Download Chapter_5

Announcements:
-
Midterm 1 coming up Wednesday Feb. 16, (two
evening times, 5-6 pm or 6-7 pm).
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Material: Chapter 1-5.
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I’ll provide key equations (last page of exam).
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I will put up a practice exam on our class web
page (http://www.wfu.edu/~gutholdm/Physics113/phy113.html)
Chapter 5: The laws of motion
Reading assignment: Chapter 5
Homework 5: CQ1, CQ14, QQ2, 3, 12, 16, 20, 21, 22, 24, 28, 38,
39, 43, 44, AE1, AF16
Due dates:
Tu/Th section: Monday Feb. 14
MWF section: Monday, Feb. 14
Remember:
Homework 4 is due Monday, Feb. 3 (section B); Wednesday, Feb. 7 (section A).
•
In this chapter we will learn about the relationship between the forces
exerted on an object and the acceleration of the object.
•
Forces
•
Newton’s three laws.
•
Free body diagrams!
•
Friction.


II. Fnet  m  a
Contact forces
- Involve physical contact between
objects.
Field forces:
-No physical contact between
objects
- Forces act through empty space
gravity
electric
magnetic
Measuring forces
- Forces are often measured by determining the elongation of a calibrated
spring.
- Forces are vectors!! Remember vector addition.
- To calculate net force on an object you must use vector addition.
Newton’s first law:
In the absence of external forces:
• an object at rest remains at rest
• an object in motion continues in motion with constant
velocity (constant speed, straight line)
(assume no friction).
Or: When no force acts on an object, the acceleration of
the object is zero.
Inertia: Object resists any attempt to change is velocity
Inertial frame of reference:
-A frame (system) that is not accelerating.
- Newton’s laws hold only true in non-accelerating (inertial)
frames of reference!
Are the following inertial frames of reference:
- A cruising car?
- A braking car?
- The earth?
- Accelerating car?
Mass
- Mass of an object specifies how much inertia the
object has.
- Unit of mass is kg.
- The greater the mass of an object, the less it
accelerates under the action of an applied force.
- Don’t confuse mass and weight (see: bit later).
Newton’s second law
(very important)
The acceleration of an object is directly proportional to
the net force acting on it and inversely proportional to its
mass.


F  m a
Fx  m  ax
Fy  m  a y
Fz  m  az
Unit of force:
• The unit of force is the Newton (1N)
• One Newton: The force required to accelerate a 1 kg mass to
1m/s2.
• 1N = 1kg·m/s2
Isaac Newton, 1643 – 1727
(English physicist, mathematician, astronomer, philosopher,
theologican)
One of the most influential scientists and people in human history.
His work laid the foundation of most of classical mechanics.
Also built the first pratical telescope, developed (with Leibniz)
differential and integral calculus
Portrait by Godfrey Kneller (1689)
http://en.wikipedia.org/wiki/Isaac_Newton
Black board example 5.1
(related to HW problem)
F2 = 8.0 N
q2 = 60°
F1 = 5.0 N
Two forces act on a hockey puck
(mass m = 0.3 kg) as shown
in the figure.
q1 = 20°
(a) Determine the magnitude and direction of the net force acting
on the puck
(b) Determine the magnitude and the direction of the pucks
acceleration.
The force of gravity and weight
• Objects are attracted to the Earth.
• This attractive force is the force of gravity Fg.


Fg  m  g
• The magnitude of this force is called the weight of the object.
• The weight of an object is, thus m·g.
The weight of an object can very with location (less weight on the moon than
on earth, since g is smaller).
The mass of an object does not vary.
Newton’s third law
“For every action there is an
equal and opposite reaction.”
If two objects interact, the force F12 exerted by object 1 on object
2 is equal in magnitude and opposite in direction to the force F21
exerted by object 2 on object 1:


F12   F21
Action and reaction forces always act on different objects.
Conceptual example:
A large man, (m = 100 kg) and a small boy (m = 50 kg) stand
facing each other on frictionless ice. They put their hands
together and push against each other so that they move apart.
Who experiences the
larger force?
larger acceleration?
larger speed?
(after they are separated)
A.
B.
C.
D.
The boy
The man
Same for both
Need more info
A.
B.
C.
D.
The boy
The man
Same for both
Need more info
A.
B.
C.
D.
The boy
The man
Same for both
Need more info
Normal force – support force acting normal (perpendicular) to surface
Where is the action and reaction force?
Black board: Free body diagram
• Analyzing forces
• Free body diagram
• Tension in a rope = magnitude of the force that the rope exerts
on object.
Applying Newton’s laws
1. Make a diagram (conceptualize)
F  0
2. Categorize:
no acceleration:
accelerating object:  F  ma
3. Isolate each object and draw a free body diagram
for each object. Draw in all forces that act on the
object.
4. Establish a convenient coordinate system.
5. Write Newton’s law for each body and each
coordinate component.  set of equations; solve
6. Finalize by checking answers.
Black board example 5.2 (on HW)
A traffic light weighing 125 N hangs from a cable tied to two
other cables fastened to a support as shown in the figure.
Find the tension in the three cables.
Black board example 5.3 (on HW)
A crate of mass m is placed on a frictionless plane of incline a = 30.
(a) Determine the acceleration of the crate.
(b) Starting from rest, the crate travels a distance d = 10.2 m to the
bottom of the incline. How long does it take to reach the bottom,
and what is its speed at the bottom?
a
a
a
a
Black board example 5.4
(on HW)
Attwood’s machine.
Two objects of mass m1 = 2.00 kg and m2 = 4.00 kg are hung over
a pulley.
(a) Determine the magnitude of the acceleration of the two objects and
the tension in the cord.
Forces of Friction
• Static friction, fs
• Kinetic friction, fk
Friction is due to the
surfaces interacting with
each other on the
microscopic level.
• sliding over bumps
• chemical bonds
time
The following empirical laws hold true about friction:
- Friction force, f, is proportional to normal force, n.
fs  msn
f k  mk n
- ms and mk: coefficients of static and kinetic friction, respectively
- Direction of frictional force is opposite to direction of relative
motion
- Values of ms and mk depend on nature of surface.
- ms and mk don’t depend on the area of contact.
- ms and mk don’t depend on speed.
- ms, max is usually a bit larger than mk.
- Range from about 0.003 (mk for synovial joints in humans) to 1 (ms
for rubber on concrete). See table 5.2 in book.
Approximate friction coefficients
Rubber on
concrete
Wood on wood
Waxed wood on
wet snow
Synovial joints
in humans
ms
mk
1.0
0.8
0.25-0.5
0.2
0.14
0.1
0.01
0.003
Black board example 5.5
(related to HW)
Measuring the coefficient of static
friction
A brick is placed on an inclined
board as shown in the figure.
The angle of incline is
increased until the block starts
to move.
a
a
a
a
Determine the static friction coefficient from the critical angle, ac, at
which the block starts to move. Calculate for ac = 26.5°.
Black board example 5.6
(on HW)
A car is traveling at 50.0 mi/h on a horizontal highway.
(a) If the coefficient of kinetic friction and static friction between
road and tires on an icy day are 0.080 and 0.1, respectively,
what is the minimum distance in which the car can stop?
(b) What are the advantages of antilock brakes?