Chapter 4: Forces & Newton’s Laws of...
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Chapter 4: Forces & Newton’s Laws of Motion •Newton’s 3 Laws •Types of Forces •Solving 1D &2D Problems •Force Vector Diagrams!!!
Transcript of Chapter 4: Forces & Newton’s Laws of...
Chapter 4: Forces & Newton’s
Laws of Motion
•Newton’s 3 Laws
•Types of Forces
•Solving 1D &2D Problems
•Force Vector Diagrams!!!
Man of the Millennium
Sir Issac Newton
(1642 -1727)
1687 Published Principia
•Invented Calculus
•3 Laws of Motion
•Universal Law of Gravity
Newton’s First Law (Law of Inertia)
An object will remain at rest or in
a constant state of motion unless
acted upon by external net forces.
Newton’s 2nd Law
The acceleration of an object is directly
related to the net external forces acting on
it and inversely proportional to its mass.
netFa
m
F ma
Net Force?
Direction of applied forces matters!!!
Opposite forces cancel!
Newton’s 3rd Law
To every force there is an equal but
opposite reaction force.
hand on wall wall on handF F
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A force is a push or a pull. The Unit is the NEWTON:
A force acts on an object.
Pushes and pulls are applied to something.
From the object’s perspective, it has a force exerted on it.
What Is a Force?
Slide 5-18
2
mkg N
s
F ma
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Contact forces are forces that act on an object by touching it at a point of contact.
The bat must touch the ball to hit it.
Long-range forces are forces that act on an object without physical contact.
A coffee cup released from your hand is pulled to the earth by the long-range force of gravity.
What Is a Force?
Slide 5-20
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Types of Mechanical Forces
Slide 5-45
Forces are Interactions
Earth on Rock Rock on EarthF F
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Every force has an agent which causes the force.
Forces exist at the point of contact between the agent and the object (except for the few special cases of long-range forces).
Forces exist due to interactions happening now, not due to what happened in the past.
Consider a flying arrow.
A pushing force was required to accelerate the arrow as it was shot.
However, no force is needed to keep the arrow moving forward as it flies.
It continues to move because of inertia.
Thinking About Force
Slide 5-75
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EXTERNAL Forces either
Speed you up
Slow you down
Change your direction
Cancel each other out!!!
The natural motion of
a body is to remain in
whatever state of
motion it is in unless
acted upon by net
external forces.
Galileo Challenged The Dogma
Of Natural Motion
Newton’s First Law (Law of Inertia)
An object will remain at rest or in
a constant state of motion unless
acted upon by external net forces.
Inertia
The resistance of an object to change its
state of motion. A measure of mass or
how much stuff an object has.
A hollow tube lies flat on a table.
A ball is shot through the tube.
As the ball emerges from the
other end, which path
does it follow?
QuickCheck 5.10
Slide 5-76
C A hollow tube lies flat on a table.
A ball is shot through the tube.
As the ball emerges from the
other end, which path
does it follow?
QuickCheck 5.10
Slide 5-77
Mass & Weight
W mg
29.8 /g m s
Calculate your weight in N.
1 lb = 4.45 N
Calculate your mass in Kg.
(g is a scalar!)
F ma
Galileo Challenged Aristotle Physics
In a vacuum, all objects fall with the same
acceleration due to gravity: 9.80 m/s2,
independent of their weight.
Rock & Feather A rock and feather fall with the same acceleration due to gravity in
a vacuum. Is the force of gravity acting on them the same?
Acceleration is not Force!
MASS IS NOT WEIGHT!!!
http://www.youtube.com/watch?v=glrC5nhWaQA
The Weight to Mass Ratio of
ALL objects always equals g! The force of gravity – the weight of an object – is greater for
a larger mass, but the larger mass has greater INERTIA and
resists a change in motion more so that the ratio of weight to
mass is a universal constant.
Perception of Weight The perception of weight comes from the support force acting
back on you. If you are in free fall you feel weightless.
Moon Mass The acceleration due to gravity on the surface of the
moon is only 1/6 as it is on the Earth. What is the weight
of a 10-kg object on the moon and on the Earth?
What is its mass on each?
Mass is the same everywhere
in the universe! 10 kg!
210 9.8 / 98E EW mg kg m s N
1 198 16.3
6 6E M EW mg m g N N M
Newton’s First Law
0 => No Change in MotionIf F
Dynamic Equilibrium Static Equilibrium
Static Equilibrium
0xF
Forces up equal the forces down. Forces sideways cancel too.
0yF
Force Vector Diagrams
Show all the External forces acting ON the body only.
W
Dynamic Equilibrium
0F If the Net Force is zero, then the object moves at a
constant speed – in dynamic equilibrium.
Newton’s 2nd Law
The acceleration of object is directly
related to the net forces acting on it and
inversely proportional to its mass.
netFa
m
F ma
Newton’s 2nd Law
2
mkg N
s
Units
F ma
Acceleration is in the direction of
the net Force but not necessarily
in the direction of velocity.
netFa
m
Force Components
x x y yF ma F ma Newton’s Second Law is a Vector equation that can be broken
down into scalar components. Since x and y directions are
independent, Newton’s Second Law can be expressed as
independent x and y equations.
F ma
Solving Force Problems
1. State the knowns and desired unknowns.
2. Draw a force vector diagram, label everything and define direction.
3. Solve for the components of each force.
4. Use Fnet = ma on each direction to generate equations.
5. Derive a solution in terms of the given knowns.
6. Enter the numbers and solve for the desired unknown.
x xF ma
Starting from rest, Sally pulls Billy on the
sled (total mass = 60kg) with a total force
of 100 N at an angle of 40 degrees above
the horizontal, as shown. After 5 seconds,
how fast is the sled moving and how far
has it traveled from where it started?
Problem
cos xF ma
cos =x
Fa
m
0
cos 100 cos 405 6.38 /
60f
F Nv v at t s m s
m kg
0fv v at
Frictional Forces Friction always opposes the applied force and is in the
opposite direction of motion. The greater the normal force
the greater the frictional force. Frictional forces always
SLOW DOWN the motion and NEVER speed it up!!!
k kf Ns sf N
Fig. 5.16, p.131
Statice vs Kinetic Friction
s kf f
Problem The magnitude of F1 is 75.0N and F2 is 50.0N. The
coefficient of friction between the block and the floor is 0.04.
How do you know which direction to put the friction? What
is the acceleration of the block?
Air Resistance Air resistance is proportional to the size and speed of an object.
WHY?
The greater the cross
sectional area of an object,
the greater amount of air
pushed out of the way – the
air pushes back! The faster
an object falls, the faster it
has to push the air out of
the way – the air pushes
back! This is air resistance.
Terminal Velocity When the air resistance balances the weight, the object stops
accelerating and it falls with constant velocity called
Terminal Velocity.
W R
m
W W
m
0
NetFa
m
R
W
+
+
Problem What is the acceleration of a sky diver when the air resistance equals
½ the total weight?
NetFa
m
W R
m
/ 2W W
m
/ 2mg mg
m
/ 2g
R
W
The Inclined Plane Orient your axes relative to the plane!!!
Why is the angle of the incline here? Prove it.
Incline Plane Problem
Draw a free-body diagram of a
block which slides down a
plane having a coeeficient of
friction of 0.05 and an
inclination of = 35.0°. If the
block starts from rest at the top
and the length of the incline is
2.00 m, find (a) the acceleration
of the block and (b) its speed
when it reaches the bottom of
the incline.
A block is pushed up a frictionless 30 incline by an applied force as shown. If F = 25 N and M = 3.0 kg, what is the magnitude of the resulting acceleration of the block?
a. 2.3 m/s2
b. 4.6 m/s2
c. 3.5 m/s2
d. 2.9 m/s2
e. 5.1 m/s2
Tension Forces Tension forces are transmitted undiminished through the rope.
Different T Same T
Force Vector Diagrams
Continuous Rope has
same T everywhere!
What is T?
Force Vector Diagrams
Align axes to simplify the problem!
Force Vector Diagrams
Note: T and a are the same! Ropes connected by ideal pulleys
have the same tension everywhere!
Draw free-body diagrams for every object!
Pulleys, Masses, Strings What is the acceleration of the system?
(If they are connected, it is the same for both masses!)
What is the tension in the string?
Compare to g and the weight of m2.
1. If it falls from rest
2. If it is dragged to the left
3. If the string is cut
FIRST: Draw free-body diagrams for each mass!!!
Problem A force F = 40 N pulls the two masses. If the table is
frictionless, find the tension in the string.
a) 13 N
b) 36 N
c) 23 N
d) 15 N
e) 28 N
1 23 , 1.5m kg m kg
An object on a rope is lowered at constant speed. Which is true?
A. The rope tension is greater than the object’s weight.
B. The rope tension equals the object’s weight.
C. The rope tension is less than the object’s weight.
D. The rope tension can’t be compared to the object’s weight.
QuickCheck 5.8
Slide 5-68
An object on a rope is lowered at constant speed. Which is true?
A. The rope tension is greater than the object’s weight.
B. The rope tension equals the object’s weight.
C. The rope tension is less than the object’s weight.
D. The rope tension can’t be compared to the object’s weight.
Constant velocity
Zero acceleration
QuickCheck 5.8
Slide 5-69
