FORCES / Vectors : identifying , drawing, adding:
displacements, forces and velocities
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TRY without hint first.
labvectors labvectors2 labvectors3 trig (TAKE HOME) ( fun lab= parachute)
1 newton = 0.22 pounds
1pound=4.5 newton
1 kilo =2.2 pounds
1 lb = 0.454 kg
1 newton = 0.22 pounds
1pound=4.5 newton
1 kilo =2.2 pounds
1 lb = 0.454 kg
PART1: VECTOR VS SCALAR
A force is a vector. A force is a push or a pull. It has a magnitude and a direction
A FORCE AFFECTS THE MOTION OF A BODY. THERE ARE 4 FUNDAMENTAL FORCES.
1)READ:
A)Fill the blanks and read.
This man is pulling the block to the _________ or @ _______. (left? right ? )
In that case the force is a pull in a specific direction.
A force is measured in Newton.
For example, the person is pulling
with a force of 100N@right
This will be the notation use.
Understand that a force not only has a magnitude (100 here) but also a unit(Newton) and a direction (@right).
A force is called a vector. A vector is quantity that no only has a magnitude and a unit but also
a direction. A vector is represented by an arrow. The magnitude of the arrow is proportional to the
magnitude of the force and the direction of the arrow has the same direction than the pull or push.
A force has a _________ (how much), a________ (of what) and a ______ (which way).
The pull F is not the only force acting on the box.
The force of gravity W (weight ) is pulling it down (in green left noted W) .
Also. The ground is supporting the box.
This support force (@ up) is called the normal force N. (in blue, noted N).
It is called n ormal because the the support force is always perpendicular to the ground.
The normal force is a reaction force. The box pushes on the ground so the ground pushes back on it.
Now It is easier to pull the box on a smooth surface (like pavement) than on grass.
This is because of the friction between the box and the ground. The friction force
depends on the surfaces in contact. The friction force always opposes motion.
It is always parallel to the ground. See the friction force f in orange.
When representing the forces as vectors, we don't have to draw the box. We can just represent the box as a point (of mass m) and
draw the forces along the x-axis and y-axis. As shown below. This is called a free-body diagram. Can you guess why ?
2) Another thing you need to understand about forces:
In Physics, a force is that which affects the motion of a body. Give some example to illustrate this statement.
3) Read and fill the blanks.
Some forces require direct c________ , unless you are a magician, you can't move a table without touching it.
But some forces don't. A ballon thrown out the window will go down. The Earth is pulling on it, without touching it.
this is the force of _____. A magnet does not need to touch a nail to attract it . this is called the __________ force.
A rubbed balloon can attract small pieces of paper without touching them. This is called the __________ force.
4) In the universe you have 4 fundamental forces: (every thing in the universe can be explained in terms of force acting on matter).
A force is the agent of change. (change in temperature, in shape, in direction, change in energy state .. )
- gravitation. the force of __________ glue all the universe together. The galaxies don't not fly apart, the moon stays in orbit
around the EArth, we stay on EArth, the galaxies stay in clusters. Gravity is a weak force. you hold on apple by a thin thread, gravity can't
break the thread. discuss
- electromagnetic force . This force glues atoms together to make molecules and molecules together to make solids or liquids.
It is responsible for electricity, magnetism and light.
It is responsble for the chemical reactions in living and non living organisms. The electromagnetism is _______ than the gravity force. (stronger ? weaker)
since a magnet can easily pull up a paper clip, defying gravity that pulls down.
- strong nuclear together. glues neutron and protons together in an atomic nucleus. discuss.
- weak nuclear force responsible for nuclear decay. (radioactivity) responsible for the Sun's light (fusion reaction).
we can not be here without this force. this force fused hydrogen atoms together make helium and heavier elements
we are made off. The stuff that makes ups were made in stars (nuclear furnace) through fusion of atoms.
Note (more advanced). During a radioactive decay a neutron is changed into a proton. During the fusion realction, a proton
is changed into a proton. This change is due to the weak force. learn more here.
short but good movie about the 4 fundamental forces
(discovery channel)
watch a movie to understand forces. chose the segment: forces and vectors
Read: Pushes and pulls are forces. Whenever you are pushing or pulling, lifting or bending, twisting or tearing, stretching or squeezing, we are exerting a force.
Go on: http://www.pbs.org/wgbh/buildingbig/lab/forces.html
and find out about different examples of force.
5) Observe this image. 2 forces are acting on the apple at rest. Can you guess what these forces are ?
What are their direction ?
http://www.deepocean.net/deepocean/index.php?science08.php
6) A circular spring scale, scaled in newtons, can be used to measure the magnitude of a force.
In class, pull on such a spring scale to get a feeling of how much is 10N, 20N or 50N
If you hang 1 kg on a spring scale, the force produced is 10 N
On Earth 1kg = 10N
The EArth is pulling on the mass of 1kg with a force of ____ N @ ______ (write the magnitude and direction).
This force is called the force of ________ or weight. The unit for mass is kg but the unit for weight is _________.
The mass is how much stuff there is in an object (how many atoms). You have the same mass on the moon or on Earth.
But you don't have the same _________. If you travel to the moon you _________ weight. If you travel to Jupiter, you _______ weight.
so 2kg = ________ N@ ______ , 3kg = _________ N@ ______, 10kg = ______N@ ____, 100kg = _____N@ _____
(hint: from kg to N, multiply by 10, the direction is always .. )
7)
A) Two tugboats are moving a barge. Tugboat A exerts a force of 3000 newtons @ right on the barge.
Tugboat B exerts a force of 5000 newtons in the same direction. What is the combined force on the barge?
Let's call this force the net force.
Fnet = _________ N @ _____________
8) Observe this image:
There are 4 forces acting on the plane.
A) Describe each force and its origin.
B) write the direction for each force :
the weight is @ ____________ but the lift is @ ____________
the thrust is @ ____________ but the drag is @ ______________
C) If the magnitude of the weight is greater than the magnitude of the lift,
that is weight > lift , the plane is moving _______________. (up ? down ? not moving up or down)
If lift > weight, the plane is moving _____________. (up ? down ? not moving up or down)
iIf lift = weight, the plane is moving _____________. (up ? down ? not moving up or down)
D) If thrust > drag, the plane is ______________ (accelerating (speeding up)? decelerating (slowing down) ? moving at a constant speed ?)
If drag > thrust , the plane is _________________ (accelerating (speeding up)? decelerating (slowing down) ? moving at a constant speed ?)
If drag = thurst , the plane is __________________ (accelerating (speeding up)? decelerating (slowing down) ? moving at a constant speed ?)
E) You can explain the lift by using Newton's third law. What is Newton third law ? (google).
So if the plan pushes @ down on the air (its weight), the air _______ back @ _______on it, as a reaction. This reaction is called the ____________.
F) Do you think in empty space (no air molecules), a space ship has to deal with drag ?
http://www.grc.nasa.gov/WWW/K-12/airplane/forces.html
G) a bird can fly because its wings push @ down (action on the air so the air ________ @ up back on him.
Why if you flip you arms you are not rising since the air is pusgin you up with the same force you are pushing the air down ?
9)
source: great website tutorial
A) What are the 2 forces acting on the skydiver (call it W and f for short)?
What are the directions ? the weight is @ _________ and the air resistance is @ __________
B ) If weight > air resistance (just after the person jumps, before opening the parachute), the person is ___________ @down.
(decelerating or slowing down ? accelerating or speeding up ? moving at a constant speed? )
As the person moves speeds up @ down, the air resistance increases (air resistance increases with speed )
so at some point weight = air resistance. When that happens, the person is moving @ ________ at a __________ speed.
(constant? increasing ? decreasing ?)
This constant speed is called the terminal _________.
so if the weight is 200 pounds @ down then the air resistance f = ____ pounds @ ______.
The 2 forces __________ each other. The net force is _________.
C) Then the person open its parachute. THat increases a lot the air resistance. (there is more surface area to push on, air resistance
increases with __________ area )
now air resistance > weight, even though the person is still moving down. Now the person is _____________.
(slowing down ? speeding up ? moving at a constant speed ? )
So for example if the weight = 200 N @ down and the air resistance = 400N @ up, the net force is ________ N @ __________
but the person is still moving down. just the speed is __________.
D) The person, with the parachute just opened, will slow down. The air resistance ___________ down too until
weight = air resistance again. When that happens, the person is moving @ ________ at a __________ speed.
(constant? increasing ? decreasing ?)
This constant speed is called the ________________ speed. Hopeflully, the ____________ is small and the person does not hurt
herslef when reaching the ground.
10) A Physics book is placed on a horizontal table.
It is not moving. Observe the first image (left).
A) 2 forces balance each other. FW = FN. Fw is the _________ @ __________.
FN is called the normal force FN. It is like a support force and can be explained
but Newton's third law The book pushes on the table (because of its weight) so the table
___________ back on it. This reaction force is called the n___________ force.
The magnitude of Fw and FN are the ____________ since te book is not moving.
So if FW = 10N@ down (also note -10N) then FN = ______ N @ ________ (also noted + 10N)
So the net force acting on the book is Fnet = _________.
Of course of the book is really heavy and the table is really strong then FW > FN (weight > support force)
what's going to happen ?
B) The normal force (support force) is always perpendicular to the surface. Observe the second image.
Can you see the normal force (support force) FN ? Can you see the weight FW ?
If the book does not slide, that means a third force is at work. WHich one ?
(a force that prevent you from sliding when you walk )
12) You are push this chair from left to right. with a force (push) P @ right.
describe all the forces acting on the chair:
P is the _______________ and direction is @ ____________
f is the ___________ force and direction is @ ____________
W is the weight and the direction is @ _______________
N is the normal force and the direction is @ __________ , perpendicular to the __________
13) This boy is leaning on the tree. Observe this picture
The force F1 is the force exerted by _________ on ________, the direction is @ ________
F2 is the force exerted by ___________ on ____________, the direction is @ __________
1 other force is acting on the boy: the ________ @ _______ (noted FW).
But since the boy is not sliding, you also have the ______ force, opposing the motion @ ________
So how many forces together ? _____.
14) Newont's third law application:
Describe the 2 action/reaction pairs : F1/F2 and F3/F4
15) read and fill blancks
In Physics, forces are not the only quantities to be vectors. Displacement is a vector too.
Displacement has not only a ________ (like 3 miles) but also a ________. (like @ North)
velocity is also a vector. It has a ________ (30mph) but also a _________ (like @ 30 degrees North of West).
acceleration is also a vector (the acceleration due to gravity is _____ @ down.
16) In Physics, the quantities that have no direction are called scalar. time is a _______
but displacement is a ____________. temperature is a ________. volume, area, length are all ____________.
velocity is ___________, density and mass are ____________. acceleration is a ____________.
In Physics, the magnitude of the displacement is called the distance. (a scalar).
the magnitude of the velocity is called the speed. ( a scalar).
so if you have 40mph @ South this is a ___________. But if you just have 40mph, in Physics, this is a _________.
3 blocks @ East is a displacement but just 2 blocks is a _________. (scalar)
17) In Physics vectors can represent the velocities of winds. Giving their magnitude and direction.
Observe the picture below. What the arrow represent ? What the numbers represent ?
If 2 arrow are //, what does it mean ?
source
PART II DRAWING FORCES, SCALING.
1) Observe and print this picture.
You are pulling the spring with a force F.
First find the magnitude of the force by using a ruler in centimeter and a scale: 1cm = 2N
then use the notation: F = __________N @ _______. (first blank is the magnitude, second is the direction)
2) Print this picture
You are pulling on this elastic strap with a force of 5N.
Draw the force if 1cm = 2N don't forget the head of the arrow.
3) Print this picture
The horse is pulling the canal boat. Draw the force with a scale 1cm = 100N
4) When an athlete throws a weight, the angle between the force and the horizontal has to be 45 degrees
so the distance (horizontal) is the maximum. Can you draw (on picture below) the force acting on the weight if
the force has a magnitude of 200N and 1 cm = 50N.
5) print the picture
The tennis racket exert a force of 1200N on the tennis ball. Call this force F1 (@right). So F1 = ____N@ ______
Because of Newton's third law, the ball ___________ back on the _________ with a force F2 such as F2 = _____N@ ______.
Draw these 2 forces if 1cm = 500N
6) print this picture
You are pulling the block with a force of 3N@ right.
draw this force if 1cm = 1N
If there is a frictional force between thetable and the block f = 2N@ left, what is the net force Fnet = ____N @_____.
7) A car is pulling a trailer (see below) with a force of 1000 N. Using 1cm = 500N
draw the force.
9) draw the 2 forces acting on the cork.
What are these 2 forces ?
PART III: displacement vs distance
displacement, force, velocity and acceleration are all vectors.
They have a magnitude (including a unit) and a direction
1) here a small animation to understand the difference between distance and displacement.
2)
Here is another movie to help you understand better.
The second part is a more advanced material
3) Observe the diagram below and answer the question.
A hamster moves from start to finish in quest for something to chew on.
The distance it travels is shown in red. This is a number and a scalar.
To find its displacement (vector) , you need to connect the start point to the end point.
This is an arrow, this is the vector displacement. The arrow has a magntitude
(length of the arrow) and a direction. (maybe 30 degrees North of West).
Now think. If the hamster comes back to its initial position.
(end=start) , then the displacement is ______ !! (length of arrow
connecting start to end). But the distance is not _____.
So you walk from Trevor 2 blocks @ North and comes back to TRevor
(you forgot your Physics lab to complete) the distance you cover is _____ blocks
but the displacement is ____ !!
The Eiffel tower is about 300m high. If you go up and down, you displacement is ____
but the distance is _____.
DO LAB VECTORS.
PART IV : ADDING VECTORS - ADDING DISPLACEMENT AND FORCES
1) READ / fill blanks
Adding vectors in 1D is very easy, it is like adding integers.
Look at the picture:
if you walk 8 blocks@ right and 6 more blocks @ rightyour total displacement = ___ blocks @ right or simply + ____
(+ is for the right direction). You can draw the displacement: it is an arrow, 14 blocks long and pointing to the ________
However, The distance is ____ blocks. (no direction)
If you walk 8 blocks @ right and 6 blocks @ left your displacement is _______ @ _______ (8 - 6 ) or just + ____
However, the distance is __________ blocks. The displacement is an arrow _______blocks long pointing to the ____________.
2) You can also add forces: Observe the image:
A) What are the 2 forces acting on the block?
B)complete, we write: F = 10N@right or just + 10N and f = ____ @ _____ or just ______.
These forces are vectors and are represented by __________ (in red). THe length of each arrow is proportional
to the __________ of the force.
C) Find the net force acting on the block. Fnet = ____ N @ ______ (add the vectors, that is add the integers).
(think like if 10 little leprechauns are pulling @ right and 2 are pulling @ left, every thing happens like only
8 are pulling @ right. the 2 @ left cancel the efforts of 2@ right)
D) The net force changes the motion of the block. You will learn in 10th grade, if there is a net force acting on an
object, the object _________________ (stop ? slows down ? speeds up (accelerates) ?
E) if the frictional force were f = 10N@ left (or noted -10N) and if the pull F = 10N@right (or +10N) then the net force
Fnet = __________. ( 10 little leprechauns are pulling @ right but another 10 are pulling @ left with the same force)
3) Consider the following picture: (a block is acted upon by 2 opposite forces)
2 forces are acting on the object:
A) F1 = 3N @ ___________ (+ 3N) and F2 = __ N @ ____ (-___ N)
B)The net force is Fnet = _______ N @ ____________ (add the integer).
C)Use a ruler to draw the net force. (arrow). Do it on scale based the 2 arrows 3N and - 8N in the picture.
4)You can add vectors to find the total displcement:
Find the displacement vector. (needs a magnitude and a direction)
A)You walk 3 blocks to the East (write A=+3) and 8 blocks to the West (write B = -8).
What is you displacement ? (Find A + B).
B)You walk 3 miles to the North and 10 miles to the south what is your displacement ?
C)You walk 10 blocks East and 10 West ?
D) You walk 20 blocks East and 10 West ?
5) velocities are vectors too. You can add them too.
you are in a train. the train is going at 100m/s@right and you walk at 1m/s@right.
a) what is your velocity (include direction) relative to a cow outside.
b) if you walk now at 1m/s @ left what is your velocity relative to the cow ?
6) A boat can travel with a speed of 20.0m/s. If it going against a current of 5.0m/s,
what is the velocity of the boat from a person standing on the shore? Draw the vector representation of this problem before solving.
Use integer: 20.0 m/s @right = + 20
5.0 m/s @ left = -5
7) A boat can travel with a speed of 20.0m/s. If it going with a current of 6.0m/s, what is the velocity of the boat from a person standing on the shore?
Draw the vector representation of this problem before solving.
8) back to adding forces. the vertical direction is independent from the horizontal direction. They ignore each other.
Add these following vectors and DRAW THE VECTOR SUM .
Example: 500N @ up + 800N @ down = 300N @ down Then draw an arrow pointing down and being proportional to the magnitude.
Remember a vector needs a magnitude (300), a unit(N for newtons) and a direction (up or down).
9) asy. Add this vectors and draw the resultant. (the sum).
Example: 16 @ right + 20 @ left = 4 @ left = - 4 (negative sign means @ left)
4 is the magnitude and left is the direction
10) add the vectors. (find the resultant)
A) 5N to the right and 5N to the left
B) 4N to the right and 6N to the left
C) 7N to the right and 5N to the left
D) 6N to the right and 4N to the right
11)REVIEW WRite if the following statements are true or false.
A) Speed is velocity in a given direction
B) The speed of a plane could be described as 300mi/h
C) The velocity of a car can be described as 60 km/h to the north.
D) Speed is a vector quantity
E) velocity is a vector quantity
12) REVIEW
A) Is the following sentence true or false ?
Five blocks south is an example of displacement
B) Then complete: Five is the ___________, blocks is the __________ and, south is the ______________.
C) what is the difference between displacement and distance ?
13)REVIEW
A) What would you total displacement if you walked from your front door, around the block, and then stopped when you reached your front door again ?
B) What is the displacement of a cyclist who travels 1 mile north, then 1 mile east, and finally 1 mile south ?
C) What is the displacement of a cyclist that travels 3 miles south, 3 miles west and 3 miles north ?
14)Practice adding vectors with the following applet. Work only in 1D
(vectors going to the right/left or up/down). Might be a quiz in class.
click here
15) Here is how to add non parallel vectors.
cut vector B and paste on top of A. Tail of B on head of A.
The vector Sum is the arrow traced from the start point (tail of A) to the end point (head of B).
16) adding forces to find the net force.
The net force gives us the direction of the motion as well as the direction of the acceleration
PART V more advanced stuff. extra
0) Do you remember our old friend Pythagorean theorem?
1)You walk 3 miles North and then 7 miles east.
What is your displacement from your starting point ?
follow the steps:
A) on a graph paper sketch the situation: First decide of a scale. like 1 cm = 1 mile.
Then in a coordinate system, start from the origin and draw (use a ruler) an arrow = 7 cm @ right (depends on your scale)
Then draw a second arrow (tail to head) on top of the previous one = 3cm@up. (that is attached to it)
like you did for your lab with the pirates.
B) To find the final displacement draw a third arrow (in a different color) from the origin to the head of the second vector.
(the end of the second vector) . this third arrow is your final vector displacement.
C) Find the length (use a ruler) of this displacement vector and convert to miles.
D) Find the direction with your protractor. Find the angle between the final vector
(the vector displacement) and the x-axis.
So displacement = D = ____ miles @___North of East
E) you could also use Algebra to find the same thing. I am going to show you how, step by step.
Pythagorean theorem gives you the length of the vector.
the length is the hypotenuse of the right angle triangle with legs 7 and 3.
Check: length = hypotenuse = square root of (32 + 72) = _________ mile. Is it the same number ?
Now let's find the angle. You need your TI.
The angle has to depend on the slope. If you increase the slope, the angle ________ and if you decrease the
angle, the slope ________. There must be some king of relationship between the slope and the angle.
And guess what ? there is !!
Le'ts find the slope of the line that goes through the hypotenuse. (see image). )
Slope = rise/run = _____. This ratio in a right triangle has a name it is called. TAN (θ).
tangent of θ. What we need now is to extract θ from the TAN. We need to undo TAN
to extract θ. Here how to proceed:
Get your TI. Go to MODE. move to DEGREE and ENTER.
then enter : 2nd TAN 3/7) ENTER YOU ARE DOING TAN-1(θ) which extract θ from the ratio.
DO you get the same angle ? you should !
2) refer to 1)
A child is playing with a car on the floor of a train that is moving eastward.
While the train travels 12.0 m (so 12m@east), the child pushes the car 2.6m northward (2.6m@north) on the floor
of the train.
A) sketch the situation. decide of a scale. 1cm = 1m. From the origin trace 1 arrow @ east and 1 arrow @ north.
trace the vector sum by connecting the origin to the head of the second arrow. (different color please)
B)The use Pythagorean theorem to find the magnitude.
Use TAN-1 (slope) to find the angle.
D = ____m @ ____ North of East
3.
A 110N force and a 55N force act on a point P. The 110N force acts due North.
THe 55 N force acts due east . WHat is the magnitude and direction of the resultant force (that is the net force
that is the the sum of the 2 forces applied to point P. (You are just adding vectors) ?
A) sketch the situation. You start from the origin . 1 arrow @ east and 1arrow @ north.
do it with a scale on a graph paper. maybe 50N = 5cm ?
REmember order does not matter said the captain.
trace the vector sum by connecting origin to the head of the north vector (by an arrow).
B) The use Pythagorean theorem to find the magnitude.
Use TAN-1 (slope) to find the angle.
Fnet = sum of the forces = ______ N @ _____ North of EAst
4.
a boat can travel 4.0 m/s in still water. It is in a river that flows at 5.5 m/s southward.
If the boat heads eastward, directly across the river, what are the direction and
magnitude of its total velocity ? (remember velocity is a vector. So total velocity is the vector sum of the
2 other velocities. Add the 2 vectors)
A) sketch on scale the situation on a graph paper by adding the vector tail to head (see pirates lab)
hint: 1 cm = 1m/s for example
from origin 1 arrow east then 1 arrow down. head to tail. Connect the origin to the head of the second vector.
B) Find the magnitude and direction
don't forget to convert back to m/s (from cm)
Final velocity = _____ m/s @ ________ South of East.
5. A plane is headed directly east at 340 mi/hr (mph) when the wind is from the south at 45 mi/hr.
What is its velocity (magnitude and direction) with respect to the ground ? (that is find the vector sum = sum of the 2 velocities)
hint: from the origin 1 vector 340mi/hr@east and then , attached to it, 45mi/ht@North.
50 mph = 1cm as a scale? Find the length of the final velocity. convert back to mph. Find the angle with the x-axis.
Final velocity = _____ mph @ _____ North of east
6). 2 soccers players kick the ball at exactly the same time. One player's foot exerts a force of 66N north.
The other's foot exerts a force of 88N east. What is the magnitude and direction of the resultant force (net force =
vector sum) on the ball ?
hint: decide of a scale. Like 10N = 1cm.
from the origin draw 88N@east as an arrow. then 66N@north attached to it. (arrow).
Then trace the net force by connecting the origin to the end of the second vector.
Fnet = _________ N @ ______ North of East
7) A boat travels at 3.8 m/s@east and heads straight across a river 240m wide.
The river flows at 1.6 m/s@down. Find the net velocity. You should know how to do by now !
Velocity net = _____ m/s @ _____South of EAst
A force is a vector. A force is a push or a pull. It has a magnitude and a direction
A FORCE AFFECTS THE MOTION OF A BODY. THERE ARE 4 FUNDAMENTAL FORCES.
1)READ:
A)Fill the blanks and read. This man is pulling the block to the _________ or @ _______. (left? right ? )
In that case the force is a pull in a specific direction.
A force is measured in Newton.
For example, the person is pulling
with a force of 100N@right
This will be the notation use.
Understand that a force not only has a magnitude (100 here) but also a unit(Newton) and a direction (@right).
A force is called a vector. A vector is quantity that no only has a magnitude and a unit but also
a direction. A vector is represented by an arrow. The magnitude of the arrow is proportional to the
magnitude of the force and the direction of the arrow has the same direction than the pull or push.
The pull F is not the only force acting on the box.
The force of gravity W (weight ) is pulling it down (in green left noted W) .
Also. The ground is supporting the box.
This support force (@ up) is called the normal force N. (in blue, noted N).
It is called n ormal because the the support force is always perpendicular to the ground.
The normal force is a reaction force. The box pushes on the ground so the ground pushes back on it.
Now It is easier to pull the box on a smooth surface (like pavement) than on grass.
This is because of the friction between the box and the ground. The friction force
depends on the surfaces in contact. The friction force always opposes motion.
It is always parallel to the ground. See the friction force f in orange.
When representing the forces as vectors, we don't have to draw the box. We can just represent the box as a point (of mass m) and
draw the forces along the x-axis and y-axis. As shown below. This is called a free-body diagram. Can you guess why ?
2) Another thing you need to understand about forces:
In Physics, a force is that which affects the motion of a body. Give some example to illustrate this statement.
3) Read and fill the blanks.
Some forces require direct c________ , unless you are a magician, you can't move a table without touching it.
But some forces don't. A ballon thrown out the window will go down. The Earth is pulling on it, without touching it.
this is the force of _____. A magnet does not need to touch a nail to attract it . this is called the __________ force.
A rubbed balloon can attract small pieces of paper without touching them. This is called the __________ force.
4) In the universe you have 4 fundamental forces: (every thing in the universe can be explained in terms of force acting on matter).
A force is the agent of change. (change in temperature, in shape, in direction, change in energy state .. )
- gravitation. the force of __________ glue all the universe together. The galaxies don't not fly apart, the moon stays in orbit
around the EArth, we stay on EArth, the galaxies stay in clusters. Gravity is a weak force. you hold on apple by a thin thread, gravity can't
break the thread. discuss
- electromagnetic force . This force glues atoms together to make molecules and molecules together to make solids or liquids.
It is responsible for electricity, magnetism and light.
It is responsble for the chemical reactions in living and non living organisms. The electromagnetism is _______ than the gravity force. (stronger ? weaker)
since a magnet can easily pull up a paper clip, defying gravity that pulls down.
- strong nuclear together. glues neutron and protons together in an atomic nucleus. discuss.
- weak nuclear force responsible for nuclear decay. (radioactivity) responsible for the Sun's light (fusion reaction).
we can not be here without this force. this force fused hydrogen atoms together make helium and heavier elements
we are made off. The stuff that makes ups were made in stars (nuclear furnace) through fusion of atoms.
Note (more advanced). During a radioactive decay a neutron is changed into a proton. During the fusion realction, a proton
is changed into a proton. This change is due to the weak force. learn more here.
short but good movie about the 4 fundamental forces
(discovery channel)
watch a movie to understand forces. chose the segment: forces and vectors
Read: Pushes and pulls are forces. Whenever you are pushing or pulling, lifting or bending, twisting or tearing, stretching or squeezing, we are exerting a force.
Go on: http://www.pbs.org/wgbh/buildingbig/lab/forces.html
and find out about different examples of force.
5) Observe this image. 2 forces are acting on the apple at rest. Can you guess what these forces are ?
What are their direction ?
http://www.deepocean.net/deepocean/index.php?science08.php
6) A circular spring scale, scaled in newtons, can be used to measure the magnitude of a force.
In class, pull on such a spring scale to get a feeling of how much is 10N, 20N or 50N
If you hang 1 kg on a spring scale, the force produced is 10 N
On Earth 1kg = 10N
The EArth is pulling on the mass of 1kg with a force of ____ N @ ______ (write the magnitude and direction).
This force is called the force of ________ or weight. The unit for mass is kg but the unit for weight is _________.
The mass is how much stuff there is in an object (how many atoms). You have the same mass on the moon or on Earth.
But you don't have the same _________. If you travel to the moon you _________ weight. If you travel to Jupiter, you _______ weight.
so 2kg = ________ N@ ______ , 3kg = _________ N@ ______, 10kg = ______N@ ____, 100kg = _____N@ _____
(hint: from kg to N, multiply by 10, the direction is always .. )
7)
A) Two tugboats are moving a barge. Tugboat A exerts a force of 3000 newtons @ right on the barge.
Tugboat B exerts a force of 5000 newtons in the same direction. What is the combined force on the barge?
Let's call this force the net force.
Fnet = _________ N @ _____________
B) Now suppose that Tugboat A exerts a force of 2000 newtons@ right on the barge and Tugboat B exerts a force of 4000 newtons in the opposite direction.
(@left). What is the combined force on the barge? fnet = __________N @ ____________
8) Observe this image:
There are 4 forces acting on the plane.
A) Describe each force and its origin.
B) write the direction for each force :
the weight is @ ____________ but the lift is @ ____________
the thrust is @ ____________ but the drag is @ ______________
C) If the magnitude of the weight is greater than the magnitude of the lift,
that is weight > lift , the plane is moving _______________. (up ? down ? not moving up or down)
If lift > weight, the plane is moving _____________. (up ? down ? not moving up or down)
iIf lift = weight, the plane is moving _____________. (up ? down ? not moving up or down)
D) If thrust > drag, the plane is ______________ (accelerating (speeding up)? decelerating (slowing down) ? moving at a constant speed ?)
If drag > thrust , the plane is _________________ (accelerating (speeding up)? decelerating (slowing down) ? moving at a constant speed ?)
If drag = thurst , the plane is __________________ (accelerating (speeding up)? decelerating (slowing down) ? moving at a constant speed ?)
E) You can explain the lift by using Newton's third law. What is Newton third law ? (google).
So if the plan pushes @ down on the air (its weight), the air _______ back @ _______on it, as a reaction. This reaction is called the ____________.
F) Do you think in empty space (no air molecules), a space ship has to deal with drag ?
http://www.grc.nasa.gov/WWW/K-12/airplane/forces.html
G) a bird can fly because its wings push @ down (action on the air so the air ________ @ up back on him.
Why if you flip you arms you are not rising since the air is pusgin you up with the same force you are pushing the air down ?
9)
source: great website tutorial
A) What are the 2 forces acting on the skydiver (call it W and f for short)?
What are the directions ? the weight is @ _________ and the air resistance is @ __________
B ) If weight > air resistance (just after the person jumps, before opening the parachute), the person is ___________ @down.
(decelerating or slowing down ? accelerating or speeding up ? moving at a constant speed? )
As the person moves speeds up @ down, the air resistance increases (air resistance increases with speed )
so at some point weight = air resistance. When that happens, the person is moving @ ________ at a __________ speed.
(constant? increasing ? decreasing ?)
This constant speed is called the terminal _________.
so if the weight is 200 pounds @ down then the air resistance f = ____ pounds @ ______.
The 2 forces __________ each other. The net force is _________.
C) Then the person open its parachute. THat increases a lot the air resistance. (there is more surface area to push on, air resistance
increases with __________ area )
now air resistance > weight, even though the person is still moving down. Now the person is _____________.
(slowing down ? speeding up ? moving at a constant speed ? )
So for example if the weight = 200 N @ down and the air resistance = 400N @ up, the net force is ________ N @ __________
but the person is still moving down. just the speed is __________.
D) The person, with the parachute just opened, will slow down. The air resistance ___________ down too until
weight = air resistance again. When that happens, the person is moving @ ________ at a __________ speed.
(constant? increasing ? decreasing ?)
This constant speed is called the ________________ speed. Hopeflully, the ____________ is small and the person does not hurt
herslef when reaching the ground.
10) A Physics book is placed on a horizontal table.
It is not moving. Observe the first image (left).
A) 2 forces balance each other. FW = FN. Fw is the _________ @ __________.
FN is called the normal force FN. It is like a support force and can be explained
but Newton's third law The book pushes on the table (because of its weight) so the table
___________ back on it. This reaction force is called the n___________ force.
The magnitude of Fw and FN are the ____________ since te book is not moving.
So if FW = 10N@ down (also note -10N) then FN = ______ N @ ________ (also noted + 10N)
So the net force acting on the book is Fnet = _________.
Of course of the book is really heavy and the table is really strong then FW > FN (weight > support force)
what's going to happen ?
B) The normal force (support force) is always perpendicular to the surface. Observe the second image.
Can you see the normal force (support force) FN ? Can you see the weight FW ?
If the book does not slide, that means a third force is at work. WHich one ?
(a force that prevent you from sliding when you walk )
12) You are push this chair from left to right. with a force (push) P @ right.
describe all the forces acting on the chair:
P is the _______________ and direction is @ ____________
f is the ___________ force and direction is @ ____________
W is the weight and the direction is @ _______________
N is the normal force and the direction is @ __________ , perpendicular to the __________
13) This boy is leaning on the tree. Observe this picture
The force F1 is the force exerted by _________ on ________, the direction is @ ________
F2 is the force exerted by ___________ on ____________, the direction is @ __________
1 other force is acting on the boy: the ________ @ _______ (noted FW).
But since the boy is not sliding, you also have the ______ force, opposing the motion @ ________
So how many forces together ? _____.
14) Newont's third law application:
Describe the 2 action/reaction pairs : F1/F2 and F3/F4
15) read and fill blancks
In Physics, forces are not the only quantities to be vectors. Displacement is a vector too.
Displacement has not only a ________ (like 3 miles) but also a ________. (like @ North)
velocity is also a vector. It has a ________ (30mph) but also a _________ (like @ 30 degrees North of West).
acceleration is also a vector (the acceleration due to gravity is _____ @ down.
16) In Physics, the quantities that have no direction are called scalar. time is a _______
but displacement is a ____________. temperature is a ________. volume, area, length are all ____________.
velocity is ___________, density and mass are ____________. acceleration is a ____________.
In Physics, the magnitude of the displacement is called the distance. (a scalar).
the magnitude of the velocity is called the speed. ( a scalar).
so if you have 40mph @ South this is a ___________. But if you just have 40mph, in Physics, this is a _________.
3 blocks @ East is a displacement but just 2 blocks is a _________. (scalar)
17) In Physics vectors can represent the velocities of winds. Giving their magnitude and direction.
Observe the picture below. What the arrow represent ? What the numbers represent ?
If 2 arrow are //, what does it mean ?
source
PART II DRAWING FORCES, SCALING.
1) Observe and print this picture.
You are pulling the spring with a force F.
First find the magnitude of the force by using a ruler in centimeter and a scale: 1cm = 2N
then use the notation: F = __________N @ _______. (first blank is the magnitude, second is the direction)
2) Print this picture
You are pulling on this elastic strap with a force of 5N.
Draw the force if 1cm = 2N don't forget the head of the arrow.
3) Print this picture
The horse is pulling the canal boat. Draw the force with a scale 1cm = 100N
4) When an athlete throws a weight, the angle between the force and the horizontal has to be 45 degrees
so the distance (horizontal) is the maximum. Can you draw (on picture below) the force acting on the weight if
the force has a magnitude of 200N and 1 cm = 50N.
5) print the picture
The tennis racket exert a force of 1200N on the tennis ball. Call this force F1 (@right). So F1 = ____N@ ______
Because of Newton's third law, the ball ___________ back on the _________ with a force F2 such as F2 = _____N@ ______.
Draw these 2 forces if 1cm = 500N
6) print this picture
You are pulling the block with a force of 3N@ right.
draw this force if 1cm = 1N
If there is a frictional force between thetable and the block f = 2N@ left, what is the net force Fnet = ____N @_____.
7) A car is pulling a trailer (see below) with a force of 1000 N. Using 1cm = 500N
draw the force.
9) draw the 2 forces acting on the cork.
What are these 2 forces ?
PART III: displacement vs distance
displacement, force, velocity and acceleration are all vectors.
They have a magnitude (including a unit) and a direction
1) here a small animation to understand the difference between distance and displacement.
2)
Here is another movie to help you understand better.
The second part is a more advanced material
3) Observe the diagram below and answer the question.
A hamster moves from start to finish in quest for something to chew on.
The distance it travels is shown in red. This is a number and a scalar.
To find its displacement (vector) , you need to connect the start point to the end point.
This is an arrow, this is the vector displacement. The arrow has a magntitude
(length of the arrow) and a direction. (maybe 30 degrees North of West).
Now think. If the hamster comes back to its initial position.
(end=start) , then the displacement is ______ !! (length of arrow
connecting start to end). But the distance is not _____.
So you walk from Trevor 2 blocks @ North and comes back to TRevor
(you forgot your Physics lab to complete) the distance you cover is _____ blocks
but the displacement is ____ !!
The Eiffel tower is about 300m high. If you go up and down, you displacement is ____
but the distance is _____.
DO LAB VECTORS.
PART IV : ADDING VECTORS - ADDING DISPLACEMENT AND FORCES
1) READ / fill blanks
Adding vectors in 1D is very easy, it is like adding integers.
Look at the picture:
if you walk 8 blocks@ right and 6 more blocks @ rightyour total displacement = ___ blocks @ right or simply + ____
(+ is for the right direction). You can draw the displacement: it is an arrow, 14 blocks long and pointing to the ________
However, The distance is ____ blocks. (no direction)
If you walk 8 blocks @ right and 6 blocks @ left your displacement is _______ @ _______ (8 - 6 ) or just + ____
However, the distance is __________ blocks. The displacement is an arrow _______blocks long pointing to the ____________.
2) You can also add forces: Observe the image:
A) What are the 2 forces acting on the block?
B)complete, we write: F = 10N@right or just + 10N and f = ____ @ _____ or just ______.
These forces are vectors and are represented by __________ (in red). THe length of each arrow is proportional
to the __________ of the force.
C) Find the net force acting on the block. Fnet = ____ N @ ______ (add the vectors, that is add the integers).
(think like if 10 little leprechauns are pulling @ right and 2 are pulling @ left, every thing happens like only
8 are pulling @ right. the 2 @ left cancel the efforts of 2@ right)
D) The net force changes the motion of the block. You will learn in 10th grade, if there is a net force acting on an
object, the object _________________ (stop ? slows down ? speeds up (accelerates) ?
E) if the frictional force were f = 10N@ left (or noted -10N) and if the pull F = 10N@right (or +10N) then the net force
Fnet = __________. ( 10 little leprechauns are pulling @ right but another 10 are pulling @ left with the same force)
3) Consider the following picture: (a block is acted upon by 2 opposite forces)
2 forces are acting on the object:
A) F1 = 3N @ ___________ (+ 3N) and F2 = __ N @ ____ (-___ N)
B)The net force is Fnet = _______ N @ ____________ (add the integer).
C)Use a ruler to draw the net force. (arrow). Do it on scale based the 2 arrows 3N and - 8N in the picture.
4)You can add vectors to find the total displcement:
Find the displacement vector. (needs a magnitude and a direction)
A)You walk 3 blocks to the East (write A=+3) and 8 blocks to the West (write B = -8).
What is you displacement ? (Find A + B).
B)You walk 3 miles to the North and 10 miles to the south what is your displacement ?
C)You walk 10 blocks East and 10 West ?
D) You walk 20 blocks East and 10 West ?
5) velocities are vectors too. You can add them too.
you are in a train. the train is going at 100m/s@right and you walk at 1m/s@right.
a) what is your velocity (include direction) relative to a cow outside.
b) if you walk now at 1m/s @ left what is your velocity relative to the cow ?
6) A boat can travel with a speed of 20.0m/s. If it going against a current of 5.0m/s,
what is the velocity of the boat from a person standing on the shore? Draw the vector representation of this problem before solving.
Use integer: 20.0 m/s @right = + 20
5.0 m/s @ left = -5
7) A boat can travel with a speed of 20.0m/s. If it going with a current of 6.0m/s, what is the velocity of the boat from a person standing on the shore?
Draw the vector representation of this problem before solving.
8) back to adding forces. the vertical direction is independent from the horizontal direction. They ignore each other.
Add these following vectors and DRAW THE VECTOR SUM .
Example: 500N @ up + 800N @ down = 300N @ down Then draw an arrow pointing down and being proportional to the magnitude.
Remember a vector needs a magnitude (300), a unit(N for newtons) and a direction (up or down).
9) asy. Add this vectors and draw the resultant. (the sum).
Example: 16 @ right + 20 @ left = 4 @ left = - 4 (negative sign means @ left)
4 is the magnitude and left is the direction
10) add the vectors. (find the resultant)
A) 5N to the right and 5N to the left
B) 4N to the right and 6N to the left
C) 7N to the right and 5N to the left
D) 6N to the right and 4N to the right
11)REVIEW WRite if the following statements are true or false.
A) Speed is velocity in a given direction
B) The speed of a plane could be described as 300mi/h
C) The velocity of a car can be described as 60 km/h to the north.
D) Speed is a vector quantity
E) velocity is a vector quantity
12) REVIEW
A) Is the following sentence true or false ?
Five blocks south is an example of displacement
B) Then complete: Five is the ___________, blocks is the __________ and, south is the ______________.
C) what is the difference between displacement and distance ?
13)REVIEW
A) What would you total displacement if you walked from your front door, around the block, and then stopped when you reached your front door again ?
B) What is the displacement of a cyclist who travels 1 mile north, then 1 mile east, and finally 1 mile south ?
C) What is the displacement of a cyclist that travels 3 miles south, 3 miles west and 3 miles north ?
14)Practice adding vectors with the following applet. Work only in 1D
(vectors going to the right/left or up/down). Might be a quiz in class.
click here
15) Here is how to add non parallel vectors.
cut vector B and paste on top of A. Tail of B on head of A.
The vector Sum is the arrow traced from the start point (tail of A) to the end point (head of B).
16) adding forces to find the net force.
The net force gives us the direction of the motion as well as the direction of the acceleration
PART V more advanced stuff. extra
0) Do you remember our old friend Pythagorean theorem?
1)You walk 3 miles North and then 7 miles east.
What is your displacement from your starting point ?
follow the steps:
A) on a graph paper sketch the situation: First decide of a scale. like 1 cm = 1 mile.
Then in a coordinate system, start from the origin and draw (use a ruler) an arrow = 7 cm @ right (depends on your scale)
Then draw a second arrow (tail to head) on top of the previous one = 3cm@up. (that is attached to it)
like you did for your lab with the pirates.
B) To find the final displacement draw a third arrow (in a different color) from the origin to the head of the second vector.
(the end of the second vector) . this third arrow is your final vector displacement.
C) Find the length (use a ruler) of this displacement vector and convert to miles.
D) Find the direction with your protractor. Find the angle between the final vector
(the vector displacement) and the x-axis.
So displacement = D = ____ miles @___North of East
E) you could also use Algebra to find the same thing. I am going to show you how, step by step.
Pythagorean theorem gives you the length of the vector.
the length is the hypotenuse of the right angle triangle with legs 7 and 3.
Check: length = hypotenuse = square root of (32 + 72) = _________ mile. Is it the same number ?
Now let's find the angle. You need your TI.
The angle has to depend on the slope. If you increase the slope, the angle ________ and if you decrease the
angle, the slope ________. There must be some king of relationship between the slope and the angle.
And guess what ? there is !!
Le'ts find the slope of the line that goes through the hypotenuse. (see image). )
Slope = rise/run = _____. This ratio in a right triangle has a name it is called. TAN (θ).
tangent of θ. What we need now is to extract θ from the TAN. We need to undo TAN
to extract θ. Here how to proceed:
Get your TI. Go to MODE. move to DEGREE and ENTER.
then enter : 2nd TAN 3/7) ENTER YOU ARE DOING TAN-1(θ) which extract θ from the ratio.
DO you get the same angle ? you should !
2) refer to 1)
A child is playing with a car on the floor of a train that is moving eastward.
While the train travels 12.0 m (so 12m@east), the child pushes the car 2.6m northward (2.6m@north) on the floor
of the train.
A) sketch the situation. decide of a scale. 1cm = 1m. From the origin trace 1 arrow @ east and 1 arrow @ north.
trace the vector sum by connecting the origin to the head of the second arrow. (different color please)
B)The use Pythagorean theorem to find the magnitude.
Use TAN-1 (slope) to find the angle.
D = ____m @ ____ North of East
3.
A 110N force and a 55N force act on a point P. The 110N force acts due North.
THe 55 N force acts due east . WHat is the magnitude and direction of the resultant force (that is the net force
that is the the sum of the 2 forces applied to point P. (You are just adding vectors) ?
A) sketch the situation. You start from the origin . 1 arrow @ east and 1arrow @ north.
do it with a scale on a graph paper. maybe 50N = 5cm ?
REmember order does not matter said the captain.
trace the vector sum by connecting origin to the head of the north vector (by an arrow).
B) The use Pythagorean theorem to find the magnitude.
Use TAN-1 (slope) to find the angle.
Fnet = sum of the forces = ______ N @ _____ North of EAst
4.
a boat can travel 4.0 m/s in still water. It is in a river that flows at 5.5 m/s southward.
If the boat heads eastward, directly across the river, what are the direction and
magnitude of its total velocity ? (remember velocity is a vector. So total velocity is the vector sum of the
2 other velocities. Add the 2 vectors)
A) sketch on scale the situation on a graph paper by adding the vector tail to head (see pirates lab)
hint: 1 cm = 1m/s for example
from origin 1 arrow east then 1 arrow down. head to tail. Connect the origin to the head of the second vector.
B) Find the magnitude and direction
don't forget to convert back to m/s (from cm)
Final velocity = _____ m/s @ ________ South of East.
5. A plane is headed directly east at 340 mi/hr (mph) when the wind is from the south at 45 mi/hr.
What is its velocity (magnitude and direction) with respect to the ground ? (that is find the vector sum = sum of the 2 velocities)
hint: from the origin 1 vector 340mi/hr@east and then , attached to it, 45mi/ht@North.
50 mph = 1cm as a scale? Find the length of the final velocity. convert back to mph. Find the angle with the x-axis.
Final velocity = _____ mph @ _____ North of east
6). 2 soccers players kick the ball at exactly the same time. One player's foot exerts a force of 66N north.
The other's foot exerts a force of 88N east. What is the magnitude and direction of the resultant force (net force =
vector sum) on the ball ?
hint: decide of a scale. Like 10N = 1cm.
from the origin draw 88N@east as an arrow. then 66N@north attached to it. (arrow).
Then trace the net force by connecting the origin to the end of the second vector.
Fnet = _________ N @ ______ North of East
7) A boat travels at 3.8 m/s@east and heads straight across a river 240m wide.
The river flows at 1.6 m/s@down. Find the net velocity. You should know how to do by now !
Velocity net = _____ m/s @ _____South of EAst