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Chapter 4. Newton’s Laws of Motion. Goals for Chapter 4. To understand the meaning of force in physics To view force as a vector and learn how to combine forces To understand the behavior of a body on which the forces “balance”: - PowerPoint PPT Presentation
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Copyright © 2012 Pearson Education Inc.
PowerPoint® Lectures forUniversity Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman
Chapter 4
Newton’s Laws of Motion
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 4
• To understand the meaning of force in physics
• To view force as a vector and learn how to combine forces
• To understand the behavior of a body on which the forces “balance”:
• Newton’s First Law of Motion: if there is no NET force on an object it will remain in the same state of motion
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 4
• To learn the relationship between mass, acceleration, and force:
Newton’s Second Law of Motion: F = ma
a = F/m
• To relate mass (quantity of matter) and weight (force on that matter from gravity)
Copyright © 2012 Pearson Education Inc.
Goals for Chapter 4
• To see the effect of action-reaction pairs:
Newton’s Third Law of Motion
Force on object a from object b is EQUAL in magnitude (and opposite in direction) to
Force on object b from object a
Copyright © 2012 Pearson Education Inc.
What are some properties of a force?
• A force is a push or a pull• A force is an interaction between two objects, or
between an object and its environment• A force is a VECTOR quantity, with magnitude and
direction.
Copyright © 2012 Pearson Education Inc.
There are four common types of forces
• #1: The normal force:
When an object pushes on a surface, the surface pushes back on the object perpendicular to the surface.
• This is a contact force.
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There are four common types of forces
• #2: Friction force: This force occurs when a surface resists sliding of an object and is parallel to the surface.
• Friction is a contact force.
Copyright © 2012 Pearson Education Inc.
There are four common types of forces II
• #3: Tension force:
A pulling force exerted on an object by a rope or cord.
• This is a contact force.
Copyright © 2012 Pearson Education Inc.
There are four common types of forces II
• #4: Weight:
The pull of gravity on an object.
• This is a long-range force, not a contact force, and is also a “field” force.
Copyright © 2012 Pearson Education Inc.
What are the magnitudes of common forces?
Copyright © 2012 Pearson Education Inc.
Drawing force vectors
• Use a vector arrow to indicate the magnitude and direction of the force.
Copyright © 2012 Pearson Education Inc.
Superposition of forces
• Several forces acting at a point on an object have the same effect as their vector sum acting at the same point.
Copyright © 2012 Pearson Education Inc.
Decomposing a force into its component vectors
• Choose coordinate system with perpendicular x and y axes.
• Fx and Fy are components of force along axes.
• Use trigonometry to find force components.
Copyright © 2012 Pearson Education Inc.
Notation for the vector sum
• Vector sum of all forces on an object is resultant of forces
• The net force.
1 2 3
R= F +F +F + = F
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Superposition of forces
• Force vectors are added using components: Rx = F1x + F2x + F3x + … Ry = F1y + F2y + F3y + …
Copyright © 2012 Pearson Education Inc.
Newton’s First Law
“An object at rest tends to stay at rest, an object in motion tends to stay
in uniform motion.”
Copyright © 2012 Pearson Education Inc.
Newton’s First Law
Mathematically,
“A body acted on by zero net force moves with constant velocity
and zero acceleration.”
Copyright © 2012 Pearson Education Inc.
Newton’s First Law II
• In part (a) net force acts, causing acceleration.
• In part (b) net force = 0 resulting in no acceleration.
Copyright © 2012 Pearson Education Inc.
When is Newton’s first law valid?
• You are on roller skates in a stopped BART car…
• The car starts to accelerate forwards.
• What happens to you?
• If no net force acts on you, you maintain a constant velocity (0!)
Copyright © 2012 Pearson Education Inc.
When is Newton’s first law valid?
• You are on roller skates in a moving BART car…
• The car starts to slow - accelerate backwards.
• What happens to you?
• If no net force acts on you, you maintain a constant velocity
Copyright © 2012 Pearson Education Inc.
When is Newton’s first law valid?• If no net force acts on you,
you maintains a constant velocity (a vector!)
• But as seen in the non-inertial frame of the accelerating vehicle, it appears that you are being pushed to the outside!
• Newton’s first law is valid only in non-accelerating inertial frames.
Copyright © 2012 Pearson Education Inc.
Newton’s Second Law
• If the net force on an object is zero, the object will not accelerate.
Copyright © 2012 Pearson Education Inc.
Newton’s Second Law
• If the net force on an object is not zero, it causes the object to accelerate.
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Newton’s Second Law
• If the net force on an object is not zero, it causes the object to accelerate.
Copyright © 2012 Pearson Education Inc.
An object undergoing uniform circular motion
• An object in uniform circular motion is accelerated toward the center of the circle.
• So net force on object must point toward the center of the circle.
Copyright © 2012 Pearson Education Inc.
Force and acceleration
• Magnitude of acceleration of an object is directly proportional to the net force on the object.
• | | = F/m
Fa
Copyright © 2012 Pearson Education Inc.
Mass and acceleration
• Magnitude of acceleration of an object is inversely proportional to object’s mass if net force remains fixed.
• | | = F/ma
Copyright © 2012 Pearson Education Inc.
Newton’s second law of motion
• The acceleration of an object is directly proportional to the net force acting on it, and inversely proportional to the mass of the object.
• The SI unit for force is the newton (N).
1 N = 1 kg·m/s2
m
F a
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Using Newton’s Second Law Ex. 4.4
• Worker pushes box of mass 40 kg, with constant force of 20N. What is acceleration?
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Using Newton’s Second Law Ex. 4.4
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Using Newton’s Second Law II—Example 4.5
• Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?
Copyright © 2012 Pearson Education Inc.
Using Newton’s Second Law II—Example 4.5
• Shove bottle of mass 0.45 kg at initial speed of 2.8 m/s a distance of 1 m before it stops. What is the magnitude and direction of force on bottle?
Copyright © 2012 Pearson Education Inc.
Using Newton’s Second Law II—Example 4.5
• We know:
• Displacement in x = +1.0 m
• Initial x velocity = +2.8 m/s
• Final x velocity = 0 m/s
• THREE THINGS!
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Using Newton’s Second Law II—Example 4.5
• vf2 = vi
2 + 2ax
• So…
• a = (vf2 - vi
2)/2x
• a = - 3.9 m/s2
• NOTE a points in the direction of f !
+x
Copyright © 2012 Pearson Education Inc.
Systems of units (Table 4.2)
• In MKS (SI) system
• force is measured in Newtons, distance in meters, mass in kilograms.
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Systems of units (Table 4.2)
• In British system, force is measured in pounds, distance in feet, mass in slugs.
• In cgs system, force in dynes, distance in centimeters, and mass is in grams.
Copyright © 2012 Pearson Education Inc.
Mass and weight
• The weight of an object (on Earth) is gravitational force that Earth exerts on it.
• The weight W of an object of mass m is
W = mg
• The value of g depends on altitude.
• On other planets, g will have an entirely different value than on the earth.
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A euro in free fall
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A bit coin in free fall?
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Don’t confuse mass and weight!
• Keep in mind that the Newton is a unit of force, not mass.
• A 2.49 x 104 N Rolls-Royce Phantom traveling in +x direction makes an emergency stop; the x component of the net force acting on its -1.83 x 104 N. What is its acceleration?
Copyright © 2012 Pearson Education Inc.
Newton’s Third Law
• If you exert a force on a body, the body always exerts a force (the “reaction”) back upon you.
• A force and its reaction force have the same magnitude but opposite directions.
• These forces act on different bodies.
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Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.
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Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
Applying Newton’s Third Law: Objects at rest
• An apple rests on a table. Identify the forces that act on it and the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
Applying Newton’s Third Law: Objects in motion
• A person pulls on a block across the floor. Identify the action-reaction pairs.
Copyright © 2012 Pearson Education Inc.
A paradox?
• If an object pulls back on you just as hard as you pull on it, how can it ever accelerate?
Copyright © 2012 Pearson Education Inc.
Free-body diagrams
A free-body diagram
is a sketch showing all the forces acting on an object.
Copyright © 2012 Pearson Education Inc.
Free-body diagrams
A free-body diagram
is a sketch showing all the forces acting on an object.
Copyright © 2012 Pearson Education Inc.
Free-body diagrams
A free-body diagram is a sketch showing all the forces acting on an object.