Download A - Eastchester High School

1
AP Physics – Mechanics – Chapter 4 – The Laws of Motion
Text chapter 4 - Reading pp. 74-97 - textbook HW -#60,61,1,2,3,7,8,13,18,20,21,69,39,40,71,75
4.1, 4.2, Forces: Balanced vs. Unbalanced; Contact vs. Field
A) Describe the motion of an object when there is
unbalanced force acting on the object: The object must
be ACCELERATING in the direction of the unbalanced
force.
Examples:
1) a box sliding down a frictionless incline plane.
2) A box orbiting the earth in a circular orbit @ constant
speed
3) A box sliding into third base
2
B) Describe the motion of an object when there are
balanced forces acting on the object: When
NO UNBALANCED force is acting on an object, it is either
at rest or moving with a constant velocity.
Examples:
1) a box on a table or a box with a parachute falling at
constant speed
2) a positive box on a non-conducting string tied to a
positive wall
3) a box sitting on a ramp
3
4.3 Newton’s 1st Law – An object at rest will remain at rest
and an object in motion will continue with a constant
velocity unless it is acted upon by a Net External Force.
(Sometimes called the Law of Inertia)
# 1) Equilibrium? (where would you see this system of forces?)
Mathematical Def. of Equilibrium: ΣF=0 N so that a=0m/s2
Sometimes it is easier to break down into components such
that: ΣFx= ΣFy=0 N.
# 2) Equilibrium?
4
# 3) Find the equilibrant (Equilibrant: a single vector
that puts the system in equilibrium)
Now go home and try HW -- #60, 61
5
4.4 Newton’s 2nd Law – The acceleration of an object is
directly proportional to the resultant or Net Force acting on
it and inversely proportional to its mass.
*** The direction of the acceleration is the same as the
direction of the net force
# 4) In the following, what is the direction of the Net Force on the block?
A) A block slides down an incline
without friction
with friction
B) A block is dragged across the ground by a force F.
Now go home and try HW -- #1,2,3,7,8,13
6
4.5 Newton’s 3rd Law – If two bodies interact, the force
exerted on body 1 by body 2 is equal in magnitude and
opposite in direction to the force exerted on body 2 by body
1.
In other words: If A ______ B, B ______ A simultaneously
with the same force.
(For every action, there is an equal and opposite reaction.)
Question: What forces act on the book?
Why doesn’t the book accelerate downward? Because of the…
Def. Normal Force -- The force that the surface exerts on
the object that is touching it. It is always drawn
perpendicular to the surface.
7
Question: If all forces are equal an opposite, why does the whoosh
bottle accelerate and the book does not?
FBD: (How many forces are ON the book/bottle?)
8
4.6 ***Applications of Newton’s Laws***: Get ready to rock!
BIG NOTE:
** When doing calculations with Newton’s Laws, if you
follow these steps consistently, you cannot
possibly make a mistake :-)
1) Draw an F.B.D. (free-body diagram)
2) Write equations for ∑Fx and ∑Fy
3) Solve equations
# 5 Find the Tension in each cable
9
# 6) A child holds a sled at rest on a frictionless surface. If the sled
weighs 100 N: 1) Draw vectors representing the three vectors acting on
the sled; 2) find the tension in the rope and the force the hill exerts on
the sled.
(Is there an easier way???)
10
# 7) An ox pulls a wagon from rest along a frictionless surface with a
force of 20 N. The wagon weighs 300 N and the ox weighs 9000 N.
A) Determine the acceleration of the wagon.
B) How far does it move in 2 s?
# 8) A 3 kg block slides down a frictionless incline. Find the acceleration of
the block and the force that the incline exerts on the block.
11
# 9) Two blocks tied together are at rest on a frictionless surface and
pulled to the right by an external force F.
a) Find the acceleration of each block in terms of F, m1, and m2
b) Find the tension between the two blocks in terms of F, m1, and m2
Now go home and try HW -- #18, 20, 21, 69
12
Think about this interesting problem:
Using massless strings and frictionless pulleys, spring scale #1 is fastened
to a fixed point on its right side, and to a 1-kg mass on its left side. Spring
scale #2 is connected to a 1-kg mass on each side sides.
Compare the two spring scales readings.
13
4.7 Forces of Friction
Friction hint in a problem: surfaces are rough (or ultra
smooth)
A) If the block is at rest, the friction is called STATIC
FRICTION.
Fs ≤ μsFn or Fs ≤ μsn
B) If the block is in motion, the friction is called
SLIDING OR KINETIC FRICTION.
Fk = μkFn or Fk = μkn
14
# 10) A 6-kg box rests on a horizontal surface.
a) If the coefficient of static friction between the box and the floor is
0.4, find the maximum horizontal force that can be applied to the box
before it “slips.”
b) If the coefficient of kinetic friction is 0.2, find the force required to
push the block horizontally at constant speed.
c) What is the force required to accelerate the block horizontally at 2
m/s2?
d) Based on this problem, sketch the graph of friction force vs. applied
force.
15
Examples coefficients of friction:
Materials
Coeff. of Static Friction μs
Coeff. of Kinetic Friction μk
Steel on Steel
Aluminum on Steel
Copper on Steel
Rubber on
Concrete
Wood on Wood
Glass on Glass
Waxed wood on
Wet snow
Waxed wood on
Dry snow
Metal on Metal
(lubricated)
Ice on Ice
Teflon on Teflon
Synovial joints in
humans
0.74
0.61
0.53
0.57
0.47
0.36
1
0.25-0.5
0.94
0.8
0.2
0.4
0.14
0.1
-
0.04
0.1
0.04
0.06
0.03
0.04
0.01
0.003
#11) (From an old AP part I)
A 2 kg block slides down a 30o incline with an acceleration of 2 m/s2.
The magnitude of the frictional force along the plane is most nearly
Now go home and try HW -- # Study examples 4.7, 4.8,D o
problems #39,40,71,75
16
#12) A 4-kg block sitting on a rough surface is attached to a 7-kg
bowling ball by a massless string strung over a massless, frictionless,
pulley. (lots of massless stuff in AP B)
a) Find the acceleration of the
system if the coefficient of
kinetic friction between the
table and the 4 kg block is 0.3.
b) Find the acceleration of the
system assuming the system is
frictionless.
b) If the system starts from rest, how long will it take the 7 kg block to hit
the ground?
17
c) Describe the motion of the 4 kg block after the 7 kg block hits the
ground.
d) Determine where on the table the 4 kg block stops, or if it launches off
the table, where it hits the ground.
18
Time for the 18th Century Atwood Machine (aka Atwood's machine),
invented in 1784 by Rev. George Atwood as a laboratory experiment to
verify the mechanical laws of motion with constant acceleration.
#13) a)Two masses are suspended from a frictionless pulley and released.
Find the acceleration of the system in terms of m, M and g.
b) Find the acceleration of the system if M = 2m in terms of m, and g.
19
#14) Two masses are suspended at the bottom of an elevator. If the
elevator accelerates upward at a rate of ¼ g, find the tension in the upper
lower cable in terms of m and g.
b) Three blocks are stacked on each other as shown below. Find the force
that the 2-kg block exerts on the 6-kg block. The answer is simple, but try
solving it by drawing an F.B.D. …
20
#15) A 10 kg block sits on an incline. Find the coefficient of static
friction.
21
#16 The coefficient of static friction between the tires of a car and the
street is µs = .77. What is the steepest angle θ of a street on which a car
can be parked (with the wheels locked) without slipping.
22
What is an accelerometer ? An accelerometer measures proper
acceleration, which is the acceleration it experiences relative to freefall
and is the acceleration felt by people and objects. Such accelerations are
popularly measured in terms of g-force.
An accelerometer at rest relative to the Earth's surface will indicate
approximately 1 g upwards, because any point on the Earth's surface is
accelerating upwards relative to the local inertial frame (the frame of a
freely falling object near the surface). To obtain the acceleration due to
motion with respect to the Earth, this "gravity offset" must be subtracted
and corrections for effects caused by the Earth's rotation relative to the
inertial frame.
Two popular accelerometers: 1) a mass on a spring; 2) a pendulum
(plumb bob on a string)
Draw the position of the bob for the
following:
1) Accelerating (speeding up) to the right
2)
Moving at constant speed to the right
3)
Moving up a ramp at constant speed
4) Speeding up, down a ramp
23
5) How could one use a plumb bob of weight w in a convertible Ford
Mustang, with the top down, moving at constant velocity, to
determine the drag force on the plumb bob? At what angle to the
vertical axis would the drag force = the magnitude of the weight w?
What is Terminal Velocity?
When an object is freely falling through air, it eventually reaches a
terminal velocity vt dependent on:
Where:
= terminal velocity,
= mass of the falling object,
= acceleration due to gravity,
= drag coefficient,
= density of the fluid through which the object is falling, and
= projected area of the object.
Mathematically, this occurs when ΣFy=0N, thus
ay=0m/s2
Draw an F.B.D.
24
Note: terminal velocity for an outstretched human near sea level is about 55 m/s. What is the terminal
velocities at higher altitudes?
Excerpted from: http://hypertextbook.com/facts/JianHuang.shtml
On 16 August 1960, US Air Force Captain Joseph Kittinger entered the record books when he stepped from the
gondola of a helium balloon floating at an altitude of 31,330 m (102,800 feet) and took the longest skydive in
history. As of 2000, his record remains unbroken.
The air is so thin at this altitude that it would make for a moderate laboratory vacuum on the surface of the
earth. With little atmosphere, the sky is essentially black and the sun's radiation is unusually intense despite
polar temperatures.
Kittinger reports in a 1960 article for National Geographic:
“Sitting in my gondola, which gently twisted with the balloon's slow turnings, I had begun to sweat lightly,
though the temperature read 36 degrees below zero Fahrenheit. Sunlight burned in on me under the edge of an
aluminized antiglare curtain and through the gondola's open door.
The density of air at 30 km is roughly 1.5 % that at sea level and thus drag is essentially negligible.
No wind whistles or billows my clothing. I have absolutely no sensation of the increasing speed with which I
fall. [The clouds] rushed up so chillingly that I had to remind myself they were vapor and not solid.”
This is not true for skydivers at ordinary altitudes, which is why they reach terminal velocity and cease to
accelerate.
According to Captain Kittinger's 1960 report in National Geographic, he was in free fall from 102,800 to
96,000 feet and then experienced no noticeable change in acceleration for an additional 6,000 feet despite
having deployed his stabilization chute. This gave him an unprecedented 3900 m (12,800 feet) over which to
accelerate. At such extreme altitudes the acceleration due to gravity is not the standard 9.81 m/s2, but the
slightly lower value of 9.72 m/s2. Using these numbers, it is possible to calculate the maximum theoretical
velocity experienced during this record-setting jump. The result is amazingly close to the value recorded in
National Geographic.
Chapter 4: Done.