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Physics B
Classwork/1-D Motion
Name:_______________________________________ Physics Period:_______
Practice Problem: If x is the displacement of a
particle, and d is the distance the particle traveled
during that displacement, which of the following
is always a true statement?
a) d = |x|
b) d < |x|
c) d > |x|
d) d > |x|
e) d < |x|
Kinematics: the branch of mechanics that
describes the motion of objects without
necessarily discussing what causes the motion.
Distance
Definition:
SI Unit:
Practice Problem: A particle moves from x =
1.0 meter to x = -1.0 meter.
a) What is the distance d traveled by the particle?
Displacement (x)
Definition:
Equation:
b) What is the displacement of the particle?
SI Unit:
Question: Does the odometer in your car
measure distance or displacement?
Practice Problem: You are driving a car on a
circular track of diameter 40 meters. After you
have driven around 2 ½ times, how far have you
driven, and what is your displacement?
Can you think of a circumstance when it would
measure both distance and displacement?
Practice Problem: Two tennis players approach
the net to congratulate one another after a game.
A
5m
B
2 m
a) Find the distance and displacement of player
A.
Average Speed
Definition:
Equation:
b) Repeat for player B.
SI unit:
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Average Velocity
Definition:
Graphical Problem
What physical feature of the graph gives the
constant velocity from A to B?
x
Equation:
B
A
t
SI unit:
Practice Problem: How long will it take the
sound of the starting gun to reach the ears of the
sprinters if the starter is stationed at the finish
line for a 100 m race? Assume that sound has a
speed of about 340 m/s.
Graphical Problem: Determine the average
velocity from the graph.
x (m)
Practice Problem: You drive in a straight line at
10 m/s for 1.0 km, and then you drive in a
straight line at 20 m/s for another 1.0 km. What
is your average velocity?
Graphical Problem: Determine the average
velocity between 1 and 4 seconds.
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Instantaneous Velocity
Definition:
Acceleration in 1-D motion has a sign!
If the sign of the velocity and the sign of the
acceleration is the same, what happens?
If the sign of the velocity and the sign of the
acceleration are different, what happens?
Practice Problem: Determine the instantaneous
velocity at 1.0 second.
Practice Problem: A 747 airliner reaches its
takeoff speed of 180 mph in 30 seconds. What is
its average acceleration?
Practice Problem: A horse is running with an
initial velocity of 11 m/s, and begins to
accelerate at –1.81 m/s2. How long does it take
the horse to stop?
Acceleration
Definition:
What does the sign of the acceleration signify?
What types of acceleration are there?
Graphical Problem
What physical feature of the graph gives the
acceleration?
Questions
If acceleration is zero, what does this mean about
the motion of an object?
v
Is it possible for a racecar circling a track to have
zero acceleration?
B
A
t
Uniform (Constant) Acceleration
Equation:
SI unit:
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Practice Problem: Determine the acceleration
from the graph.
Draw Graphs for Stationary Particles
x
v
t
a
t
t
Draw Graphs for Constant Non-zero Velocity
x
v
t
a
t
t
Determine the displacement of the object from 0
to 4.0 seconds (using the graph above)
Draw Graphs for Constant Non-zero Acceleration
x
How would you describe the motion of this
particle?
v
t
a
t
t
Kinematic Equations
Describe the motion
Equation 1:
Equation 2:
Equation 3:
Practice Problem: What must a particular
Olympic sprinter’s acceleration be if he is able to
attain his maximum speed in ½ of a second?
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Practice Problem: A plane is flying in a
northwest direction when it lands, touching the
end of the runway with a speed of 130 m/s. If the
runway is 1.0 km long, what must the
acceleration of the plane be if it is to stop while
leaving ¼ of the runway remaining as a safety
margin?
Practice Problem: You are driving through
town at 12.0 m/s when suddenly a ball rolls out
in front of you. You apply the brakes and
decelerate at 3.5 m/s2.
a) How far do you travel before stopping?
b) When you have traveled only half the
stopping distance, what is your speed?
Practice Problem: On a ride called the
Detonator at Worlds of Fun in Kansas City,
passengers accelerate straight downward from 0
to 20 m/s in 1.0 second.
a) What is the average acceleration of the
passengers on this ride?
c) How long does it take you to stop?
b) How fast would they be going if they
accelerated for an additional second at this rate?
d) Draw x vs t, v vs t, and a vs t graphs for this.
c) Sketch approximate x-vs-t, v-vs-t and a-vs-t
graphs for this ride.
Free Fall
Definition:
Practice Problem: Air bags are designed to
deploy in 10 ms. Estimate the acceleration of the
front surface of the bag as it expands. Express
your answer in terms of the acceleration of
gravity g.
Acceleration due to Gravity:
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c) What is the ball’s velocity when you catch it?
Practice Problem: You drop a ball from rest off
a 120 m high cliff. Assuming air resistance is
negligible,
a) how long is the ball in the air?
d) Sketch approximate x-vs-t, v-vs-t, a-vs-t
graphs for this situation.
b) what is the ball’s speed and velocity when it
strikes the ground at the base of the cliff?
Symmetry in Free Fall
When something is thrown straight upward
under the influence of gravity, and then returns
to the thrower, this is very symmetric.
The object spends half its time traveling up;
half traveling down.
Velocity when it returns to the ground is the
opposite of the velocity it was thrown upward
with.
2
Acceleration is 9.8 m/s and directed
DOWN the entire time the object is in the air!
c) sketch approximate x-vs-t, v-vs-t, a-vs-t
graphs for this situation.
Practice Problem: You throw a ball straight
upward into the air with a velocity of 20.0 m/s,
and you catch the ball some time later.
a) How long is the ball in the air?
Homework Problem: Below is some data for a
car in the Pinewood Derby. Using these data,
work the following problem:
Pinewood Derby
x(m)
t(s)
b) How high does the ball go?
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0
0
2.3
1.0
9.2
2.0
20.7
3.0
36.8
4.0
57.5
5.0
On your graph paper, do the following.
a) Draw a position vs time graph for the car.
b) Draw tangent lines at three different points on the
curve to determine the instantaneous velocity at all three
points.
c) On a separate graph, draw a velocity vs time graph
using the instantaneous velocities you obtained in the
step above.
d)From your velocity vs time graph, determine the
acceleration of the car.
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Physics B
Classwork: 2 and 3D Motion
Homework problem
Name:_____________________
Case 3: Ball A is dropped from rest at the
top of the cliff at exactly the same time
Ball B is thrown vertically upward with
speed vo from the foot of the cliff such
that Ball B will collide with Ball A. Derive
an expression for the amount of time that
will elapse before they collide.
Case 1: Ball A is dropped from rest at the
top of a cliff of height h as shown. Using
g as the acceleration due to gravity,
derive an expression for the time it will
take for the ball to hit the ground.
A
h
Case 4: Ball A is dropped from rest at
the top of the cliff at exactly the same
time Ball B is projected vertically upward
with speed vo from the foot of the cliff
directly beneath ball A. Derive an
expression for how high above the ground
they will collide.
Case 2: Ball B is projected vertically
upward from the foot of the cliff with an
initial speed of vo. Derive an expression
for the maximum height ymax reached by
the ball.
h
vo
B
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2-Dimensional Motion
Definition:
Sample Problem
A roller coaster rolls down a 20o incline
with an acceleration of 5.0 m/s2.
a) How far horizontally has the
coaster traveled in 10 seconds?
Examples:
Solving 2-D Problems
Resolve all vectors into components.
Work the problem as two one-dimensional
problems.
Re-combine the results for the two
components at the end of the
problem.
b) How far vertically has the coaster
traveled in 10 seconds?
Sample Problem
You run in a straight line at a speed of 5.0
m/s in a direction that is 40o south of
west.
a) How far west have you traveled in
2.5 minutes?
Sample Problem
A particle passes through the origin with
a speed of 6.2 m/s in the positive y
direction. If the particle accelerates in
the negative x direction at 4.4 m/s2
a) What are the x and y positions at
5.0 seconds?
b) How far south have you traveled
in 2.5 minutes?
b) What are the x and y components
of velocity at this time?
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Bertrand
Projectile Motion
Something is fired, thrown, shot, or
hurled near the earth’s surface.
Vertical Component of Velocity
Characteristics:
Horizontal velocity is __________
Equations:
Vertical velocity is __________
Air resistance is __________
1-Dimensional Projectile
Definition:
Launch angle
Definition:
Examples:
Why is the launch angle important?
You calculate vertical motion only.
The motion has no horizontal component.
Zero Launch angle
What does a zero launch angle imply?
2-Dimensional Projectile
Definition:
Sample Problem
The Zambezi River flows over Victoria
Falls in Africa. The falls are
approximately 108 m high. If the river is
flowing horizontally at 3.6 m/s just
before going over the falls, what is the
speed of the water when it hits the
bottom? Assume the water is in freefall
as it drops.
Examples:
You calculate vertical and horizontal
motion.
Horizontal Component of Velocity
Characteristics:
Equation:
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Sample Problem
An astronaut on the planet Zircon tosses
a rock horizontally with a speed of 6.75
m/s. The rock falls a distance of 1.20 m
and lands a horizontal distance of 8.95 m
from the astronaut. What is the
acceleration due to gravity on Zircon?
Resolving the velocity
Use speed and the launch angle to find
horizontal and vertical velocity
components.
Then proceed to work problems just like
you did with the zero launch angle
problems.
Sample problem
A soccer ball is kicked with a speed of
9.50 m/s at an angle of 25o above the
horizontal. If the ball lands at the same
level from which is was kicked, how long
was it in the air?
Sample Problem
Playing shortstop, you throw a ball
horizontally to the second baseman with a
speed of 22 m/s. The ball is caught by the
second baseman 0.45 s later.
a) How far were you from the second
baseman?
Sample problem
Snowballs are thrown with a speed of 13
m/s from a roof 7.0 m above the ground.
Snowball A is thrown straight downward;
snowball B is thrown in a direction 25o
above the horizontal. When the snowballs
land, is the speed of A greater than, less
than, or the same speed of B? Verify your
answer by calculation of the landing speed
of both snowballs.
b) What is the distance of the
vertical drop?
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Projectiles launched over level ground
These projectiles have highly symmetric
characteristics of motion.
Position graphs for 2-D projectiles
Trajectory of a 2-D Projectile launched
over level ground
Sketch:
Velocity graphs for 2-D projectiles
Characteristics:
Acceleration graphs for 2-D projectiles
Range of a 2-D Projectile launched over
level ground
Definition:
Maximum height of a projectile launched
over level ground
Notes:
Sample problem
A golfer tees off on level ground, giving
the ball an initial speed of 42.0 m/s and
an initial direction of 35o above the
horizontal.
a) How far from the golfer does the ball
land?
Acceleration of a projectile launched over
level ground
Notes:
Velocity of a projectile launched over
level ground
Notes:
b)The next golfer hits a ball with the
same initial speed, but at a greater angle
than 45o. The ball travels the same
horizontal distance. What was the initial
direction of motion?
Time of flight for a projectile launched
over level ground
Notes:
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Free Response Preparation #1
A cannonball is fired at an angle of 45o above the horizontal at an initial velocity of 77 m/s. The cannon is located at
the top of a 120 m high cliff, and the cannonball is fired over the level plain below.
a) Draw a representation of the trajectory of the cannonball from launch until it strikes the plain below the cliff.
Label the following: A: The point where the projectile is traveling the slowest; B: The point where the projectile has
the same speed as it does at launch; C: The point where the projectile is traveling the fastest.
b) Calculate the total time from launch until the cannonball hits the plain below the cliff.
c) Calculate the horizontal distance that the cannonball travels before it hits the plain below the cliff.
d) Calculate the maximum height attained by the cannonball.
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Free Response Preparation #2
A soccer player on Krypton kicks a ball directly toward a fence from a point 35 meters away. The initial
velocity of the ball is 25 m/s at an angle of 40o above the horizontal. The top of the fence is 3.0 meters
above the ground. The ball hits nothing while in flight, and, since Krypton has no atmosphere, air
resistance is nonexistent. The acceleration due to gravity on Krypton is 12 m/s 2.
a. Sketch the problem
b. Determine the time it takes for the ball to reach the plane of the fence.
c. Will the ball hit the fence? If so, how far below the top of the fence will it hit? If not, how
far above the fence will it pass?
d. Sketch the horizontal and vertical components of the ball’s velocity as functions of time until
the ball reaches the plane of the fence. Draw and label your axes!
e. What is the minimum speed the soccer player must give to the ball if it is to just hit the
bottom of the fence at the same time it hits the ground?
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Physics B
Classwork and Notes: Newtons’ Laws I
Name:_________________
Force
Sample Problem
Definition:
a) A monkey hangs by its tail from a tree
branch. Draw a force diagram
representing all forces on the monkey.
What does a force do?
Newton’s First Law
b) Now the monkey hangs by both hands
from two vines. Each of the monkey’s
arms are at a 45o from the vertical. Draw
a force diagram representing all forces on
the monkey.
What happens if there is zero net
force on a body?
Mass and Inertia
Definition of mass (physics
definition):
Does zero net force mean there is no
force at all on a body?
Definition of inertia:
Sample Problem
A heavy block hangs from a string
attached to a rod. An identical string
hangs down from the bottom of the block.
Which string breaks
a) when the lower string is pulled with a
slowly increasing force?
Draw a force diagram and a free-body
diagram for a book resting on a table.
b) when the lower string is pulled with
a quick jerk?
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Newton’s Second
Law
A catcher stops a 92 mph pitch in his
glove, bringing it to rest in 0.15 m. If the
force exerted by the catcher is 803 N,
what is the mass of the ball?
Definition:
Equation:
SI Units:
A 747 jetliner lands and begins to slow to a
stop as it moves along the runway. If its
mass is 3.50 x 105 kg, its speed is 27.0 m/s,
and the net braking force is 4.30 x 105 N
a) what is its speed 7.50 s later?
Working 2nd Law
Problems
1. Draw a force or free body diagram.
2. Set up 2nd Law equations in each
dimension.

Fx = max and/or Fy = may
3. Identify numerical data.
x-problem and/or y-problem
4. Substitute numbers into equations.
“plug-n-chug”
5. Solve the equations.
b) how far has it traveled in this time?
Sample Problems
Newton’s Third Law
In a grocery store, you push a 14.5-kg
cart with a force of 12.0 N. If the cart
starts at rest, how far does it move in
3.00 seconds?
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Definition:
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Bertrand
Sample Problem
You rest an empty glass on a table.
a) How many forces act upon the glass?
Newton’s 2nd Law
in 2-D
b) Identify these forces with a free
body diagram.
Identify all forces and draw a force diagram.
Problem must be resolved into x- and yproblems.
Follow the procedure for 1-D problems!
Sample Problems
A surfer “hangs ten”, and accelerates
down the sloping face of a wave. If the
surfer’s acceleration is 3.50 m/s2 and
friction can be ignored, what is the angle
at which the face of the wave is inclined
above the horizontal?
c) Are these forces equal and opposite?
d) Are these forces an action-reaction
pair?
Sample Problem
(similar to #17)
A force of magnitude 7.50 N pushes
three boxes with masses m1 = 1.30 kg, m2
= 3.20 kg, and m3 = 4.90 kg as shown. Find
the contact force
(a) between boxes 1 and 2.
How long will it take a 1.0 kg block initially
at rest to slide down a frictionless 20.0 m
long ramp that is at a 15o angle with the
horizontal?
(b) between boxes 2 and 3.
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Apparent weight
An object acted on by three forces moves
with constant velocity. One force acting
on the object is in the positive x direction
and has a magnitude of 6.5 N; a second
force has a magnitude of 4.4 N and points
in the negative y direction. Find the
direction and magnitude of the third
force acting on the object.
Definition:
Elevator rides
Why do you feel lighter or heavier during
parts of an elevator ride?
Draw force diagrams for an elevator
ride when you are ascending.
Mass and Weight
Definition of Weight:
Equation for Weight:
Stationary at Beginning
the ground the ascent
floor
Constant
velocity
between
floors
Slowing at
top floor
Draw force diagrams for an elevator
ride when you are descending.
Sample Problem
A man weighs 150 pounds on earth at sea
level. Calculate his
a) mass in kg.
b) weight in Newtons.
Stationary at Beginning
the top floor the descent
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Constant
velocity
between
floors
Slowing at
the
ground
floor
Bertrand
Sample Problem
b) moving upward and slowing at
3.2 m/s2?
An 85-kg person is standing on a
bathroom scale in an elevator. What is the
person’s apparent weight
a) when the elevator accelerates
upward at 2.0 m/s2?
c) moving downward and speeding
up at 3.2 m/s2?
b) when the elevator is moving at
constant velocity between floors?
d) moving upward and speeding up
at 3.2 m/s2?
c) when the elevator begins to slow
at the top floor at 2.0 m/s2?
Normal force
Definition:
Sample Problem
A 5-kg salmon is hanging from a fish scale
in an elevator. What is the salmon’s
apparent weight when the elevator is
a) at rest?
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In what direction is the normal force
relative to a surface?
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Bertrand
Normal force on flat surface
Sample problem
A 5.0-kg bag of potatoes sits on the
bottom of a stationary shopping cart.
Sketch a free-body diagram for the bag
of potatoes. Now suppose the cart moves
with a constant velocity. How does this
affect the free-body diagram?
Normal force on ramp
Sample problem
Find the normal force exerted on a 2.5-kg
book resting on a surface inclined at 28o
above the horizontal.

Normal force not associated with
weight.
If the angle of the incline is reduced, do
you expect the normal force to increase,
decrease, or stay the same?
Sample problem
A gardener mows a lawn with an oldfashioned push mower. The handle of the
mower makes an angle of 320 with the
surface of the lawn. If a 249 N force is
applied along the handle of the 21-kg
mower, what is the normal force exerted
by the lawn on the mower?
Draw a free body diagram for the
skier.
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Bertrand
Sample problem
Larry pushes a 200 kg block on a
frictionless floor at a 45o angle below the
horizontal with a force of 150 N while
Moe pulls the same block horizontally with
a force of 120 N.
a) Draw a free body diagram.
b) What is the acceleration of the
block?
c) What is the normal force exerted
on the block
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Physics B
Classwork/Notes: Applications of Newton’s Laws
Name:____________________
Friction
Definition:
What causes friction?
How is friction useful?
How does friction depend on normal
force?
Static Friction
Definition:
Equation:
What are some implications of the fact
that the static friction equation is an
inequality?
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Static friction and applied horizontal force
Draw a force diagram representing the force
of static friction on a level surface.
Sample Problem
A 10-kg box rests on a ramp that is laying
flat. The coefficient of static friction is
0.50, and the coefficient of kinetic
friction is 0.30.
a) What is the maximum horizontal force
that can be applied to the box before it
begins to slide?
Static friction on a ramp
Draw a force diagram representing the force
of static friction on a ramp.
b) What force is necessary to keep the
box sliding at constant velocity?
Kinetic Friction
Definition:
Sample Problem
A 10-kg wooden box rests on a ramp that
is lying flat. The coefficient of static
friction is 0.50, and the coefficient of
kinetic friction is 0.30. What is the
friction force between the box and ramp
if
a) no force horizontal force is applied to
the box?
Equation:
How does the magnitude of kinetic friction
compare to the magnitude of static friction?
b) a 20 N horizontal force is applied to
the box?
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Bertrand
c) a 60 N horizontal force is applied to
the box?
Sample Problem
A 10-kg wooden box rests on a wooden ramp.
The coefficient of static friction is 0.50,
and the coefficient of kinetic friction is
0.30. What is the friction force between the
box and ramp if
a) the ramp is at a 25o angle?
Laboratory
Determine the coefficients of static and
kinetic friction between the wooden block
(felt side) and the cart track. The only
additional equipment you may use is a meter
stick, a clamp, and a pole.
Write a mini-lab report that includes only
the following:
procedure: one for determination of each
kind of friction.
analysis: include diagrams (free-body),
calculations, and results for each kind of
friction.
It is necessary to type the procedure
section, but the rest of the report may
be hand-written.
Tension
Definition:
What causes tension?
b) the ramp is at a 45o angle?
Sample problem
a) A 1,500 kg crate hangs motionless
from a crane cable. What is the tension in
the cable? Ignore the mass of the cable.
c) what is the acceleration of the box when
the ramp is at 45o?
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b) Suppose the crane accelerates the
crate upward at 1.2 m/s2. What is the
tension in the cable now?
Bertrand
Hooke’s Law
Definition:
Connected objects
What do connected objects subject to a
force have in common?
Sample problem
A 5.0 kg object (m1) is connected to a 10.0
kg object (m2) by a string. If a pulling
force F of 20 N is applied to the 5.0 kg
object as shown,
Equation:
A)
what is the acceleration of the
system? (Assume no friction; draw the
figure and proceed).
What is meant by the term restoring
force?
Sample problem
A 1.50 kg object hangs motionless from a
spring with a force constant of k = 250
N/m. How far is the spring stretched
from its equilibrium length?
B)
what is the tension in the string
connecting the objects? (Assume no
friction)
Sample problem
Mass 1 (10 kg) rests on a frictionless
table connected by a string to Mass 2 (5
kg). Find
a) the acceleration of each block. (Draw
the figure and proceed).
Sample problem
A 1.80 kg object is connected to a spring
of force constant 120 N/m. How far is
the spring stretched if it is used to drag
the object across a floor at constant
velocity? Assume the coefficient of
kinetic friction is 0.60.
b) the tension in the connecting string.
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Bertrand
Sample problem
Mass 1 (10 kg) rests on a table connected
by a string to Mass 2 (5 kg). Find the
minimum coefficient of static friction for
which the blocks remain stationary.
Uniform Circular Motion
Definition:
Why
is
uniform
accelerated?
Sample problem
Mass 1 (10 kg) rests on a table connected
by a string to Mass 2 (5 kg). If s = 0.30
and k = 0.20, what is
a) the acceleration of each block? (Draw
the figure and proceed).
circular
motion
What is centrifugal force?
When a car turns, you feel as if you are
flung to the outside? Why?
As a general rule, when you feel flung in a
certain direction, in what direction is the
acceleration?
b) the tension in the connecting string?
Acceleration in Uniform Circular Motion
In what direction does it point?
Sample problem
Two blocks are connected by a string as
shown in the figure. What is the
acceleration, assuming there is no
friction? (Draw the figure and proceed).
Centripetal Acceleration
Definition:
Equation
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Bertrand
Centripetal Force
Definition:
Equation:
Sample problem
A 1200-kg car rounds a corner of radius r
= 45 m. If the coefficient of static
friction between tires and the road is
0.93 and the coefficient of kinetic
friction between tires and the road is
0.75, what is the maximum velocity the
car can have without skidding?
Sample problem
You whirl a 2.0 kg stone in a horizontal
circle about your head. The rope attached
to the stone is 1.5 m long. What is the
tension in the rope?
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Bertrand
Work
Sample problem
Jane uses a vine wrapped around a pulley to lift a
70-kg Tarzan to a tree house 9.0 meters above
the ground.
a) How much work does Jane do when she
lifts Tarzan?
Definition:
Equation:
Units of Work (SI System)
b) How much work does gravity do when
Jane lifts Tarzan?
Question: If a man holds a 50 kg box at arms
length for 2 hours as he stands still, how much
work does he do on the box?
Sample problem
Joe pushes a 10-kg box and slides it across the
floor at constant velocity of 3.0 m/s. The
coefficient of kinetic friction between the box
and floor is 0.50.
a) How much work does Joe do if he
pushes the box for 15 meters?
Question: If a man holds a 50 kg box at arms
length for 2 hours as he walks 1 km forward,
how much work does he do on the box?
Question: If a man lifts a 50 kg box 2.0 meters,
how much work does he do on the box?
b) How much work does friction do as Joe
pushes the box?
Work and Energy
Work changes mechanical energy.
Sample problem
A father pulls his child in a little red wagon with
constant speed. If the father pulls with a force of 16
N for 10.0 m, and the handle of the wagon is inclined
at an angle of 60o above the horizontal, how much
work does the father do on the wagon?
Positive work ________________ mechanical
energy.
Negative work ________________ mechanical
energy.
The two forms of mechanical energy are called:
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Bertrand
Kinetic Energy
b) Did air resistance do positive, negative
or zero work on the acorn? Why?
Definition:
Equation:
c)
How much work was done by air
resistance?
Units of Energy (SI System):
Sample problem
A 10.0 g bullet has a speed of 1.20 km/s.
a) What is the kinetic energy of the bullet?
d) What was the average force of air
resistance?
b) What is the bullet’s kinetic energy if the
speed is halved?
Constant force and work: draw and label graph
c)
What is the bullet’s kinetic energy if the
speed is doubled?
The Work-Energy Theorem
Definition:
Variable force and work: draw and label graph
Equation:
Sample problem
An 8.0-g acorn falls from a tree and lands on the
ground 10.0 m below with a speed of 11.0 m/s.
a) What would the speed of the acorn have
been if there had been no air resistance?
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Springs
Why is the work done by a spring when it is
stretched or compressed negative?
Sample problem
It takes 1000 J of work to compress a certain
spring 0.10 m.
a) What is the force constant of the spring?
Equation for work done by spring:
b) To compress the spring an additional
0.10 m, does it take 1000 J, more than
1000 J, or less than 1000 J? Verify your
answer with a calculation.
Graph for stretching of spring
F
Sample Problem
How much work is done by the force shown
when it acts on an object and pushes it from x =
0.25 m to x = 0.75 m?
x
Sample problem
A spring with force constant 250 N/m is initially
at its equilibrium length.
a) How much work must you do to stretch
the spring 0.050 m?
Figure from “Physics”, James S. Walker, Prentice-Hall 2002
Sample Problem
How much work is done by the force shown
when it acts on an object and pushes it from x =
2.0 m to x = 4.0 m?
b) How much work must you do to
compress it 0.050 m?
Figure from “Physics”, James S. Walker, Prentice-Hall 2002
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Bertrand
Power
Unit of Power (SI system):
Force types
Conservative forces:
Work is path independent.
Work along a closed path is zero.
Work changes potential energy.
Examples: gravity, springs
Non-conservative forces:
Work is path dependent.
Work along a closed path is NOT zero.
Work changes mechanical energy.
Examples: friction, drag
Unit of Power (British system):
Definition:
Definition:
Equation:
Potential energy
Conversion from horsepower to Watts:
Equation (gravity):
The kilowatt-hour
Definition:
Equation (spring):
Sample problem
A man runs up the 1600 steps of the Empire
State Building in 20 minutes seconds. If the
height gain of each step was 0.20 m, and the
man’s mass was 80.0 kg, what was his average
power output during the climb? Give your
answer in both watts and horsepower.
Conservative forces and Potential energy
Equation:
What happens to potential energy when a
conservative force does positive work?
What about when a conservative force does
negative work?
Sample problem
Calculate the power output of a 0.10 g fly as it
walks straight up a window pane at 2.0 cm/s.
More on paths and conservative forces.
Q: Assume a conservative force
moves an object along the
various paths. Which two works
are equal?
Q: Which two works, when
added together, give a sum of
zero?
Figure from “Physics”, James S. Walker, Prentice-Hall 2002
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Sample problem
A box is
moved in the
closed path
shown.
a) How
much work
is done by
gravity when
the box is
moved along
the path A->B->C?
Sample problem
If 30.0 J of work are required to stretch a spring
from a 2.00 cm elongation to a 4.00 cm
elongation, how much work is needed to stretch
it from a 4.00 cm elongation to a 6.00 cm
elongation?
Figure from “Physics”, James S. Walker, Prentice-Hall 2002
Law of Conservation of Energy
Statement:
b) How much work is done by gravity when the
box is moved along the path A->B->C->D->A?
Sample problem
A box is moved in
the closed path
shown.
a) How much work
would be done by
friction if the box
were moved along
the path A->B->C?
Law of Conservation of Mechanical Energy
Equations:
Pendulums and Energy Conservation
Q: Where in pendulum swing is mechanical
energy all potential energy?
Figure from “Physics”, James S. Walker, Prentice-Hall 2002
b) How much work is done by friction when the
box is moved along the path A->B->C->D->A?
Q. What kind of potential energy exists in
pendulum? Give the equation.
Sample problem
A diver drops to the water from a height of 20.0
m, his gravitational potential energy decreases by
12,500 J. How much does the diver weigh?
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Q: Where in pendulum swing is mechanical
energy all kinetic energy?
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Springs and Energy Conservation
Q: Where in spring oscillatin is mechanical
energy all potential energy?
For 2.0 m
Q. What kind of potential energy exists in a
spring? Give the equation.
For 0.0 m
Q: Where in spring oscillation is mechanical
energy all kinetic energy?
Sample problem
Problem from “Physics”, James S. Walker, Prentice-Hall 2002
A 1.60 kg block slides with a speed of 0.950 m/s
on a frictionless, horizontal surface until it
encounters a spring with a force constant of 902
N/m. The block comes to rest after compressing
the spring 4.00 cm. Find the spring potential
energy, U, the kinetic energy of the block, K, and
the total mechanical energy of the system, E, for
the following compressions: 0 cm, 2.00 cm, 4.00
Sample problem
What is the speed of the pendulum bob at point B if it is
released from rest at point A?
40o
1.5 m
For 0 cm
A
B
Sample problem
Problem from “Physics”, James S. Walker, Prentice-Hall 2002
A 0.21 kg apple falls from a tree to the ground, 4.0
m below. Ignoring air resistance, determine the
apple’s gravitational potential energy, U, kinetic
energy, K, and total mechanical energy,
E, when its height above the ground is each of the
following: 4.0 m, 2.0 m, and 0.0 m. Take ground
level to be the point of zero potential energy.
For 2.00 cm
For 4.0 m
For 4.00 cm
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Law of Conservation of Energy
Equations:
For 0.50 m
Work done by non-conservative forces
Wnet = Wc + Wnc
Wc = -U
Wnet = K
K = -U + Wnc
Wnc = U + K = E
Sample problem
Problem from “Physics”, James S. Walker, Prentice-Hall 2002
Catching a wave, a 72-kg surfer starts with a
speed of 1.3 m/s, drops through a height of 1.75
m, and ends with a speed of 8.2 m/s. How much
non-conservative work was done on the surfer?
For 1.00 m
Pendulum lab
Figure out how to demonstrate conservation of
energy with a pendulum using the equipment
provided. The photogates must be set up in
“gate” mode this time.
The width of the pendulum bob is an important
number. To get it accurately, use the caliper.
Turn in just your calculations, which must
clearly show the speed you predict for the
pendulum bob from conservation of energy, the
speed you measure using the caliper and
photogate data, and a %difference for the two.
Sample problem
Problem from “Physics”, James S. Walker, Prentice-Hall 2002
A 1.75-kg rock is released from rest at the
surface of a pond 1.00 m deep. As the rock falls,
a constant upward force of 4.10 N is exerted on it
by water resistance. Calculate the
nonconservative work, Wnc, done by the water
resistance on the rock, the gravitational potential
energy of the system, U, the kinetic energy of the
rock, K, and the total mechanical energy of the
system, E, for the following depths below the
water’s surface: d = 0.00 m, d = 0.500 m, d =
1.00 m. Let potential energy be zero at the
bottom of the pond.
For 0.00 m
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Physics B
Notes: Momentum
Momentum (p)
Name:_________________
Momentum change of Lazy Ball:
Definition:
Equation: one particle
Momentum change of Bouncy Ball:
Equation: multiple particles
Units:
Impulse (J)
Definition:
Sample Problem
Calculate the momentum of a 65-kg
sprinter running east at 10 m/s.
What does impulse change?
Equations:
Sample Problem
Calculate the momentum of a system
composed of a 65-kg sprinter running east
at 10 m/s and a 75-kg sprinter running
north at 9.5 m/s.
Units: N s or kg m/s (same as momentum)
What characterizes impulsive forces?
Impulse (J) on a graph
Change in momentum
Equation:
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Sample Problem
Suppose a 1.5-kg brick is dropped on a
glass table top from a height of 20 cm.
A) What is the magnitude and
direction of the impulse necessary to
stop the brick?
Law of Conservation of Momentum
Definition:
Equation:
Sample problem
A 75-kg man sits in the back of a 120-kg
canoe that is at rest in a still pond. If the
man begins to move forward in the canoe
at 0.50 m/s relative to the shore, what
happens to the canoe?
B) If the table top doesn’t shatter,
and stops the brick in 0.01 s, what is
the average force it exerts on the
brick?
C) What is the average force that the
brick exerts on the table top during
this period?
External versus internal forces
External forces are
Internal forces are
What can external forces do that internal
forces cannot?
Explosions
What type of forces exist in an explosion
(external or internal?)
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What is conserved in an explosion?
Collisions
Definiton:
What is not conserved in an explosion?
What is conserved in all collisions?
Recoil
Definition:
Collision Types
Describe an elastic collision.
Which of Newton’s three laws is most
applicable to recoil?
Describe a perfectly inelastic collision.
What is conserved in both elastic and
inelastic collisions?
Sample problem
Suppose a 5.0-kg projectile launcher
shoots a 209 gram projectile at 350 m/s.
What is the recoil velocity of the
projectile launcher?
What is conserved in an elastic collision
but not conserved in an inelastic collision?
Sample Problem
An 80-kg roller skating grandma collides
inelastically with a 40-kg kid. What is
their velocity after the collision? What is
the change in kinetic energy?
Sample problem
An exploding object breaks into three
fragments. A 2.0 kg fragment travels
north at 200 m/s. A 4.0 kg fragment
travels east at 100 m/s. The third
fragment has mass 3.0 kg. What is the
magnitude and direction of its velocity?
Sample Problem
A fish moving at 2 m/s swallows a
stationary fish which is 1/3 its mass.
What is the velocity of the big fish and
after dinner?
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Sample Problem
A car with a mass of 950 kg and a speed
of 16 m/s to the east approaches an
intersection. A 1300-kg minivan traveling
north at 21 m/s approaches the same
intersection. The vehicles collide and
stick together. What is the resulting
velocity of the vehicles after the
collision?
2-Dimensional Collisions
What key concept do you need to
remember when you work 2-dimensional
collisions problems, either elastic or
inelastic?
Sample problem
Sample Problem – elastic collision
A 500-g cart moving at 2.0 m/s on an air
track elastically strikes a 1,000-g cart at
rest. What are the resulting velocities of
the two carts?
Sample Problem
Suppose three equally strong, equally
massive astronauts decide to play a game
as follows: The first astronaut throws the
second astronaut towards the third
astronaut and the game begins. Describe
the motion of the astronauts as the game
proceeds. Assume each toss results from
the same-sized "push." How long will the
game last?
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Mechanical Wave
Definition:
Wave types: transverse
Definition:
Draw a wave; label the parts
Examples
Wave types: longitudinal
Definition:
Speed of a wave
Equation 1:
Equation 2:
Examples
Period of a wave
Equation:
Reflection of waves
Definition:
.
Problem: Sound travels at approximately
340 m/s, and light travels at 3.0 x 108 m/s.
How far away is a lightning strike if the
sound of the thunder arrives at a location 2.0
seconds after the lightning is seen?
Characteristics of Fixed-end reflection
Characteristics of Open-end reflection
Problem: The frequency of an oboe’s A is
440 Hz. What is the period of this note?
What is the wavelength? Assume a speed of
sound in air of 340 m/s.
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Refraction of waves
Definition:
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Principle of Superposition
Definition:
What can change when a wave refracts?
What never changes when a wave refracts?
Sound
What type of wave is sound?
Constructive interference
Definition:
How does the oscilloscope display a pure
tone?
Picture of waveforms undergoing
constructive interference:
What does a Fourier transform look like
for a pure tone?
Destructive interference.
Definition:
How does the oscilloscope display a
complex tone?
Picture of waveforms undergoing
destructive interference:
What does a Fourier transform look like
for a complex tone?
Sample Problem: Draw the waveform
from its two components.
Doppler Effect
Definition:
Approaching sound has ________ pitch.
Retreating sound has ________ pitch.
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Standing Wave
Open-end standing waves
1st harmonic
Definition:
What role does reflection play in
formation of a standing wave?
2nd harmonic
What role does superposition play in a
standing wave?
3rd harmonic
Fixed-end standing waves
1st harmonic
Mixed standing waves
1st harmonic
2nd harmonic
2nd harmonic
3rd harmonic
3rd harmonic
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Sample Problem
How long do you need to make an organ
pipe that produces a middle C (256 Hz)?
The speed of sound in air is 340 m/s.
A) Draw the first harmonic.
Resonance
Definition:
Beats
Definition:
B) Calculate the pipe length.
Drawing:
C) What is the wavelength and
frequency of the 2nd harmonic?
Diffraction
Definition:
Double-slit or multi-slit diffraction
Equation:
Sample Problem
How long do you need to make an organ
pipe whose fundamental frequency is a Csharp (273 Hz)? The pipe is closed on one
end, and the speed of sound in air is 340
m/s.
A) Draw the fundamental.
Single slit diffraction
Equation:
Sample Problem
Light of wavelength 360 nm is passed
through a diffraction grating that has
10,000 slits per cm. If the screen is 2.0 m
from the grating, how far from the
central bright band is the first order
bright band?
B) Calculate the pipe length.
C) What is the wavelength and
frequency of the 2nd harmonic?
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Sample Problem
Graph:
Light of wavelength 560 nm is passed through
two slits. It is found that, on a screen 1.0 m
from the slits, a bright spot is formed at x =
0, and another is formed at x = 0.03 m? What
is the spacing between the slits?
x(m)
t
Definitions:
Amplitude
Sample Problem
Light is passed through a single slit of width
2.1 x 10-6 m. How far from the central bright
band do the first and second order dark bands
appear if the screen is 3.0 meters away from
the slit? Assume 560 nm light.
Period
Frequency
Ideal Springs
What makes springs ideal?
Periodic Motion
Definition:
Hooke’s Law
Equation:
What are mechanical devices that
undergo periodic motion called?
Period of a spring
Equation:
Simple Harmonic Motion
Definition:
Sample Problem
Calculate the period of a 300-g mass
attached to an ideal spring with a force
constant of 25 N/m.
Simple Harmonic Oscillators
Definition:
Examples:
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Bertrand
Sample Problem
A 300-g mass attached to a spring
undergoes simple harmonic motion with a
frequency of 25 Hz. What is the force
constant of the spring?
Sample problem
A spring of force constant k = 200 N/m is
attached to a 700-g mass oscillating
between x = 1.2 and x = 2.4 meters.
Where is the mass moving fastest, and
how fast is it moving at that location?
Sample Problem
An 80-g mass attached to a spring hung
vertically causes it to stretch 30 cm from
its unstretched position. If the mass is
set into oscillation on the end of the
spring, what will be the period?
Sample problem
A spring of force constant k = 200 N/m is
attached to a 700-g mass oscillating
between x = 1.2 and x = 2.4 meters. What
is the speed of the mass when it is at the
1.5 meter point?
Sample Problem
You wish to double the force constant of
a spring. You
A. Double its length by connecting it to
another one just like it.
B. Cut it in half.
C. Add twice as much mass.
D. Take half of the mass off.
Sample problem
A 2.0-kg mass attached to a spring
oscillates with an amplitude of 12.0 cm
and a frequency of 3.0 Hz. What is its
total energy?
Conservation of Energy
Where does maximum kinetic energy
occur?
Where does maximum potential energy
occur?
Where does maximum total energy occur?
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Pendulums
When is a pendulum a good approximation
of a simple harmonic oscillator?
Pendulum Forces
Equation:
Sample problem
Predict the period of a pendulum
consisting of a 500 gram mass attached
to a 2.5-m long string.
Sample problem
Suppose you notice that a 5-kg weight
tied to a string swings back and forth 5
times in 20 seconds. How long is the
string?
Sample problem
The period of a pendulum is observed to
be T. Suppose you want to make the
period 2T. What do you do to the
pendulum?
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A hollow tube of adjustable length, open at both
ends, is held in midair as shown. A tuning fork
with frequency 320 Hz vibrates at one end of the
tube and causes the air in the tube to vibrate at its
fundamental frequency. The speed of sound in
the laboratory is 343 m/s.
a) Draw the fundamental standing wave inside
the tube.
b) Determine the length of the tube that will
support this fundamental frequency.
c) Determine the next higher frequency at which
this air column would resonate. Draw the
standing wave represented by this frequency.
(Do not change the length of the tube.)
The tube is now submerged in a large, graduated
cylinder filled with water. The tube is slowly
raised out of the water and the same tuning fork,
vibrating with frequency 320 Hz, is held a fixed
distance from the top of the tube.
d) Determine the height h of the tube above the
water when the air column resonates for the first
time.
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S116B4 (15 points) Your teacher gives you a slide
with two closely spaced slits on it. She also gives
you a laser with a wavelength λ = 632 nm. The
laboratory task that you are assigned asks you to
determine the spacing between the slits. These slits
are so close together that you cannot measure their
spacing with a typical measuring device.
a. From the list below, select the additional
equipment you will need to do your
experiment by checking the line next to each
item.
_____Meterstick
_____Ruler
_____Tape measure
_____Light-intensity meter
_____Large screen
_____Paper
_____Slide holder
_____Stopwatch
d. Outline the procedure that you would use to
make the needed measurements, including how
you would use each piece of the additional
equipment you checked in a.
e.
Using equations, show explicitly how you
would use your measurements to calculate
the slit spacing.
b. Draw a labeled diagram of the experimental
setup that you would use. On the diagram,
use symbols to identify carefully what
measurements you will need to make.
c.
On the axes below, sketch a graph of
intensity versus position that would be
produced by your setup, assuming that the
slits are very narrow compared to their
separation.
46
A172 B2. A block of mass M is resting on a
horizontal, frictionless table and is attached as
shown above to a relaxed spring of spring
constant k. A second block of mass 2M and
initial speed vo collides with and sticks to the
first block Develop expressions for the
following quantities in terms of M, k, and vo
a. v, the speed of the blocks immediately after
impact
b. x, the maximum distance the spring is
compressed
c. T, the period of the subsequent simple
harmonic motion
47
(e)
Calculate the frequency of oscillation of
the 8.0 kg block (NEW).
S117 B1 (15 points)
An ideal spring of unstretched length 0.20 m is
placed horizontally on a frictionless table as
shown above. One end of the spring is fixed and
the other end is attached to a block of mass M =
8.0 kg. The 8.0 kg block is also attached to a
massless string that passes over a small
frictionless pulley. A block of mass m = 4.0 kg
hangs from the other end of the string. When this
spring-and-blocks system is in equilibrium, the
length of the spring is 0.25 m and the 4.0 kg
block is 0.70 m above the floor.
(a)
(f)
Calculate the maximum speed attained
by the 8.0 kg block (NEW).
On the figures below, draw free-body
diagrams showing and labeling the
forces on each block when the system
is in equilibrium.
(b)
Calculate the tension in the string
(REVIEW).
(c)
Calculate the force constant of the
spring (REVIEW).
The string is now cut at point P.
(d)
Calculate the time taken by the 4.0 kg
block to hit the floor (REVIEW)..
48