chapter 4: forces & newton’s laws of motion
TRANSCRIPT
No Slide TitleChapter 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
Newton’s 3rd Law
To every force there is an equal but opposite reaction force.
hand on wall wall on handF F= −
© 2013 Pearson Education, Inc.
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?
© 2013 Pearson Education, Inc.
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?
Support Forces-Normal Forces
Support force is a reaction force and will balance the applied force until the
material breaks.
Forces are Interactions Earth on Rock Rock on EarthF F= −
© 2013 Pearson Education, Inc.
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
EXTERNAL Forces either
Speed you up Slow you down Change your direction Cancel each other out!!!
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
CA 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
Calculate your mass in Kg.
(g is a scalar!)
F ma=
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?
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
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.
Acceleration is not Force! MASS IS NOT WEIGHT!!!
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.
Universal Law of Gravity
−=
Inside the Earth the Gravitational Force is Linear.
Acceleration decreases as you fall to the center (where your speed is the greatest) and then the acceleration increases
but in the opposite direction, slowing you down to a stop at the other end…but then you would fall back in again,
bouncing back and forth forever!
Gravitational Force INSIDE the Earth
Finding little g Calculate the acceleration of gravity acting on you at the
surface of the Earth. What is g?
2 you E
GMa R
= Independent of your mass! This is why a rock and feather fall with the same acceleration!
Source of the Force
This is your WEIGHT!
=
Calculate the acceleration of gravity acting on you at the surface of the Earth. What is g?
2 you E
a x m
= g!
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 1 98 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 =∑
Show all the External forces acting ON the body only.
Force Vector Diagrams Align axes to simplify the problem!
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=∑
Acceleration is in the direction of the net Force but not necessarily
in the direction of velocity.
netFa 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 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.
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! It shows you the components to put into Newton’s 2nd Law!
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
60f F Nv v at t s m s
m kg θ
0fv v at= +
Problem The magnitude of F1 is 75.0N and F2 is 50.0N. Ignore
friction. What is the acceleration of the block?
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!!!
µ=k kf Ns sf Nµ=
Fig. 5.16, p.131
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?
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 0.04 and an inclination of = 15.0°. 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.
What does the Scale Read?
Tension Forces Tension forces are transmitted undiminished through the rope.
Different T Same T
What is T?
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= =
The three blocks are pushed across a rough surface by a 40-N force. If the coefficient of kinetic friction between each of the blocks and the surface is 0.20, determine the magnitude of the force exerted by m2 on m3.
a) 20 N b) 30 N c) 10 N d) 15 N e) 25 N
Problem 1 2 32 , 3 , 5m kg m kg m kg= = =
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
Problem
In the figure shown, the coefficient of kinetic friction between the block and the incline is 0.29. What is the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley. Draw the free body diagrams for each mass. Derive a general solution for the acceleration in terms of M, and g, box it, then put the numbers in and get a numerical value – then box that too. Then find a numerical value for the tension in the string. Box that. Show all your work and make it pretty! Use 3 significant figures.
2M
M
30
Man of the MillenniumSir Issac Newton
Slide Number 3
Slide Number 4
QuickCheck 5.10
QuickCheck 5.10
Mass & Weight
Rock & Feather
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 Aristotle PhysicsIn a vacuum, all objects fall with the same acceleration due to gravity: 9.80 m/s2, independent of their weight.
Acceleration is not Force!MASS IS NOT WEIGHT!!!
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
Slide Number 26
Force Vector Diagrams
Force Vector Diagrams
Slide Number 36
Slide Number 37
Slide Number 38
Acceleration is in the direction of the net Force but not necessarily in the direction of velocity.
Newton’s First Law
Tension Forces
•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
Newton’s 3rd Law
To every force there is an equal but opposite reaction force.
hand on wall wall on handF F= −
© 2013 Pearson Education, Inc.
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?
© 2013 Pearson Education, Inc.
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?
Support Forces-Normal Forces
Support force is a reaction force and will balance the applied force until the
material breaks.
Forces are Interactions Earth on Rock Rock on EarthF F= −
© 2013 Pearson Education, Inc.
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
EXTERNAL Forces either
Speed you up Slow you down Change your direction Cancel each other out!!!
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
CA 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
Calculate your mass in Kg.
(g is a scalar!)
F ma=
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?
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
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.
Acceleration is not Force! MASS IS NOT WEIGHT!!!
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.
Universal Law of Gravity
−=
Inside the Earth the Gravitational Force is Linear.
Acceleration decreases as you fall to the center (where your speed is the greatest) and then the acceleration increases
but in the opposite direction, slowing you down to a stop at the other end…but then you would fall back in again,
bouncing back and forth forever!
Gravitational Force INSIDE the Earth
Finding little g Calculate the acceleration of gravity acting on you at the
surface of the Earth. What is g?
2 you E
GMa R
= Independent of your mass! This is why a rock and feather fall with the same acceleration!
Source of the Force
This is your WEIGHT!
=
Calculate the acceleration of gravity acting on you at the surface of the Earth. What is g?
2 you E
a x m
= g!
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 1 98 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 =∑
Show all the External forces acting ON the body only.
Force Vector Diagrams Align axes to simplify the problem!
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=∑
Acceleration is in the direction of the net Force but not necessarily
in the direction of velocity.
netFa 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 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.
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! It shows you the components to put into Newton’s 2nd Law!
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
60f F Nv v at t s m s
m kg θ
0fv v at= +
Problem The magnitude of F1 is 75.0N and F2 is 50.0N. Ignore
friction. What is the acceleration of the block?
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!!!
µ=k kf Ns sf Nµ=
Fig. 5.16, p.131
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?
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 0.04 and an inclination of = 15.0°. 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.
What does the Scale Read?
Tension Forces Tension forces are transmitted undiminished through the rope.
Different T Same T
What is T?
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= =
The three blocks are pushed across a rough surface by a 40-N force. If the coefficient of kinetic friction between each of the blocks and the surface is 0.20, determine the magnitude of the force exerted by m2 on m3.
a) 20 N b) 30 N c) 10 N d) 15 N e) 25 N
Problem 1 2 32 , 3 , 5m kg m kg m kg= = =
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
Problem
In the figure shown, the coefficient of kinetic friction between the block and the incline is 0.29. What is the magnitude of the acceleration of the suspended block as it falls? Disregard any pulley mass or friction in the pulley. Draw the free body diagrams for each mass. Derive a general solution for the acceleration in terms of M, and g, box it, then put the numbers in and get a numerical value – then box that too. Then find a numerical value for the tension in the string. Box that. Show all your work and make it pretty! Use 3 significant figures.
2M
M
30
Man of the MillenniumSir Issac Newton
Slide Number 3
Slide Number 4
QuickCheck 5.10
QuickCheck 5.10
Mass & Weight
Rock & Feather
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 Aristotle PhysicsIn a vacuum, all objects fall with the same acceleration due to gravity: 9.80 m/s2, independent of their weight.
Acceleration is not Force!MASS IS NOT WEIGHT!!!
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
Slide Number 26
Force Vector Diagrams
Force Vector Diagrams
Slide Number 36
Slide Number 37
Slide Number 38
Acceleration is in the direction of the net Force but not necessarily in the direction of velocity.
Newton’s First Law
Tension Forces