chapter 5 forces force & vectors forces kinematics: describes how an object moves dynamics:...
TRANSCRIPT
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Chapter 5Forces
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Force & Vectors
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Forces
• Kinematics: Describes how an object moves
• Dynamics: Describes why an object moves
• Newton’s three laws of motion, describe the “dynamics” of why objects move
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Forces and Interaction
• Force – a “push or pull”
• Contact Force – you physically push on a wall
• Long-range Force – like magnets or gravity
• Force – a vector quantity. Has what two parts.
• SI Unit – the Newton abbreviated as “N”
• Superposition of Forces : forces combine according to vector addition
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4 Types Forces• Gravitational forces
• The Earth pulls and holds the moon in orbit• The moon pulls and causes tide changes
• Electromagnetic forces• due to electric charges, both static and moving.
• Strong Nuclear Forces • holds particles in the nucleus together. (Strongest
of the 4)• Weak Nuclear Forces
• Radioactive decay
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Newton’s Three Laws of Physics
The apple was at rest, what started it in
motion?
Why did the apple accelerate?
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Newton’s 1st Law
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• An object at rest will stay at rest unless a force acts on it.• Here, the girl is at rest until acted on by the force imposed
by the cannonball.
Newton’s 1st Law
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Newton’s 1st Law• An object at rest will stay at rest unless a force
acts on it.• Here, the skateboard/log combination is at rest
until acted on by the force imposed by the rocket.
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Newton’s 1st Law• An object in motion will continue in a straight line until
acted on by some “outside” force.
• Consider a baseball that is pitched to a batter. What force causes the ball to change direction?
Hit
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Newton’s 1st Law
• An object in motion will continue in a straight line until acted on by some “outside” force.
• Consider the space shuttle turning while in space flight. What produces the forces?
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Newton’s 1st law• An object in motion will continue in a straight line
until acted on by some “outside” force.
• Consider the space shuttle when landing. What produces the forces?
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Multimedia
• The car and the wall
• The motorcyclist
• The truck and the ladder
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Weight and Mass
Mass:
A measure of the amount of matter in an object has.Symbol (m) Unit (kg)
Weight:
The gravitational force exerted on a body
Symbol (W) Unit (N Newton)
W mg
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Weight
A Motor cycle weights 2450N. What is its mass?
W mg /m W g
2
2450
9.8 ms
Nm
250m kg
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Homework
• WS 5a 1-10
• WS 5a (b) 1-11
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Newton’s 2nd Law
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Newton’s 2nd Law
• Acceleration is directly proportional to the magnitude of the net force.
• Acceleration is inversely proportional to the mass of the object.
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Newton’s 2nd Law
netFam
F ma
• Acceleration depends on both mass and the net force
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Acceleration depends on net force
• A force of 10N accelerates the box
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Acceleration depends on net force
• A force of 20N accelerates the box twice as fast
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Acceleration depends on mass
• A force of 10N accelerates the box
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Acceleration depends on mass
• A force of 10N accelerates the smaller box faster
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Free-body diagrams WS 5b #1
Draw the free-body diagram for a book is at rest on a table top. normalF
gravityF
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A girl is suspended motionless from a bar which hangs from the ceiling by two ropes. A free-body diagram for this situation looks like this:
gravityF
tensionFtensionF
Free-body diagrams WS 5b #2
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An egg is free-falling from a nest in a tree. Neglect air resistance. A free-body diagram for this situation looks like this:
gravityF
Free-body diagrams WS 5b #3
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A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. A free-body diagram for this situation looks like this:
gravityF
normalF
appFfrictionF
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If the net force is zero, there is no acceleration
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If the net force is not zero, there is acceleration
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Net Force
• If there is no movement–The net force is zero
• If there is no acceleration–The net force is zero
• If there is acceleration–The net force is not zero.
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Homework
• WS 5b (FBD)– 3-10
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Newton’s 1st Law Equilibrium Situation
• An object at rest will stay at rest unless a force acts on it.
• An object in motion will continue in a straight line until acted on by some “outside” force.
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Newton’s Second Law – Non-Equilibrium Situation
• The result of a Non-Equilibrium situation is that the body, will begin to move.
amFFFF
...321
1F
1F
2F 1F F ma
1 2F F F ma
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Newton’s Second Law – Non-Equilibrium Situation
• Two 50g masses are placed 40cm on either side of a fulcrum. What is the Net force?
• If left mass slides 20cm right, what happens?
• If the left mass slides 20cm right and grows to 100g, what type of situation is this?
amFFFF
...321
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Newton’s 2nd law e.g.• What net force is required to accelerate a
1500kg race car at 3.0m/s2?
F ma21500 (3.0 / )F kg m s
4500F N
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A truck with a mass of 710kg starts from rest and travels 40m in 3.0s
What Fnet acts on the car?
21
1
2d v t at
2
2da
t 2
2(40 )
3
ma
s
28.8 ms
a
6248F N
F ma
Newton’s 2nd law e.g.
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Newton’s 2nd law e.g.
A 873kg dragster, starting from rest, accelerates to a speed of 26.3m/s in .59s
a) Find the acceleration
b) Find the average force on the dragster
2 1v v at 2 1v va
t
244.6 m
sa
F ma 38935F N
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Newton’s 2nd law WS5d #1• An artillery shell has a mass of 55kg. The
shell leaves the 1.5m long barrel at a velocity of 770m/s.
• What is the force the gun applies to the shell?– Step 1 Find the acceleration– Step 2 Find the Net Force
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Newton’s 2rd Law WS5d #1• What is the force the gun applies to the shell?
2 22 1 2v v ad
2 22 1
2
v va
d
2 2(770 ) (0 )
2(1.5)
m ms sa
m
F ma
2
555 (2 10 )ms
F kg x
71.1 10F x N2
52 10 ms
a x
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Newton’s 2rd Law WS 5c #5
• A car, mass 1225kg traveling at 105km/hr slows to a stop in 53m.
• What is the size and direction of the force that acted on the car?
– Step 1 Unit conversion km/hr to m/s– Step 2 Find the acceleration– Step3 Find the Force
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Newton’s 2nd Law WS 5d #51000 1
105 ( )( ) 29.21 3600
km mhr s
m hr
km s
2 22 1 2v v ad
2 22 1
2
v va
d
F ma
9800F N
28.0 ms
a
2 2(0 ) (29.2 )
2(53 )
m ms sa
m
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Homework
• WS 5c– 1-5
• WS 5d– 1,2
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Newton’s 3rd Law
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Newton’s 3rd Law
• When one object exerts a force on a second object, the second exerts a force on the first that is equal in magnitude but opposite in direction.
• For every action there is an equal and opposite re-action.
• Action – Reaction force pair
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Newton’s 3rd LawExample
• A book rests on a table• The force from the weight
of the book pushes down.• The table provides a
supportive force up.
• Normal force (N) is perpendicular to the surface
W mg
N mg
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Friction
• Friction is a force like any other force
• Friction acts on materials that are in contact with each other
• Friction slows down motion
• Forces due to friction are always in the opposite direction of the motion.
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Friction• There are two types of friction:
– Kinetic (Sliding) friction: The force that opposes the motion of a moving object
– Static friction: The force that oppose the start of motion.
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Friction
• The force of friction depends on
1) The force pushing down (weight)
2) The surface materials in contact with each other
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Friction
f NF F
fF force of friction
coeffiecient of friction
NF Normal force
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• A horizontal force of 30N pushes a 12kg crate across a floor at a constant velocity. Find the coefficient of sliding friction.
Friction Example
gravityF
normalF
appFfrictionF
app fF F
f NF F f
N
F
F
2
30
12 (9.8 )ms
N
kg
.25
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Friction e.g.• A 4kg block has a
coefficient of friction of .22 .
• What is the force of friction for the 4kg block?
• What is the Fnet? • What is the acceleration?
Fapp=20N4kg
f NF F
2.22(4 )(9.8 )mf sF kg
8.6fF N
net app fF F F
20 8.6 11.3netF N N N netF ma
22.8 ms
a
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Homework
• WS 5e• 1-3
• p. 102• 13-16
• Quiz Newton’s 3 laws
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Newton’s laws review• Newton’s First Law - An object remains at
rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposed force.
• Newton’s first law describes an Equilibrium Situation.
• An Equilibrium Situation is one in which the acceleration of a body is equal to zero.
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Newton’s laws review
• Newton’s Second Law – If there is a non-zero net force on a body, then it will accelerate.
• Newton’s Second Law describes a Non-equilibrium Situation.
• A Non-equilibrium Situation is one in which the acceleration of a body is not equal to zero.
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Newton’s laws review
• Newton’s Third Law - for every action force there is an equal, but opposite, reaction force.
• Newton’s Third Law says forces must come in pairs.
• Paired force internal to a system have a Net Force of zero.
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Quiz
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• A horizontal force of 35N pushes on a two block system as shown. If the coefficient of sliding friction is .25, what is the acceleration of the system?
Friction Example
gravityF
normalF
appFfrictionF
2.25(4 5 )(9.8 )mf sF kg kg
f NF F
net app fF F F
35 22.1netF N N 22.1fF N
4kg5kg
Two block system
12.95
9
Na
kg
21.44 ms
a
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Friction e.g.• Two blocks are in contact with each other. The 4kg
block has a coefficient of friction of .22 . The two blocks are accelerated together at 1.2m/s2.
• What is the force of friction for the 4kg block? • What is the Fnet? • What is the coefficient of friction for the gold block?
Fapp=30N4kg
5kg
appFfF
W
N
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Homework
• WS 5f– #’s1-3
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Newton’s 2nd law
• Three identical blocks of 15kg are connected as shown and have a coefficient of friction of 0.3. If the system is pulled to the right, what is the tension at T1?
• At T2?• At T3?
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• A block rests on a table and is attached to a hanging mass suspended by a pulley.
• Does the block move?• What might stop the block from moving?
FPull
Newton’s 2nd Law e.g
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• A 2kg block rests on a table and is attached to a hanging .7kg mass suspended by a pulley.
• The coefficient of sliding friction is .25, if the block was set in motion, would it continue to move?
• Use the direction of motion as positiveFPull
Newton’s 2nd Law e.g
.7kg
2W m g
T
1W m g
N
fF T
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Newton’s 2nd Law e.g • A 2kg block rests on a table and is attached to a
hanging .7kg mass suspended by a pulley. The coefficient of friction between the block and table is
2.25(2 )(9.8 )mf sF kg
.7kg
0.25
4.9fF N
2.7 (9.8 )ms
W kg
6.8W N
fFnet T W F T
6.8 4.9Fnet N N
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FPull
.7kg
2W m g
T
1W m g
N
fF T
Newton’s 2nd Law e.g
net fF T F W T
net fF W F
total fm a W F
1 2 2 1( )a m m m g m g
2 1
1 2
m g m ga
m m
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• Two unequal masses are suspended on either side of a pulley. What will happen?
• Draw the FBD for each mass.
gravityF
tensionF
gravityF
tensionF
2 2netF T m g
2 2m a T m g
1 1netF m g T
1 1m a m g T
Direction of positive motion
1 1T m g m a 2 2T m a m g
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• Two unequal masses are suspended on either side of a pulley. What will happen?
Direction of positive motion
1 1T m g m a 2 2T m a m g
1 1 2 2m g m a m a m g
1 12 2m g m g m a m a
1 12 2( ) ( )g m m a m m
1
1
2
2
( )
( )
g m ma
m m
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• Two unequal masses are suspended on either side of a pulley. What will happen?
• Draw the FBD for each mass.
gravityF
tensionF
gravityF
tensionF
1 2netF W T T W
Direction of positive motion
1 2netF W W
1 2tm a m g m g
1 2
1 2
( )g m ma
m m
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Homework
• WS 5g 4-5
• WS 5f 1-3
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1) What upward force does the mass exert on the scale when the elevator is not moving?
2) What force is exerted when the elevator accelerates upward at 1.5m/s2
500g
500g
500g
A spring scale hangs in an elevator and supports a 4.9N package.
4.9Fscale W N
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2) What force is exerted when the elevator accelerates upward at 1.5m/s2
21.5 ms
a
500g
500g
500g
A spring scale hangs in an elevator and supports a 4.9N package.
Fm
a 2
4.9500
9.8 /
Nm g
m s
2.5 (1.5 / ) .75elevatorF kg m s N
.75 4.9 5.65netF N N N
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Newton’s 2rd Law e.g.
• A bowling ball and a baseball are simultaneously dropped from the top of a football stadium.
• Use Newton’s 2nd Law to predict which ball will hit the ground first.
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Newton’s 2rd Law e.g. • Use Newton’s 2nd Law to predict which ball will
hit the ground first.– Step 1 draw the FBD for both objects– Step 2 Calculate the net force for both objects– Step 3 Calculate the acceleration for both
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Newton’s 2nd Law e.g. • Use Newton’s 2nd Law to predict which ball will
hit the ground first.
bowlingW baseW
25 (9.8 )ms
W kg49W N
21.0 (9.8 )ms
W kg
9.8W NF
am
F
am
25 (9.8 )
5
ms
kga
kg 21.0 (9.8 )
1.0
ms
kga
kg
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A 4500kg helicopter accelerates upward at 2m/s2.What lift force is exerted?
2 24500 (2 ) 4500 (9.8 )m mlift s sF kg kg
Flift
W
net liftF F W
netF ma
liftF ma W
53100liftF N
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Inclined Plane Problems• Draw the FBD for the piano on the inclined plane.
• Resolve the Normal Force (N) and the force of friction (Ff) into their x and y components.
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Inclined Plane Problems• We can do this problem by resolving only one force.• Rotate the FBD so that the N is in the y plane and the Ff
is in the x plane.
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N
W
W
W
cosW W
sinW W
Inclined Plane Problems
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Inclined Plane Problems
sinF W cosF W
A 120kg create rest on an incline plane at 35o.
W
fFN N
fF
W
sinF W cosF W
N
fF
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Inclined Plane Problems
sinF W cosF W
cosN W
A 120kg create rest on an incline plane at 35o.sinF W
2120 (9.8 )sin 35ms
F kg
674.6F N
cosF W 2120 (9.8 )cos35ms
F kg
963.3F N W
fFN
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WS 5H #1A hockey puck (m = 0.5kg) is placed on an icy incline (no friction) shown below. The puck is then released and allowed to slide.
•Draw the FBD•Draw the modified FBD
24 cosF W
N
sinF W
fFN
fF
W
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WS 5H #1
sinF W cosF W
cosN W
A hockey puck (m = 0.5kg) is placed on an icy incline (no friction) shown below. The puck is then released and allowed to slide. sinF W
2.5 (9.8 )sin 24ms
F kg
1.99F N
cosF W 2.5 (9.8 )cos 24ms
F kg
4.47F N
W
fFN
24
Net fF W F
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FBD• A boy pushing a lawn mower with 125N of force at an
angle of 25o ?
• Draw the Free Body Diagram.
Fnorm
W=mg
Ffric
Fapp
Fnorm
W=mg
Ffric
Fapp
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Homework
• WS 5i 1-5
• Chapter test
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FF
WF
FF
WF
8kg 4kg 2kg
4kg5kg
Two block system
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F
WF
F
Inclined Plane Problems
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A car is coasting to the right and slowing down. A free-body diagram for this situation looks like this:
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Free Body diagrams
• If the net forces are zero, the FBD is balanced
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Forces cont.
• FBD’s to Fnet
• Fnet to F=ma
• Horizontal pulley example
• Atwood’s pulley example
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Home Work
• P106 # 5,7,13
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Home Work
• P106 # 22,24
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Homework
• P. 106 #’s 27,28
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A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. A free-body diagram for this situation looks like this:
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A skydiver is descending with a constant velocity. Consider air resistance. A free-body diagram for this situation looks like this:
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A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration. A free-boy diagram for this situation looks like this
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A football is moving upwards towards its peak after having been booted by the punter. A free-body diagram for this situation looks like this:
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Examples of zero net force?
• A book on a desk
• A sky diver with a parachute open
• A bike moving at a constant speed.
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Free Body diagrams
• If the net forces are NOT zero, the FBD is NOT balanced
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Examples of non zero net force
• A book sliding across a desk
• A sky diver falling without a parachute
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C
BA