Embed Size (px)
Citation preview
1/15/2019
1
FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/EPHYSICS
RANDALL D. KNIGHT
Chapter 6 Lecture
Slide 6-2© 2017 Pearson Education, Inc.
Slide 6-2
Chapter 6 Dynamics I: Motion Along a Line
IN THIS CHAPTER, you will learn to solve linear force-and-motion problems.
Slide 6-3© 2017 Pearson Education, Inc.
Slide 6-3
Chapter 6 Preview
Slide 6-4© 2017 Pearson Education, Inc.
Slide 6-4
Chapter 6 Preview
1/15/2019
2
Slide 6-5© 2017 Pearson Education, Inc.
Slide 6-5
Chapter 6 Preview
Slide 6-6© 2017 Pearson Education, Inc.
Slide 6-6
Chapter 6 Preview
Slide 6-7© 2017 Pearson Education, Inc.
Slide 6-7
Chapter 6 Preview
Slide 6-8© 2017 Pearson Education, Inc.
Slide 6-8
Chapter 6 Preview
1/15/2019
3
Slide 6-9© 2017 Pearson Education, Inc.
In the absence of a net force, an object is at rest or moves with constant velocity.
Its acceleration is zero, and we say that it is in equilibrium.
The Equilibrium Model
The concept of equilibrium is essential for the engineering analysis of stationary objects such as bridges.
When the acceleration is zero, then Newton’s second law in two dimensions becomes:
Slide 6-10© 2017 Pearson Education, Inc.
Mechanical Equilibrium
Slide 6-11© 2017 Pearson Education, Inc.
Slide 6-11
Example 6.2 Towing a Car up a Hill
Slide 6-12© 2017 Pearson Education, Inc.
Slide 6-12
Example 6.2 Towing a Car up a Hill
1/15/2019
4
Slide 6-13© 2017 Pearson Education, Inc.
Slide 6-13
Example 6.2 Towing a Car up a Hill
Slide 6-14© 2017 Pearson Education, Inc.
Slide 6-14
Example 6.2 Towing a Car up a Hill
Slide 6-15© 2017 Pearson Education, Inc.
Slide 6-15
Example 6.2 Towing a Car up a Hill
Slide 6-16© 2017 Pearson Education, Inc.
The essence of Newtonian mechanics can be expressed in two steps:• The forces on an object determine its
acceleration .
• The object’s trajectory can be determined by usingin the equations of kinematics.
Using Newton’s Second Law
1/15/2019
5
Slide 6-17© 2017 Pearson Education, Inc.
Slide 6-17
Problem-Solving Strategy: Newtonian Mechanics
Slide 6-18© 2017 Pearson Education, Inc.
Slide 6-18
Problem-Solving Strategy: Newtonian Mechanics
Slide 6-19© 2017 Pearson Education, Inc.
Slide 6-19
Example 6.3 Speed of a Towed Car
Slide 6-20© 2017 Pearson Education, Inc.
Slide 6-20
Example 6.3 Speed of a Towed Car
1/15/2019
6
Slide 6-21© 2017 Pearson Education, Inc.
Slide 6-21
Example 6.3 Speed of a Towed Car
Slide 6-22© 2017 Pearson Education, Inc.
Slide 6-22
Example 6.3 Speed of a Towed Car
Slide 6-23© 2017 Pearson Education, Inc.
Slide 6-23
Example 6.3 Speed of a Towed Car
Slide 6-24© 2017 Pearson Education, Inc.
Slide 6-24
Example 6.3 Speed of a Towed Car
1/15/2019
7
Slide 6-25© 2017 Pearson Education, Inc.
Constant Force
Slide 6-26© 2017 Pearson Education, Inc.
Slide 6-26
Mass: An Intrinsic Property
A pan balance, shown in the figure, is a device for measuring mass.
The measurement does not depend on the strength of gravity.
Mass is a scalar quantity that describes an object’s inertia.
Mass describes the amount of matter in an object.
Mass is an intrinsic property of an object.
Slide 6-27© 2017 Pearson Education, Inc.
Slide 6-27
Gravity: A Force
Gravity is an attractive, long-range force between any two objects.
The figure shows two objects with masses m1and m2 whose centers are separated by distance r.
Each object pulls on the other with a force:
where G = 6.67 × 10–11 N m2/kg2 is the gravitational constant.
Slide 6-28© 2017 Pearson Education, Inc.
Slide 6-28
Gravity: A Force
The gravitational force between two human-sized objects is very small.
Only when one of the objects is planet-sized or larger does gravity become an important force.
For objects near the surface of the planet earth,
where M and R are the mass and radius of the earth, and g = 9.80 m/s2.
1/15/2019
8
Slide 6-29© 2017 Pearson Education, Inc.
Slide 6-29
Gravity: A Force
The magnitude of the gravitational force is FG = mg, where
All objects on the same planet, regardless of mass, have the same free-fall acceleration!
The figure shows the free-body diagram of an object in free fall near the surface of a planet.
With , Newton’s second law predicts the acceleration to be
Slide 6-30© 2017 Pearson Education, Inc.
Slide 6-30
Weight: A Measurement
When you weigh yourself, you stand on a spring scale and compress a spring.
The reading of a spring scale is FSp, the magnitude of the upward force the spring is exerting.
Let’s define the weight of an object to be the reading FSp of a calibrated spring scale when the object is at rest relative to the scale.
That is, weight is a measurement, the result of “weighing” an object.
Because FSp is a force, weight is measured in newtons.
Slide 6-31© 2017 Pearson Education, Inc.
Slide 6-31
Weight: A Measurement
A bathroom scale uses compressed springs which push up.
When any spring scale measures an object at rest, .
The upward spring force exactly balances the downward gravitational force of magnitude mg:
Weight is defined as the magnitude of FSp when the object is at rest relative to the stationary scale:
Slide 6-32© 2017 Pearson Education, Inc.
Slide 6-32
Weight: A Measurement
The figure shows a man weighing himself in an accelerating elevator.
Looking at the free-body diagram, the y-component of Newton’s second law is:
The man’s weight as he accelerates vertically is
You weigh more as an elevator accelerates upward!
1/15/2019
9
Slide 6-33© 2017 Pearson Education, Inc.
Slide 6-33
Weightlessness
The weight of an object which accelerates vertically is
If an object is accelerating downward with ay = –g, then w = 0.
An object in free fall has no weight!
Astronauts while orbiting the earth are also weightless.
Does this mean that they are in free fall? Astronauts are weightless as they orbit the earth.
Slide 6-34© 2017 Pearson Education, Inc.
Slide 6-34
Static Friction
A shoe pushes on a wooden floor but does not slip.
On a microscopic scale, both surfaces are “rough” and high features on the two surfaces form molecular bonds.
These bonds can produce a force tangent to the surface, called the static friction force.
Static friction is a result of many molecular springs being compressed or stretched ever so slightly.
Slide 6-35© 2017 Pearson Education, Inc.
Slide 6-35
Static Friction
The figure shows a rope pulling on a box that, due to static friction, isn’t moving.
Looking at the free-body diagram, the x-component of Newton’s first law requires that the static friction force must exactly balance the tension force:
points in the direction opposite to the way the object would move if there were no static friction.
Slide 6-36© 2017 Pearson Education, Inc.
Slide 6-36
Static Friction
Static friction acts in response to an applied force.
1/15/2019
10
Slide 6-37© 2017 Pearson Education, Inc.
Slide 6-37
Static Friction
Static friction force has a maximum possible size fs max.
An object remains at rest as long as fs < fs max. The object just begins to slip when fs = fs max. A static friction force fs > fs max is not physically
possible:
where the proportionality constant μs is called the coefficient of static friction.
Slide 6-38© 2017 Pearson Education, Inc.
Slide 6-38
Kinetic Friction
The kinetic friction force is proportional to the magnitude of the normal force:
where the proportionality constant μk is called the coefficient of kinetic friction. The kinetic friction direction is
opposite to the velocity of the object relative to the surface. For any particular pair of
surfaces, μk < μs.
Slide 6-39© 2017 Pearson Education, Inc.
Slide 6-39
Rolling Motion If you slam on the brakes
hard enough, your car tires slide against the road surface and leave skid marks. This is kinetic friction.
A wheel rolling on a surface also experiences friction, but not kinetic friction.
The portion of the wheel that contacts the surface is stationary with respect to the surface, not sliding.
The interaction of this contact area with the surface causes rolling friction.
Slide 6-40© 2017 Pearson Education, Inc.
Slide 6-40
Rolling Friction
A car with no engine or brakes applied does not roll forever; it gradually slows down.
This is due to rolling friction.
where μr is called the coefficient of rolling friction.
The rolling friction direction is opposite to the velocity of the rolling object relative to the surface.
The force of rolling friction can be calculated as
1/15/2019
11
Slide 6-41© 2017 Pearson Education, Inc.
Slide 6-41
Coefficients of Friction
Slide 6-42© 2017 Pearson Education, Inc.
Slide 6-42
A Model of Friction
Slide 6-43© 2017 Pearson Education, Inc.
Slide 6-43
Causes of Friction
All surfaces are very rough on a microscopic scale.
When two surfaces are pressed together, the high points on each side come into contact and form molecular bonds.
The amount of contact depends on the normal force n.
When the two surfaces are sliding against each other, the bonds don’t form fully, but they do tend to slow the motion.
Slide 6-44© 2017 Pearson Education, Inc.
Slide 6-44
Drag
The air exerts a drag force on objects as they move through the air.
Faster objects experience a greater drag force than slower objects.
The drag force on a high-speed motorcyclist is significant.
The drag force direction is opposite the object’s velocity.
1/15/2019
12
Slide 6-45© 2017 Pearson Education, Inc.
Slide 6-45
Drag
For normal-sized objects on earth traveling at a speed v which is less than a few hundred meters per second, air resistance can be modeled as
A is the cross-section area of the object.
ρ is the density of the air, which is 1.3 kg/m3, at atmospheric pressure and 0ºC, a common reference point of pressure and temperature.
C is the drag coefficient, which is a dimensionless number that depends on the shape of the object.
Slide 6-46© 2017 Pearson Education, Inc.
Slide 6-46
Drag
Cross-section areas for objects of different shape.
Slide 6-47© 2017 Pearson Education, Inc.
Slide 6-47
Example 6.7 Air Resistance Compared to Rolling Friction
Slide 6-48© 2017 Pearson Education, Inc.
Slide 6-48
Example 6.7 Air Resistance Compared to Rolling Friction
1/15/2019
13
Slide 6-49© 2017 Pearson Education, Inc.
Slide 6-49
Example 6.7 Air Resistance Compared to Rolling Friction
Slide 6-50© 2017 Pearson Education, Inc.
Slide 6-50
Example 6.7 Air Resistance Compared to Rolling Friction
Slide 6-51© 2017 Pearson Education, Inc.
Slide 6-51
Terminal Speed
The drag force from the air increases as an object falls and gains speed.
If the object falls far enough, it will eventually reach a speed at which Fdrag = FG.
At this speed, the net force is zero, so the object falls at a constant speed, called the terminal speed vterm:
Slide 6-52© 2017 Pearson Education, Inc.
Slide 6-52
Example 6.10 Make Sure the Cargo Doesn’t Slide
1/15/2019
14
Slide 6-53© 2017 Pearson Education, Inc.
Slide 6-53
Example 6.10 Make Sure the Cargo Doesn’t Slide
EXAMPLE 6.10 Make sure the cargo doesn’t slide
MODEL
Let the box, which we’ll model as a particle, be the object of interest.
Only the truck exerts contact forces on the box.
The box does not slip relative to the truck.
If the truck bed were frictionless, the box would slide backward as seen in the truck’s reference frame as the truck accelerates.
The force that prevents sliding is static friction.
The box must accelerate forward with the truck: abox = atruck.
Slide 6-54© 2017 Pearson Education, Inc.
Slide 6-54
Example 6.10 Make Sure the Cargo Doesn’t Slide
Slide 6-55© 2017 Pearson Education, Inc.
Slide 6-55
Example 6.10 Make Sure the Cargo Doesn’t Slide
Slide 6-56© 2017 Pearson Education, Inc.
Slide 6-56
Example 6.10 Make Sure the Cargo Doesn’t Slide
1/15/2019
15
Slide 6-57© 2017 Pearson Education, Inc.
Slide 6-57
Example 6.10 Make Sure the Cargo Doesn’t Slide
Slide 6-58© 2017 Pearson Education, Inc.
Slide 6-58
Chapter 6 Summary Slides
Slide 6-59© 2017 Pearson Education, Inc.
Slide 6-59
General Principles
Slide 6-60© 2017 Pearson Education, Inc.
Slide 6-60
General Principles
1/15/2019
16
Slide 6-61© 2017 Pearson Education, Inc.
Slide 6-61
Important Concepts
Slide 6-62© 2017 Pearson Education, Inc.
Slide 6-62
Important Concepts
Slide 6-63© 2017 Pearson Education, Inc.
Slide 6-63
Applications
Slide 6-64© 2017 Pearson Education, Inc.
Slide 6-64
Applications
