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?

http://www.physicsclassroom.com/mmedia/kinema/cnv.html

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 ---- m/s– 36 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!

Describe the motion of each car… what type is it?

Do Now: write the answer in your duo tang.

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!

http://www.physicsclassroom.com/mmedia/vectors/vd.html

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:

Use this one!

The BIG 4 Equations!

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.

• It is (a):– contact force between 2 surfaces that opposes

acceleration.– Push or pull on an object (a force).– Measured in Newtons (N).

friction song!

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 2nd 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 Guberman-pfeffer

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 3rd 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 3rd 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)

= 300 kg • km/hr (15 kg) • v

Total 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 = F d

• 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.