given moment
 v is pointing tangent to the circle
 ac is pointing towards the center of the circle
 If the object suddenly broke from circular motion
would travel in line tangent to circle
A car goes around a curve at 20. m/s. If the radius of the
curve is 50. m, what is the centripetal acceleration of the
car?
1.
Pick correct acceleration equation.
2.
Plug in numbers.
3.
Solve
Two identical cars are going around two corners at 30
m/s. Each car can handle up to 1 g. The radius of the
first curve is 50 m and the radius of the second is 100 m.
Do either of the cars make the curve? (find the ac)
 Yes, second car makes it.
50 m
100 m
 Use an electronic balance to get object mass for the
first chart.
 Use a spring scale to get weights in N. Use data from
yesterday to calculate object acceleration. Then
calculate mass from F=ma.
Choose the most
appropriate form of the
acceleration equation
given your data.
a = d/t2
 Circular Motion Lab
 Work time
 Circular Motion Worksheet
 Conceptual Problems
Assignments:
1. Newton’s Laws Conceptual Problems – MONDAY
2. Parachute Lab LATE
 Make sure you have these
equations!
Know this and
this!
 Goggles!!
Balance penny on the hanger.
2. Slowly start to swing the hanger until it and the
penny are going in a circle.
3. Calculate the centripetal acceleration and force of
the penny.
1.
Find time for 10 rotations, then divide
by 10 to find T.
 Notes Ch 12.3 “Newton’s 3rd Law”
 Work time
 Force and Momentum Problems due MONDAY
 Circular Motion Worksheet
 Conceptual Problems
Assignments:
1. Parachute Lab LATE
2. Circular Motion Worksheet LATE
3. Newton’s Laws Conceptual Problems – MONDAY
4. Force and Momentum Probs - MONDAY
Objectives
Explain what happens when objects exert forces on other
objects.
2. Calculate momentum.
3. Describe conservation of momentum.
1.
An ice skater holding a basketball
is standing on the surface of a
frozen pond. The skater throws the
ball forward. At the same time, the
skater slides on the ice in the
opposite direction.
1. Is the force on the ball greater
than, less than, or equal to the
opposite force on the skater?
Explain your answer.
2. Is the acceleration of the ball
greater than, less than, or equal
to the acceleration of the
skater? (Hint: F=ma) Explain
your answer.
Newton’s 3rd Law
〉 For every force, there is an equal and opposite reaction
force.
〉Ex: Friction works to stop motion.
〉Air pushes down, balloon goes up
〉Ball changes direction when hit.
Details
 Forces always occur in pairs.
 For every action force, there is an equal and opposite
reaction force.
 Forces in the pair do NOT act on the SAME object.
 Girl pushes on wall, wall pushes on her.
Details
 Equal forces don’t always have equal effects.
 Ex: The action force of Earth pulling on a falling object is
much more obvious than the force of the object pulling
on Earth.
 Action force of bullet firing creates a reaction force
that causes the gun to “kick” or “snap”.
Momentum = mass in motion
Momentum is proportional to mass and velocity.
 Which has more, a car going 30 mph or 90 mph?
 Which has more, a pebble sliding across the floor or
a person sliding at the same speed?
Force is related to change in momentum.
 As the time of the change becomes longer, the force needed to
cause the change in momentum becomes smaller.
Moving your hand back as you catch a ball
means less force.
Calculating straight line momentum
 momentum = mass x velocity, or p = mv
 SI units = kilograms times meters per second (kg•m/s).
 Momentum and velocity are in the same direction.
 Momentum increases as mass or velocity increase.
Momentum
Calculate the momentum of a 6.00 kg bowling
ball moving at 10.0 m/s down the alley toward the
pins.
1. List the given and unknown values.
Given:
mass, m = 6.00 kg
velocity, v = 10.0 m/s (toward the pins)
Unknown: momentum, p = ? kg • m/s (and
direction)
2. Write the equation for momentum.
momentum = mass x velocity
p = mv
3. Insert the known values into the equation, and
solve.
p = mv = 6.00 kg  10.0 m/s
p = 60.0 kg • m/s (toward the pins)
Triskaidekaphobia is the fear of what?
 Tri =
 Deka =
BONUS POINT: What does friggatriskaidekaphobia
mean?
 Notes Ch 12.3 “Newton’s 3rd Law”
 Work time
 Force and Momentum Problems due TODAY
 Conceptual Problems due TODAY
 Conservation of Momentum due WEDNESDAY
 Circular Motion Worksheet LATE
Assignments:
1. Newton’s Laws Conceptual Problems – TODAY
2. Force and Momentum Probs – TODAY
3. Conservation of Momentum due WEDNESDAY
Collisions conserve momentum
〉 TOTAL momentum is the same before and after a
collision.
〉 This is the law of conservation of momentum
〉 Possible situations…
〉Objects collide and bounce off each other.
〉Objects stick together and move in direction of the greater
momentum
Objects collide and bounce… momentum same before
and after…
2 objects before = 2 objects after
m1v1 + m2v2 = m1v1’ + m2v2’
Objects collide and stick together… momentum same
before and after…
2 objects before = 1 object after
m1v1 + m2v2 = (m1 + m2)v’
Objects stick together and move in direction of the greater momentum
 Identify the action and reaction forces when a ball is
lifted and let go.
 Conservation of momentum results …
 1 ball =
 2 balls =
 3 balls =
 When two objects collide, the momentum
(increases/decreases / stays the same)
 What happens if you drop one ball on each side at the
same time? Why?
 Imagine you drop 3 balls, it moves 2 that hit, and move
3 again. How is this an example of conservation of
momentum?
 Read the following phrases. Do you notice anything
odd?
Bird in the
the hand
Once in a
a lifetime
Paris in the
the spring
 Discuss Test Details
 Catapult Momentum Lab
 Work time
 Circular Motion Worksheet LATE
 Force and Momentum Problems LATE
 Conceptual Problems LATE
 Conservation of Momentum due WEDNESDAY
Assignments:
1. Newton’s Laws Conceptual Problems – LATE
2. Force and Momentum Probs – LATE
3. Conservation of Momentum due WEDNESDAY
 Includes paper and performance test on MON Nov. 2.
 MC and word problems
 Projectile motion lab test
 Work solo or with a partner.
 YOU will provide the materials to build the catapult.
 Read through the lab.
 Check suggested materials.
 Start planning now, build Thursday & Friday, test
MONDAY
Granny Smith set her luggage down on a train as it was
passing the Soul Ace Hotel. She walked forward at 1.5
kph. Half an hour later she reached the front of the
train. Unable to find a place to sit, she headed back for
her luggage. The train was passing City Hall which is 10
km from the hotel.
 How fast was the train traveling?
 HINT: speed = distance/time
 Catapult Momentum Labs?
 Gyroscope Activity and Ch 12 Review
 Plan for Catapult/bring materials
 Work time
 Conservation of Momentum due TODAY
 Other missing assignments
Assignments:
1. Newton’s Laws Conceptual Problems – LATE
2. Force and Momentum Probs – LATE
3. Conservation of Momentum due WEDNESDAY
Put this in your notebook…
1.
Wind the string down towards the movable ring and pull.
What factor determines whether the gyroscope balances or
falls?
2.
3.
Use Newton’s 2nd Law to explain #1.
Draw force diagrams of the spinning gyroscope on…
 the pedestal
 a finger
 loop of string
It is estimated that the Earth weighs 6 sextillion (1021) tons.
 How much more would the Earth weigh if one sextillion
tons of concrete and stone were used to build a big wall?
 Catapult Lab Test
 Research, design catapult
 Start planning for experiment AND work on report
 Work time
 All previous assignments LATE
Assignments:
1. Newton’s Laws Conceptual Problems – LATE
2. Force and Momentum Probs – LATE
3. Conservation of Momentum due LATE
What do the following have in common?
 Ichabod Crane
 A missing head
 Katrina van Tassel
 Catapult Lab Test
 Research, design catapult
 Plan experiment, test, work on report
 Work time
 Ch 12 Review
 All other previous assignments LATE
Ch 12 “Laws of Motion” test MONDAY
Assignments:
1. Ch 12 Review due TODAY
2. Catapult Report due MONDAY
Don’t be that guy!
Prep for the lab test.
A watch was discounted 20% and then another 30% at the
register during a sale. Would the price be lower if there was
one discount of 50%? Why or why not?
 Hint: Assume the watch was $100.
 Catapult Lab Test
 Get target distance, 10 minutes to prep
 3 shots
 Ch 12 “Laws of Motion” paper test
 Use notes and a calculator.
 Quiet until ALL tests are in.
Assignments:
1. Ch 12 Review LATE
2. Catapult Report due TODAY
Don’t be that guy!
 Get car times and masses online.
 cars.findthebest.com or www.zeroto60times.com
 Decide to use either 0-60 mph or quarter mi times.
 convert kg to lbs by x 2.2
 Use numbers to calculate acceleration and force.
 Everything in the study of motion is either a vector or a
scalar.
Examples
Distance
Displacement
Speed
Velocity
Mass
Acceleration
Time
Momentum
Force
A scalar is fully described by its magnitude/number
 Examples: Distance, Speed, Mass, Time
Vectors have a magnitude AND a direction
 Examples: Displacement, Velocity, Acceleration, Force
 Write scalars with normally
 x
 m
 t
 Write vectors by
 Putting an arrow over it: v
 Using bold font: v
 Using italic font: v
Decide if the following quantities are a vector or a scalar.
Write ‘S’ for scalar and ‘V’ for vector.
 The acceleration of a car
 Vector
 How far you walk to school
 Scalar
 The number of students in a classroom
 Scalar
 The velocity of a bird
 Vector
 The displacement of a flight
 Vector
 The time it takes to get to school
 Scalar
 The mass of a pencil
 Scalar
 The Force required to push a truck
 Vector
 How fast a person runs
 Scalar
 A person walks 20 m northwest
 Vector
Draw vectors as an arrow
 Length of the arrow is its magnitude
 Direction of the arrow it its direction
 Define the direction of using 0 to 360 degrees.
Vectors can be added.
 Tip to Tail method
 Put the tip of one vector to the tail of another
 Draw the resultant vector from that
A
+
B
=
B
A
A+B
To subtract vectors, add the opposite.
 Same process as addition
A
+
-B
=
-B
A
 Multiplying and Dividing vectors by a scalar only
changes the magnitude
 Direction is unaffected
 Example: 5*B
B
B
B
B
B
B
To fully describe a vector, break it into components.
 Each vector has an x and y component
 The components determine how far in the x and y
direction a vector goes
A
Ax
Ay
Write vectors using their components.
 We use ^
x to represent the x-direction and
represent the y-direction
 We can write vector A as…
A = 4^
x+ 3 ^y
A
4
3
^
yto
If we know the components of a vector, we can find its
magnitude by using the Pythagorean Theorem
 A2 + B2 = C2





^
x
Example: A = 4 + 3
|A|2 = 42 + 32
|A|2 = 16 + 9
|A|2 = 25
|A| = 5
^
y
 When we add/subtract vectors, add/subtract their
corresponding components
 Add/Subtract x components from x components and y
components from y components
^
^
 Example add A = 4 ^
+
3
to
B
=
2
x+ 5 ^y
x y
A + B = (4 + 2)^x + (3 + 5) ^
y
A + B = 6^
x+ 8 ^
y
Simulate dropping a boiled egg. Would the eggs survive?
Show data to verify!
Hints:
 Calculate the force the egg experiences when it lands.
 Boiled eggs will usually crack if they experience a force
more than 25 N.
 Find the mass of the parachute, cup, “egg”, clips, etc
and convert to kg.
 Average chicken eggs have a mass of 57 g (.057 kg).
Create a poster to explain the following situations: force
and acceleration of the penny and “egg”
 Diagram the motion of the penny on the hanger.
 Calculate the centripetal acceleration and force of the
penny on the hanger.