PHYSICS SKILLS REVIEW



Grade 10 PB Science

Unit 1:

Physics

Table of Contents

Intro to Physics………..………page 2

Algebra………………….…………page 3

Scalars and Vectors………….page 6

Intro to Kinematics…………..page 7

Physics and Graphs………….page 10

Kinematics………………….…...page 20

Dynamics………………………….page 27

INTRO TO PHYSICS

• We’ve discovered that our universe follows a set of rules

• We’ve used the process of science to figure out what these rules are

• Our study of physics will involve you learning about some of the truths that science has uncovered about our world!

WHAT IS PHYSICS?

• The branch of science called physics has developed out of the efforts of men and women to explain _________________________________________

• Physics can be defined as: ____________________________________________________

____________________________________________________________________________

• Physics has been so successful at explaining how our universe works that it’s laws encompass a remarkable variety of phenomena

• One consequence of this success is that we’ve had to break physics into a number of smaller pieces:

1. _____________________________________________________

2. _____________________________________________________

3. _____________________________________________________

4. _____________________________________________________

5. _____________________________________________________

6. _____________________________________________________

7. _____________________________________________________

HOW PHYSICS WORKS:

• the most common, meaningful and efficient way to express a ‘rule of the universe’ is in the form of a ___________________________

• ____________________ is actually a condensed version of a ‘rule of the universe’!

• these equations allow us to make _________________ if we are able to provide the equation with enough information

• physics and it’s equations grant us the power to predict the future!

BUT: before we can ‘do’ physics, we need to have some basic math skills that will allow us to use the equations effectively and efficiently…

ALGEBRA:

It is essential that you are able to manipulate algebraic expressions. This process is often a fundamental step in solving physics & chemistry problems.

Algebra: What is it?

The main difference between “normal math” and algebra is that algebra uses variables as well as “ordinary” numbers. An “ordinary” number is nothing more than a symbol which represents some fixed or constant amount. As an example, consider “2”. This “2” thing is really just a symbol which we know to represent one precise location on the number line: the number we call “two”.

• Variables are ______________________

• It is essential that the consequence of this be understood: being numbers, _________________________________________________________________________

• Unlike the constant value numbers (like 2), variables may represent any value, and in fact may represent several different values at the same time, or even all values

• When written as part of an equation, the value of the variable is understood to be “_______________________________________________________________”

• An equation is considered true if _____________________________________

Example:

• consider the algebraic equation 2F = 10

• This equation contains two constant value numbers (which we call “numbers” for short): the 2 and the 10, and the variable number F (which we call “variables” for short) which makes this an algebraic equation

• The variable F represents any number which will make the equation true

• This particular equation is simple enough that it has almost certainly occurred to you that if F = 5 (and nothing else), then the equation would be true

• By saying that F = 5, we can say that “the equation has been solved: F = 5”.

• algebraic equations are not always so obvious

• Consider x3 + 6x2 - 7x = 0 ... it is not very obvious that x represents three values: -7, 0 and 1, any one of which will make this equation true (confirm this on your own)

• Throughout this course we will aim to improve your skill at “solving equations”.

Algebra: How does it work?

• Before working with algebraic equations, it is worth noting that the appearance of an equation (algebraic or not) may be changed while not affecting the trueness of the equation itself

• The general rule here is that if an equation is true, then it will still be true if ____________________________________________________________________________________________________________________________________________________

Said more simply, you may safely:

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________

• Changing the appearance of an equation can make it more obvious of which values of the variable are solutions, which makes this a valuable technique

• Some rules:

▪ An operation is always done to the whole side of an equation

E.g. (nothing can be done to “b” or “c” until “d” is dealt) with

▪

• We will first get some practice with the technique by applying it to purely numerical equations and then applying the same ideas to algebraic expressions

Examples:

Solve the following equations for all variables:

1. a = b – c 2. [pic]

3. a = bc +d 4. a = b2(c+d)

Worksheet - Algebra

Solve each of the following equations for the number indicated.

a) 3 + 4 = 7 (solve for 3) b) 10 - 8 = 2 (solve for 10)

c) 10 - 2 - 3 = 5 (solve for 2) d) 15 - (9 + 1) = 5 (solve for 1)

e) 2(3) = 6 (solve for 3) f) 18 ÷ 6 = 3 (solve for 18)

g) 15 ÷ 3 = 5 (solve for 3) h) 24 ÷ (6 + 2) = 3 (solve for 6)

i) 42 = 16 (solve for 4) j) (5 + 2)2 = 49 (solve for 5)

k) (3 + 2)2 + 5 = 30 (solve for 2) l) [pic](solve for 3)

For each of the equations below, solve for all of the variables found in the equation.

a) A = B + C b) A = B ÷ C

c) A = B + CD d) A = (B + C)D

e) A = BC + DE2 f) A2 = B2 + CD

g) A = πr2 h) a2 + b2 = c2

SCALARS & VECTORS

• We will come across and use two different 'kinds' of measurements as we study physics:

1. Scalars

2. Vectors

 

• Because these two measurements have fundamental differences we must:

a) _____________________________________________________________

b) _____________________________________________________________

 

SCALARS:

• Scalar measurements tell us only the magnitude of the quantity being measured

- Scalars numbers tell us "how many"

 

ex)

 

• The symbols used to denote scalars are usually letters

 

• scalars can be added, subtracted, multiplied, divided, etc. just as 'regular'

- numbers can be ('regular' numbers are scalars…)

 

VECTORS:

• Vector measurements tell us the magnitude of the quantity being measured and the direction over which it is be measured

• Vector numbers tell us "how many" and "where"

 

ex)

 

• The symbols used to denote vectors are usually letters with a small arrow above them

 

• Vectors can be added, subtracted, divided, etc. but we must modify the process used according to the direction attached to the quantity

- You CAN'T treat vectors like 'regular' numbers!

 

• we will learn how to add vectors that exist in a single dimension in this course…

INTRO TO KINEMATICS

• before we can hope to understand the physics of the moving world, we need to define some important terms used in this branch of physics

o the branch of physics that deals with motion is called kinematics

o as it turns out, our universe behaves in a very predictable fashion

▪ it appears to obey some very simple rules that can be summarized in the form of mathematical equations

▪ before we can understand and use these rules, we need to be able to measure and define a few fundamental quantities:

DISTANCE & DISPLACEMENT:

• these expressions will appear in a few of the kinematics equations we will be using

Distance (s): - a scalar quantity that measures the space an object moves through our

three dimensional world

- is equal to the sum of the distances moved in any and all

spatial dimensions/directions

- measured in SI base units called metres (m)

Displacement (s):

- a vector quantity that measures the space an object moves through our

three dimensional world

- is equal to the vector sum of the distances moved in any and all

spatial dimensions/directions

- measures a _________________________ (ie: the distance between the starting point and the ending point)

- measured in SI base units called metres (m)

Example:

An MMC student walks 200 m [E] to get to school. After school this same student walks 50 m [W] to get to work.

i) What is the total distance this student walked?

ii) What is the displacement of the student?

TIME (Δt):

• whenever objects move through spatial dimensions, they are also moving through the dimension of time

o unlike spatial dimensions, all physical objects can only move in one direction through time: ________________!

• during our study of kinematics we will see that the kinematics equations require that objects moves through time

o this movement in the time dimension is represented as the as ‘change in time” or Δt in equations

o expressed in SI base units called seconds (s)

SPEED & VELOCITY:

Speed:

- a scalar quantity that measures how far an object travels (distance) in a given time

- expressed in SI base units called metres per second (ms-1)

Velocity:

- a vector quantity that measures the displacement of an object in a given time

- expressed in SI base units called metres per second (ms-1)

Different ‘kinds’ of Speed/Velocity:

|“Kind of Speed” |“Kind of Velocity” |Definition |

|u | | |

|v | | |

|vavg |[pic] | |

|Δv |[pic] | |

ACCELERATION ([pic]):

- an object experiences an acceleration whenever it’s velocity changes

o acceleration is equivalent to the rate of change of velocity

o if an object’s speed remains constant (ie: doesn’t change) the object is NOT accelerating!

o expressed in base units called metres per second2 (ms-2) (it can also be called “metres per second per second”)

Convention:

o _________________________________________________________________

o _________________________________________________________________

WORKSHEET: DISTANCE & DISPLACEMENT

REMEMBER: All vector answers should contain 2 parts: a number and a direction!!

1. During a ride in a hot air balloon, a group of people are carried 50m [N], 625m [S] and then 50 m [N].

a) Calculate the total distance covered by the balloon.

b) Calculate the total displacement of the balloon.

2. A physics student went on a vacation last summer to the Black Hills in South Dakota. They travelled 1000 km [S] from Winnipeg to the hills, saw the sights and made the 1000 km [N] return trip home a week later. Upon their arrival back home they discovered that they left their suitcase in a hotel at Sturgis while on their way home (located 750km [S] of Winnipeg).

a) Calculate the distance and displacement experienced by the

student

b) Calculate the distance and displacement experienced by the

suitcase

3. During an exceptional round of golf, a player drives their ball 100 m [N] down the 7th fairway. The player then hits a 75 m, 6-iron approach shot (also north) that flies over the green. Amazingly the player holes a 5 m chip shot (south) to birdie the par 4 hole. What a play!

a) Calculate the distance and displacement experienced by the ball

4. During a tennis rally the ball crosses the net 13 times. The court is 30 m long, faces east-to-west and the person in the western court served the ball.

a) Determine who won the rally

b) What is the total distance covered by the ball?

c) What displacement does the ball experience?

5. During a Buckeye football game, the quarterback throws a ‘long bomb’ to a wide receiver. During its flight, the ball reached a maximum height of 15 m [U] before it started falling back down, and during this time flew 30m [E], where it was caught. The receiver then ran it another 15 m [E] for a touchdown.

a) Determine the distance and displacement experienced in the up-down

dimension by the ball

b) Determine the distance and displacement experienced by the ball in the

east-west dimension.

PHYSICS & GRAPHS

• graphs serve as pictures of mathematical relationships

o because physics suggests that the universe behaves according to a set of mathematical relationships, graphs should also serve as pictures of physics relationships

• we will be creating three different kinds of graphs in this section of the course:

1. ________________________________________________________

- these graphs are also called _____________________________

2. ________________________________________________________

3. ________________________________________________________

POSITION – TIME GRAPHS

• these graphs show the _________________ of an object as time ticks by

o ____________ is plotted as the independent variable (x – axis)

o distance or position is plotted as the dependent variable (y – axis)

Important Features:

o the ___________ of the line on a d – t graphs represents an object’s ___________

VELOCITY - TIME GRAPHS

• these graphs show the velocity of an object as time ticks by

o time is plotted as the independent variable (x – axis)

o velocity is plotted as the dependent variable (y – axis)

Important Features:

o the ___________ of the line on a v – t graph represents an objects ________________

o the ___________ under the line represents an objects _________________

ACCELERATION – TIME GRAPHS

• these graphs show the acceleration of an object as time ticks by

o time is plotted as the independent variable (x – axis)

o acceleration is plotted as the dependent variable (y – axis)

Important Features:

o the ___________ under the line represents an object’s _________________

• we must be able to use the information contained in any one of the three motion graphs to create the other two

Examples:

1. A bird flies at a rate of 10 ms-1 for 5 seconds. Create the corresponding d – t, v – t and a – t graphs.

2. A car accelerates from rest at a rate of 5.0 ms-2 for 5 seconds. Create the corresponding d – t, v – t and a – t graphs.

d-t, v-t, a-t Graphs

1) From the following d-t graphs calculate the velocity:

2) From the following v-t graphs calculate the displacement and acceleration:

3) Calculate the change in velocity for the following a-t graphs

4) A boat travels at a constant velocity of 12 ms-1 for 5 s. Draw a v-t graph and a d-t graph to represent this motion.

5) A car accelerates from rest at a constant rate of 2 ms-2 for 10 s. Draw an a-t graph and a v-t graph to represent this motion.

6) A sprinter is traveling at a velocity of 10 ms-1 and slows down to rest in 2 s. Draw a v-t graph and a d-t graph to represent this motion.

7) A stone falls at a constant rate of 10 ms-2 for 3 s. Draw a d-t, v-t and a-t graph.

- when considering more complicated scenarios, we will often generate more complicated graphs

- in situations like this, it is often easier to consider these graphs as being made up of various sections

o build these graphs in pieces!

o analyze these graphs in pieces!

Example:

A cat is sitting under a tree when it sees a bird across a large yard. The cat accelerates at a rate of 2.0 ms-2 for 4 seconds in hopes of catching lunch. The bird however, sees the cat coming and flies out of the cat’s reach. The cat continues to chase the bird while running at a top speed of 8.0 ms-1 for another 4 seconds before running into a fence.

Draw the d-t, v-t and a-t graphs that summarize this scenario. Be sure to include a data chart for each of the graphs!

Graphing Worksheet

1. What does the slope of the following graphs represent?

a) d-t graph

b) v-t graph

c) a-t graph

2. What does the area under the following graphs represent?

a) d-t graph

b) v-t graph

c) a-t graph

3. Generate a data chart from the following scenarios and then graph the line.

i) A truck moves down the highway at a constant speed of 25 ms-1 for 10 seconds

Draw the corresponding d-t, v-t and a-t graphs

ii) A car drives down Henderson Highway at a constant speed of 15ms-1 for 8 seconds

Draw the corresponding d-t, v-t and a-t graphs

iii) A person walks due east at a rate of 2 ms-1 for 5 seconds and then walks due west at a rate of 3 ms-1 for 5 seconds

a) Draw the corresponding v-t graph

b) Draw the corresponding d-t graph

iv) A motorcycle accelerates at a rate of 4.4 ms-2 for 8 seconds

Draw the corresponding d-t, v-t and a-t graphs

v) As an object falls to the Earth it is accelerated at a rate of 9.8 ms-2 by gravity. A penny is dropped from a tall building and falls for 10 seconds.

a) Draw the corresponding v-t graph

b) Draw the corresponding d-t graph

4. i) Sketch a d-t graph based on the following description:

a) object begins at a displacement of zero

b) object moves to the right at a constant velocity of 5.0 ms-1 for 5 seconds

c) object stops moving for 3 seconds

d) object moves to the right at a constant velocity of 10 ms-1 for 5 seconds

e) object stops moving for 2 seconds

ii) Sketch the corresponding v-t graph

iii) Sketch the corresponding a-t graph

5. i) Sketch a v-t graph based on the following description:

a) object moves to the right at a constant velocity of 15 ms-1 for 5 seconds

b) accelerates to the right at 4 ms-2 for 5 seconds

c) accelerates to the left at 4 ms-2 for 5 seconds

d) stops moving for 5 seconds

ii) Sketch the corresponding a-t graph

6. i) Sketch an a-t graph based on the following description:

a) object moves at a constant velocity of 100 ms-1 for 4 seconds

b) object slows down at a rate of 25 ms-2 for 3 seconds

c) object moves at a constant velocity of 20 ms-1 for 4 seconds

7. The following graphs describe an object that is moving. Explain in your own words what the object is doing:

[pic]

KINEMATICS

• any object that moves through the 3-dimensional space of our universe seems to obey a few simple and fundamental rules

• we used graphs in the previous section of this unit to try to develop an understanding of these rules

o we were able to create a series of algebraic expressions which describe these rules in the form of mathematics

▪ all of these expressions had their roots based in one of the three kinds of graphs that we created

o in this section of the course we will be learning how to use these expressions/equations to make accurate and precise predictions about the outcomes of different scenarios

EQUATIONS FOR CALCULATING AVERAGE/UNCHANGING VELOCITY:

EQUATION FOR CALCULATING CHANGING VELOCITIES/ACCELERATION:

vavg = average speed/velocity (ms-1)

v = velocity ‘after’ (ms-1)

u = velocity ‘before’ (ms-1)

s = change in distance/displacement (m)

Δt = change in time (s)

a = rate of acceleration (ms-2)

HOW TO SOLVE WORDS PROBLEMS:

• solving word problems becomes a simple task if you attempt to solve them in a series of small steps:

o an acronym can be used to memorize the steps involved in solving word problems: __________________

G: Write out all _______________

o be sure to include 3 vital pieces of information with each given:

1. ___________________________

2. ___________________________

3. ___________________________

U: Identify the _________________

o make sure you know what it is you’re looking for

E: Write out the _______________ that you must use to solve the problem

o ___________________________________________________________________________________________________________________________________________________________________________________________________

S: ____________ the problem

o make sure the units attached to all quantities you’re working with don’t conflict

▪ if they do, perform the required conversions

o be sure to include units with your answer (and direction if working with vectors)

Examples:

1. A boat travels a distance of 350 m in 20 seconds. Determine:

a) the speed of the boat (in ms-1)

b) the speed of the boat (in kmh-1)

2. Suppose a car travels at a constant speed of 10 ms-1. How many metres would it move in:

a) 1 s

b) 1 min

c) 1 h

3. A bacterium can move at a uniform rate of 100 μms-1. How long would it take this bacterium to move 1.0 m?

4. Jules Verne wrote a book called Around the World in Eighty Days. What was his average speed in ms-1 and kmh-1 if the radius of the Earth is 6400 km?

5. You live 3.5 km from school and are going to be late for class! You hop in your parents’ car and decide to speed to try to make it to school on time. The posted speed limit is 60 kmh-1 but instead you travel 70 kmh-1 from your home to the school. How much time did you save by speeding vs obeying the speed limit?

6. If it takes 0.08 s for an air bag to stop a person, what is the rate of acceleration of a person moving 13.0 kms-1 who comes to a complete stop in this time?

7. An object accelerates at 9.8 ms-2 when falling. How many seconds does it take an object to change its speed from 4.5 ms-1 to 19.4 ms-1?

8. What is an object’s final velocity if it accelerates at 2.0 ms-2 [F] for 2.3 s from a velocity of 50 kmh-1 [F]?

WORKSHEET - Kinematics

1. For the following, state the symbol and the corresponding unit(s):

a) distance

b) displacement

c) speed

d) velocity

e) acceleration

2. Give an example where velocity and acceleration are negative.

3. Can the velocity of an object be negative when its acceleration is positive? Explain.

4. Can the velocity of an object be positive when its acceleration is negative? Explain.

5. A boy walks 13 km in 2.0 h. What is his average speed in kmh-1 and ms-1?

6. A high school athlete runs 1.00 X 102 m in 12.20 s. What is her average speed in kmh-1 and ms-1?

7. A bullet is shot from a rifle with a velocity of 720.0 ms-1 [E].

a) What time is required for the bullet to strike a target 324.0 m to the

east?

b) What is the velocity of the bullet in kmh-1? (magnitude and direction!)

8. A rocket launched into outer space travels 240 000 km during the first 6.0 h after launching. What is the average speed of the rocket in kmh-1 and ms-1?

9. Light from the sun reaches the earth in 8.3 min. The speed of light is 3.00 X 108 ms-1. In kilometers, how far away is the earth from the sun?

10. An athlete accelerates by 2.5 ms-2 for 1.5 s. What is her change in speed at the end of 1.5 s?

11. A skier is moving at 1.8 ms-1 just after leaving the gates. 3.7 s later has reached a speed of 8.3 ms-1. What is the average acceleration experience by this skier?.

12. A bus with an initial speed of 12 ms-1accelerates at 0.62 ms-2 for 15 s. What is the final speed of the bus in ms-1 and kmh-1?

13. As a truck approaches a stop light it slows down by 45 kmh-1 in 0.002 h. Calculate the acceleration of the truck

14. How much time has passed if an object has experienced an average acceleration of 5.0ms-2 while its velocity has changed by 50 kmh-1?

15. A snowmobile reaches a final speed of 90 kmh-1 after accelerating at 1.2 ms-2 for 17 s. What was the initial speed of the snowmobile?

16. A NASA space shuttle touches down on a runway at an initial speed of 340 kmh-1 and accelerates at a rate of -4.40 ms-2. How much time does it take for the shuttle to stop?

17. A baseball player running at 6.0 ms-1 slides into home plate and stops in 2.5 s. What is the average acceleration of the baseball player?

18. A person drops a tennis ball from a tall building. What will be the speed of the ball after it falls for 4.0 seconds? The acceleration due to gravity is 9.8 ms-2.

19. A car is moving at a constant 88 kmh-1 when a dog suddenly appears on the road ahead. The driver immediately brakes to avoid hitting the dog. If the reaction time of the driver is 0.2 s, how far has the car moved (in m) by the time the driver touches the brake pedal?

20. An octopus can accelerate rapidly by squirting a stream of water for propulsion. An octopus moving at 0.35 kmh-1 accelerates at 5.5 ms-2 to a final speed of 3.5 ms-1. What is the elapsed time during the acceleration?

21. A sports car accelerates from rest to 100 kmh-1 in 6.4 s. What is the cars acceleration in ms-2?

22. A motorcycle starts from rest and accelerates at a rate of 6.0 ms-2 for 5 seconds. Calculate its final velocity.

DYNAMICS

• We have just finished studying kinematics

• We defined kinematics as: _______________________________

• Our next topic is related to motion but chooses to address a different aspect of it

• Dynamics seeks to identify _________________________________

• Dynamics is defined as: ____________________________________________

• Collectively the study of kinematics and dynamics together is called __________________

• the first person to explain why motion happens was an English scholar named Isaac Newton

• it makes sense to begin our study of dynamics by considering what he ‘discovered’…

NEWTON’S LAWS:

• Much of what we will study is the result of the work of Sir Isaac Newton, arguably the most brilliant person who has ever lived

• Newton clarified the physics of dynamics with what we now refer to as “Newton’s Laws of Motion” of which there are three, referred to simply as “Newton’s first law”, “Newton’s second law”, and “Newton’s third law”

• Prior to Newton, it was believed that an object must have a force applied to keep it moving.

• Greek academic _________________ was one of the great minds of antiquity who presented this idea as being a truth of our universe

• This is a very reasonable conclusion to make, as it seems to be true everywhere we look

▪ _______________________________________________________

▪ _______________________________________________________

Example: a moving car is moving because of the engine producing a force - if the engine is shut off while the car is moving, the car will soon stop.

• Tuscan physicist, astronomer, philosopher and mathematician _____________________ challenged this idea, with a simple thought experiment

o he argued that if an object is pushed it will slide on a surface, travel some distance, and then stop

o If a smoother surface is used, _______________________________________

o If an even smoother surface is used, __________________________________

o He concluded that if a perfectly smooth surface could be made, then the object should go for ever

▪ ______________________________________________________________________________________________________________________

NEWTON’S FIRST LAW:

• Newton formalized Galileo’s findings in what we now call Newton’s First Law:

• It can be stated as: “_________________________________________________________________________________________________________________________________”.

o First let’s clear up the “net” in “net force”.

o Force is a vector, and the phrase “net force” means “______________________________________________________________”

o We abbreviate force with _____ and net force as ________ or ΣF (the “Σ” symbol is the Greek letter “sigma” which is used in math for “sum of”).

o Newton’s first law is typically used in one of two ways:

▪ if you ever have an object moving with constant velocity, then you can conclude that _____________________________________________

- Conversely, if you are told (or determine) that there is no net force on an object, then you can conclude that it must be moving with constant velocity

- Realize in all of this that “constant velocity” may also mean being at rest (constant velocity of zero).

▪ Of course if an object is not moving with constant velocity, then we describe it as accelerating, and __________________________________________________________.

• left to themselves, objects just do whatever they are already doing in terms of their velocity.

o Think of a hockey puck: if it sits at rest on the ice, then it will continue to sit at rest. If it is sliding along the ice (ideally there would be no friction at all - so let’s assume that, ignoring for now the little friction that would be there), then it will continue sliding along the ice until something “messes with it” (exerts a force on it).

• Newton’s 1st law is also sometimes described as the “_________________________”

o This law suggests that inertia is a ____________________________

▪ All matter exhibits this trait of “not slowing down”

- This trait is called inertia

▪ Inertia is a fundamental property of matter

NEWTON’S SECOND LAW:

• This law makes the above numerical

• It can be said in words: “____________________________________________________________________________________________________________________________________________________________________________________________________________________________”

o This is simply saying that an object will accelerate

o the amount of acceleration depends on the net force (how hard it is being pushed) as well as on the object’s mass (massive things are harder to accelerate).

• This can also be stated in equation form:

[pic] Fnet = Net force (N)

m = mass (kg)

a = acceleration (ms-2)

• remember that we must have mass measured in kilograms (the SI unit of mass), and acceleration in ms-2

• Units: The units that will result for F in the above equation are rather strange: kg⋅ms-2

o This unit is kind of clumsy, so we invent a new unit, which we call a _________________

ie: ________________________

o A more familiar unit of force is the pound. It may be helpful to know that a pound is the same thing as about 4.45 newtons. (1 lb = 4.45 N).

Examples:

1. What acceleration will the following objects experience if an unbalanced force of 50 N is applied to:

a) a 40 kg person

b) a 3 g penny

2. A skateboarder of mass 60 000 g undergoes an acceleration of 12.6 ms-2. What is the net force acting on the skateboarder?

3. What is the mass (in grams) of a penny knowing that a net force of 3.0 x 10-2 N results in the penny accelerating at the rate of 9.8 ms-2?

Free Body Diagrams

In nearly all situations, more than one force acts on an object.

An object accelerating across the floor experiences:

- A downward force of gravity, Fg

- An upward force of the surface, or normal force, FN

- The applied accelerating force, Fa

The forces will add together to a resultant force that is called a net force

Free Body Diagrams (FBD) help you visualize the forces acting on an object:

Fg always acts ____________________

FN always acts ____________________ to the surface

- it stops the object from falling through the surface

Ff is always _____________ to the surface of contact and _______________ the motion of the object

Fa is any push or pull

- applied forces through a string or rope are called tension forces

Drawing Rules

1. Draw a sketch of the object completely removed from its physical surroundings. (Often the force vectors are drawn from a dot at the centre of the object)

2. Draw vectors representing the forces acting on the object. The vectors must show the direction of the force. It is also useful to approximate the magnitude of the force, so the length of the vector is important. But in first drawing the vectors, it is often not clear what the length should be so an approximate length can be shown.

3. Do not include forces exerted on the surroundings by the object.

4. When finding the net force acting on an object from a free-body diagram, use the rules for vector addition.

Examples

1. A steel ball is falling through water. Assume that the gravitational force is larger than the frictional force of the water.

2. A rectangular box is pulled to the left with a horizontal force. There is friction between the box and the flat surface. The force to the left is larger than the frictional force.

The Vector Nature of Newton’s 2nd Law

2 things to remember

1. When more than one external force is acting on an object, the object accelerates in the direction of the net force; this net force may be determined by the vector addition of all the individual forces that are acting on the object.

2. If the net force acting on an object is zero (Fnet = 0N), the object is not accelerating (a = ms-2). This either means:

a. The object is at rest

b. The object is moving at a constant velocity

Examples:

1. Two horses pull a carriage, each with a force of 220N. If the carriage is being pulled down a rough gravel road (Ff = 20N), what is the net force acting on it?

2. A box of books is pushed across the room with an applied force of 150N [L]. There is friction between the box and the carpet which is equal to 80N. If the mass of the box is 10kg, what is the acceleration of the box?

3. A baby carriage with a mass of 50kg is being pushed along a rough sidewalk with an applied horizontal force of 200N, and it has a constant velocity of 3.0ms-1. What is the other horizontal force acting on the carriage, and what is the magnitude of that force?

NEWTON’S THIRD LAW:

• This law is often seen as the most confusing of the three

• It is popularly known as “________________________________________________________________________”

o this is NOT very useful, and is also misleading

• a ‘better’ version of Newton’s 3rd law is _____________________

o the first subscript found after a force symbol tells which object is exerting the force, the second subscript is for the object that is having the force applied to

o this law states that every force is actually an interaction between two objects

▪ ______________________________________________________________________________________________________________________

▪ ______________________________________________________________________________________________________________________

▪ Forces always occur in pairs!!

Example: When you kick a ball there is an interaction between your foot and the ball.

- The ball gets pushed forwards with a force from

your foot.

- Simultaneously, your foot will experience a force

from the ball - the same size, but in the opposite direction.

NEWTON’S LAWS

1. Explain the following scenarios in terms of net force and acceleration referring to Newton’s Laws.

a) Why is it easier to push a shopping cart when it is empty opposed to when it is full of groceries?

b) A magician can pull a tablecloth out from underneath dishes without breaking them. How does this work?

c) Why do you move towards the dashboard when you slam on the brakes?

d) Your science textbook is resting in your backseat as you drive home from school. All of a sudden, you turn sharply and your textbook slides across the backseat and hits the door. Why did it do this?

2. Calculate the net force acting on the blocks (be sure to indicate direction).

a) 6 N 10 N b) 7.2 N

5.5 N

3.2 N

3. A net force of 28 N is used to push a 10 kg box across the ground. What is the acceleration of the box?

4. A net force of 65 N is used to push a 4.3 kg toy across the ground. Find the toy’s acceleration.

5. A student pushes a 10 kg object and makes it accelerate at 3.2 ms-2. What is the net force.

6. A student pushes a 5.4 kg object and makes it accelerate a -2.5 ms-2. What is the net force acting on the object?

7. A student pushes his 1100 kg car down the street with a force of 150 N to the right. A second student pushes the same car to the right with a force of 78 N. Find the acceleration of the car. (Ignore friction)

8. A 1350 kg car moves at a constant velocity of 23 ms-1 for 5 seconds. What is the net force on the car?

9. A girl pushes a 13.5 kg object with a force of 75 N across a table. The force of friction between the object and the table is 48 N. Find the acceleration of the object.

|Code |Outcome description |Understanding Level |

| | |Level 1 |Level 2 |Level 3 |

|1.1 |Algebra |Sometimes manipulates algebraic expressions correctly |Usually manipulates algebraic expressions correctly |Consistently manipulates algebraic expressions |

| | |(50-75%) |(75-90%) |correctly (90-100%) |

|1.2 |Identify scalars/vectors |Sometimes correctly identifies scalars and vectors (50-75%) |Consistently correctly identifies scalars and vectors | |

| | | |(75 – 100%) | |

|1.3 |Distance/displacement |Sometimes correctly solves distance/displacement problems |Usually correctly solves distance/displacement problems |Consistently correctly solves distance/displacement |

| |problems |(50-75%) |(75-90%) |problems (90-100%) |

|1.4 |Speed/velocity problems |Sometimes correctly solves speed/velocity problems (50-75%) |Usually correctly solves speed/velocity problems |Consistently correctly solves speed/velocity problems |

| | | |(75-90%) |(90-100%) |

|1.5 |Acceleration |Sometimes correctly solves acceleration problems (50-75%) |Usually correctly solves acceleration problems (75-90%) |Consistently correctly solves acceleration problems |

| | | | |(90-100%) |

|1.6 |General graphing skills |Consistently demonstrates an understanding of 1 of the |Consistently demonstrates an understanding of 2 of the |Consistently demonstrates an understanding of 3 of the|

| | |following skills: |skills listed in level 1 |skills listed in level 1 |

| | |Correct x and y axis | | |

| | |Labelled axis | | |

| | |Correct units | | |

|1.7 |Interpreting graphing |Consistently demonstrates the ability to create motion graphs| | |

| |problems |from a word problem | | |

|1.8 |Creating motion graphs |Consistently demonstrates an understanding of 3 of the skills|Consistently demonstrates an understanding of 4 of the |Consistently demonstrates an understanding of 5 of the|

| |(student generated graphs)|listed below: |skills listed in level 1 |skills listed in level 1 |

| | |Using a d-t graph, create a v-t and a-t graph | | |

| | |Using a v-t graph, create a d-t and a-t graph | | |

| | |Using an a-t graph, create a d-t and v-t graph | | |

| | |Calculate displacement (area) | | |

| | |Calculate acceleration (slope) | | |

|1.9 |Interpreting graphs |Consistently demonstrates an understanding of 3 of the skills|Consistently demonstrates an understanding of 4 of the |Consistently demonstrates an understanding of 5 of the|

| |(based on provided graphs)|listed below: |skills listed in level 1 |skills listed in level 1 |

| | |Direction of motion | | |

| | |Determine distance/displacement | | |

| | |Determine average velocity/speed | | |

| | |Determine average acceleration | | |

| | |Determine type of acceleration (-/+) | | |

|1.10 |Newton’s Laws |Can identify the correct law to explain a scenario OR given a|Can identify the correct law to explain a scenario AND | |

| | |scenario, can identify the correct law |given a scenario, can identify the correct law | |

|1.11 |Free Body Diagrams |Given a word problem, can sometimes sketch an accurate free |Given a word problem, can usually sketch an accurate | |

| | |body diagram (using vectors with correct magnitude and |free body diagram (using vectors with correct magnitude | |

| | |correct labels) (50-75%) |and correct labels) (75-100%) | |

|1.12 |Newton’s Second Law (F=ma)|Consistently demonstrates an understanding of 1 of the skills|Consistently demonstrates an understanding of 2 of the |Consistently demonstrates an understanding of 3 of the|

| | |listed below: |skills listed in level 1 |skills listed in level 1 |

| | |Determine net force given a free body diagram | | |

| | |Determine net force given a word problem | | |

| | |Can solve problems by manipulating F=ma | | |

-----------------------

d - t

v - t

a - t

slope

area

s/m

s/m

s/m

t/s

t/s

t/s

v/ms-1

v/ms-1

v/ms-1

t/s

t/s

t/s

a/ms-2

a/ms-2

t/s

t/s

a/ms-2

t/s

FN

Ff

Fg

Fa

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