Transcript Changes of Motion

Science 20
Unit B: Changes in Motion
1.1a) Average Speed
• Average Speed is the total distance traveled
divided by the total time taken.
• Equation:
v = d/t
– Units:
m/s or km/h
1.1b) Scalar and Vector quantities
• 2 types of quantities:
– Scalar = magnitude, no direction.
– Vector = magnitude and direction.
• Why is there a difference?
• What is the difference between these 2?
– Speed.
– Velocity
1.1c) Instantaneous Velocity and
Speed
• Average velocity/speed gives the average at
all times of motion; instantaneous gives it
for a specific time/point.
• We use instantaneous velocity/speed when
asked to calculate the speed/velocity.
• Used to study:
– Kinematics = how objects move.
• Uniform and Uniform accelerated motion.
– Dynamics = why objects move.
The Physics Classroom
1.1d) Uniform Motion
• Motion where velocity is constant.
• Use the formula for average velocity.
• The displacement changes at the same rate
as the time.
• Watch the car… is it uniform motion?
• Why is it almost impossible for uniform
motion to occur? What force is this?
which is uniform?
1.1e) Non-uniform Motion
• Motion where speed or direction (or both)
change.
• Most common in everyday life… why?
• When you speed up, is it uniform motion or
not? Why?
1.1f) Converting units
• When converting using the metric system,
use khdmdcm (king Henry danced merrily
down country meadows); each letter is a
division of 10.
• Conversion factors are used to help you
change more than 1 unit at a time; from
km/h to m/s.
• Try these:
– 23 km/h ---– 36 m/s ------
m/s
km/h
1.1 Assignment
• Please complete the following:
– Page 169 #1 and 3.
– Page 171 #5.
– Review page.
1.2a) Identifying and Solving
problems
• Rearranging an equation to find the
“unknown”.
• 2 basic rules:
1.When you move a variable to the other side of
the equal sign = opposite math operation.
2.What you do to 1 side, do to the other!
• Try these:
– V = d/t (solve for t)
– KE = ½ mv2 (solve for v)
Practice
• If Dana takes her eyes off the road for 2.0s
to get a CD, how far did she travel if she is
going:
–
–
–
–
30 km/h
50 km/h
80 km/h
110 km/h
1.2b) Driving at night
• At night, 60m can be lit up using the
headlights of a car.
• Flip to page 175 and try #1.4.
Assignment
• Please try the following:
– Page 177 #1 and 4.
– On a sheet of paper, write 2 things that you
learned about physics today! Put in your duo
tang for the do nows!
Do Now: write the answer in your duo tang.
Describe the motion of each car… what type is it?
Topic 1.3a) Average Velocity
• Is a vector; has a direction and a value.
• Uses displacement NOT distance; what is
the difference?
–Distance has no direction.
–Displacement does!
–Example: Navigating with a map.
Speed vs. Velocity
• Scalar = speed, distance, time.
• Vector = velocity, displacement, time.
• Both use similar equations BUT velocity
uses displacement divided by time.
v =d/t
• v = velocity (m/s)
• d = displacement (m)
• t = time (s)
Problems
• Turn to page 182 in your text and work
through 1.8 with me.
• Try 1.9 on the same page.
1.3b) Vectors
• Vectors are represented by arrows; direction of
arrow = direction of vector.
• Draw vectors from tip to tail!
• Direction can be found 2 ways:
– Coordinate system (Math- unit circle)
– Navigation system (N S E W)
• 2 ways to determine value:
– Graphical (draw all to scale and measure).
– Analytical (draw a sketch and solve using
formulas and trig).Most common!
a) Adding vectors
• Sketch the vectors; creating a triangle.
• The order DOES NOT matter!
• Find the angle and resulting velocity (include
direction in answer).
• State the angle starting from the tail of the
resultant vector.
Resultant = the
vector I get by
adding them
together!
b) Examples
• A car drives 10km [E] and then 7 km [N].
Determine its displacement.
c) Vector Components
• To solve, find the x and y component of the
vector.
• Use Trigonometry to do this.
– Sin, Cos, Tan.
• This is what we did with projectile motion!
• Pythagoras can be used to determine the
resultant velocity!
• Label angle as degrees ___ of ___.
1.4 Graphing motion
• Uniform motion = constant velocity.
• Uniform accelerated motion = constant
acceleration.
• Used to tell the “story” of the motion.
• 2 graphs:
– 1. Position vs. time (d vs. t)
– 2. Velocity vs. time (v vs. t)
• What should they look like? Why?
Lesson 8: Graphs
• What does the slope represent (for both)?
•What does the area under the v-t graph represent?
graphing review
Assignment
• Please complete the following:
– Distance, Displacement, Velocity and Speed
worksheet.
– Vector Components worksheet
– Page 193 # 3 and 4.
1.5 Accelerated Motion
• Acceleration = change in velocity over a
specific time interval.
• When something speeds up or slows down.
• Formula:
a = v /t
Units: m/s2
1.5b) Graphing Accelerated
motion
• Velocity changes, this changes the shape of
the graph you are looking for.
• Displacement is found by the area under the
v vs. t graph.
• Acceleration can be positive (speeding up)
and negative (slowing down).
• Acceleration is equal to the slope of the line
in a v vs.t graph.
Assignment
• Please complete the following:
– Graphing questions worksheet.
– transformers graphing assignment.
– Kinematics: acceleration.
1.6 Displacement during
acceleration
• When an object is accelerating, the
displacement can be found using:
The BIG 4
Equations!
Use this one!
1.6b) Free falling objects
• Do you accelerate when you fall? Why?
• You can find the displacement, time,
velocity and acceleration using the 4
equations on the last slide.
• The acceleration due to gravity is:
a = 9.81 m/s2
Free falling objects
• Hypothesized by 2 Greeks:
– Aristotle = uniform motion.
– Galileo = uniform accelerated motion.
• Why are there different explanations?
• Galileo was right! The acceleration due to
gravity is 9.81m/s2 towards the centre of the
earth. Air resistance is negated.
• Solve these problems using the big 4
equations.
Initial velocity is always 0m/s in
free fall questions; if it is thrown
down, that changes!
Acceleration is always due to
gravity!
Assignment
• Please complete the following:
– Big 4 questions: Uniform accelerated motion
– Free fall pre-lab; lab write-up.
1.7a) Stopping distance
• Reaction distance = distance car travels as
driver reacts.
• Braking distance = distance car travels from
moment brakes are engaged to full stop.
• Stopping distance = reaction + braking
distance.
• Depends on the initial velocity of vehicle.
Apply the Brakes
1.7b) Area of no return
• When driving, the area right before the
intersection is the area of no return… if it is
yellow, you have to go.
• How long should a yellow light last for?.
• Turn to page 218 and try #39 to determine
this.
1.8) A closer look at braking
• The Force of friction determines how fast a
vehicle stops.
friction song!
• It is (a):
– contact force between 2 surfaces that opposes
acceleration.
– Push or pull on an object (a force).
– Measured in Newtons (N).
static vs. kinetic friction
1.8b) Net force
• Adding all of the forces that are on an
object together is the net force.
• When a car is stopping there are 3 forces:
– Force of friction between tires and road.
– Force of air resistance.
– Force applied to the brakes.
Friction
1.8c) Mass
• Scalar quantity, measured in kilograms (kg).
• The quantity of matter in an object.
• The more mass, the larger the force needed
to stop the object.
• Which would stop first: a mini cooper or a
semi-truck? Why?
Your Weight On Other Worlds
Kinematics vs. Dynamics
• Kinematics = how things move (big 4
equations).
• Dynamics = why things move (Newton’s
forces).
• A balanced system is where all forces
balance, the net force is 0N and there is no
acceleration.
1.8d) Newton’s
nd
2
Law
• An object will accelerate in the direction of
the net force.
• Equation:
F = ma
where F = net force (N)
m = mass (kg)
a = acceleration (m/s2)
1.8e) Free body diagrams
• Diagrams that show all the forces acting on the
object (in the proper direction).
• Draw these for every question!
Incline planes
a) examples
• I want to push my tarantula’s 8.7kg cage across the table. I
push with 29N of force, and there is a force due to friction
of 8N between the table and the cage. Determine how
much the cage will accelerate.
Assignment
• Please complete the following:
– Complete #1 and 4a,c,e,g on page 220.
– Read through and highlight the important
points in the Forces and Friction readings.
– Complete #1-4 on “an introduction to forces”.
1.9) Newton’s First Law
• An object in motion will stay in motion and
an object at rest will stay at rest unless acted
on by another force.
• Applied force = force put on object that
opposes friction.
• Known as the law of inertia (property of an
object to resist changes in state of motion).
Newton’s first law!
Assignment
• Please complete the following:
–
–
–
–
#6-10 on “an introduction to dynamics”
Newton’s 1st and 2nd law problems.
Dynamics #1 – Newton’s Laws
Chapter 1 review questions (evens only).
Changes of Motion- Unit B
Topic 2: Collisions
2.1a) Momentum
• Mass x velocity.
• Vector quantity.
• Found using the formula:
p = mv
Where: p = momentum (kg*m/s)
m = mass (kg)
v = velocity (m/s)
Virtual Laboratory: Momentum
Example 1: A 1000 kg car is moving at 10km/h.
Determine the momentum of the car.
Newton Rap, by Matthew Gubermanpfeffer
2.1b) Protective equipment
• Why does a goalie wear protective
equipment?
• Both a hockey puck and a soccer ball have
mass and velocity; but one can be
compressed more. Which one? Why is this
important?
2.2) Change in momentum
• Because mass stays constant, in order for
momentum to change, the velocity must
change.
• Newton’s 2nd law says that when a net force
is acting on an object, it must change
momentum. The greater the momentum;
the greater the force required to stop it.
Example:
A 2.1kg owl flying at a velocity of 15m/s (E) strikes my car
when it was traveling 30 m/s (W).
a) Determine the force acting on the owl if the time for
impact was 0.0067s.
b) Predict if the owl and car stuck together or bounced
apart.
2.2b) Factors that affect
momentum change.
•
Uses the formula:
p = Ft
•
Depends on 2 things:
1. Force applied to the object.
2. Time interval for momentum change
•
So, a large momentum change is either
due to:
–
–
A large force and small time interval.
A small force and a long time interval.
Dog sledding
• A team of dogs can match a team of horses
when it comes to change in momentum.
• Turn to page 250 and read through the
problem.
Assignment
• Please complete the following:
– Page 251 #2- 6.
2.3) Impulse
• The change in momentum of an object.
• The product of the net force and the time
interval of that force on an object.
• Units: N*s
• Formula:
impulse = F*t
where F = net force (N)
t = time interval (s)
Example
• Which has the:
–
–
–
–
Greatest velocity change?
Greatest acceleration?
Greatest momentum change?
Greatest Impulse?
2.4) Forces and Newton’s
•
rd
3
law
There are 3 classes of collisions:
1. Primary: 2 vehicles collide.
2. Secondary: occupant with interior of vehicle.
3. Tertiary: internal organs collide with body.
•
Safety devices are designed to minimize
damage of collisions; using Newton's
laws.
2.4b) Newton’s
rd
3
Law
• States that every action force has an equal, but
opposite reaction force.
• If you push on a desk; the desk pushes back
with you with the same force, opposite
direction.
• Equation:
F1 = -F2
• What is the reaction force to the following?
– Action: the tires on a car push on the road…
– Action: while swimming, you push the water backwards...
– Action: the earth pulls down on a ball…
a. Examples
• When a rifle fires a bullet, the force the rifle exerts on the
bullet is exactly the same (but in the opposite direction) as
the force the bullet exerts on the rifle… so the rifle “kicks
back”. The bullet has a mass of 15 g and the rifle is 6.0 kg.
The bullet leaves the 75 cm long rifle barrel moving at 70
m/s.
a) Determine the acceleration of the bullet.
b) Determine the force on the bullet.
c) Determine the acceleration of the rifle.
d) Explain why the bullet accelerates more than the rifle if
the forces are the same.
b. Lawnmower example
• If I push on a lawn mower, it pushes back on me with an
equal, but opposite force. Explain why we don’t both just
stay still.
– These forces are acting on different bodies (and there are other
forces to consider).
– It doesn’t matter to the lawn mower that there is a force on me… all
that matters to the lawn mower is that there is a force on it, so it
starts to move!
– Another action-reaction pair to consider is that I am pushing
backwards on the ground, and it pushes forwards on me.
Assignment
• Please complete the following:
– Page 256 #5, 6, 10.
2.5) Conservation of Momentum
•
•
Momentum can be transferred from 1
object to another in a collision; it is
conserved.
3 types of collisions:
1. Rebound
2. Hit and stick
3. Explosion
2.5b) The law
• If there is no net force on an object, the
initial momentum = the final momentum.
• Uses this equation:
Σpbefore = Σpafter
Example- stick
• A 15-kg medicine ball is thrown at a velocity of 20 km/hr
to a 60-kg person who is at rest on ice. The person catches
the ball and subsequently slides with the ball across the ice.
Determine the velocity of the person and the ball after the
collision.
Before Collision
After Collision
Person
0
(60 kg) • v
Medicine ball
(15 kg) • (20 km/hr)
(15 kg) • v
Total
= 300 kg • km/hr
300 kg • km/hr
300
Example- non stick
• A 3000-kg truck moving with a velocity of 10 m/s hits a
1000-kg parked car. The impact causes the 1000-kg car to
be set in motion at 15 m/s. Assuming that momentum is
conserved during the collision, determine the velocity of
the truck immediately after the collision.
Before Collision
After Collision
Truck
3000 • 10 = 30 000
3000 • v
Car
0
1000 • 15 = 15 000
Total
30 000
30 000
Forensic engineering
• Uses these concepts to build models of car
crashes and recreate the incident.
Assignment
• Please Complete the following:
– Momentum worksheet.
– Pages 44/45.
2.6) Design a Helmet
• You are the designer… of a helmet for an
egg! Please read the attached assignment
and complete in groups.
1. Potential Energy
• Stored energy; energy due to position.
• When using gravitational potential energy, use
the following formula:
– Ep =mgh
• Where m = mass, g = gravitational acceleration and h =
height from ground.
• Depends on 2 things:
– Force acting on the object (gravitational potential
energy = Fg).
– Displacement of the object.
2. Kinetic Energy
• Energy of motion.
• When an object is released it
has a speed; kinetic energy.
• The kinetic energy is equal to
the work done.
• Formula:
Ek = ½ mv2
• Where m = mass, v = speed.
When someone levitates, does the Potential energy change? Why?
levitation video
3. Work
• Scalar quantity; can be negative if done in
opposing direction of force.
• Use the formula:
– W=Fd
• Where W = work, F = force and d = displacement.
• Units = Joule (J).
Review
• Chapter reviews are at the end of each
chapter; use them to review for the unit
exam!
• Chapter #1: Pages 235-239 (do evens only)
• Chapter #2: Pages 281-283 (do odds only).
• Full unit review: Pages 285- 291.