Physics Study Guide
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Transcript of Physics Study Guide
7/16/2019 Physics Study Guide
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Kinematics: the branch of mechanics that
describes the motion of objects without
necessarily discussing what causes the motion.
Distance
Definition:
SI Unit:
Displacement (∆x)
Definition:
Equation:
SI Unit:
Question: Does the odometer in your car
measure distance or 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) Find the distance and displacement of player
A.
b) Repeat for player B.
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|
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?
b) What is the displacement of the particle?
Practice Problem: You are driving a car on a
circular track of diameter 40 meters. After youhave driven around 2 ½ times, how far have you
driven, and what is your displacement?
Average SpeedDefinition:
Equation:
SI unit:
1
A B5 m 2 m
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Average Velocity
Definition:
Equation:
SI unit:
Practice Problem: How long will it take thesound 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.
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
What physical feature of the graph gives the
constant velocity from A to B?
Graphical Problem: Determine the average
velocity from the graph.
Graphical Problem: Determine the average
velocity between 1 and 4 seconds.
5/30/2013 2 Bertrand/Perkins
t
x
A
B
x (m)
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Instantaneous Velocity
Definition:
Practice Problem: Determine the instantaneous
velocity at 1.0 second.
Acceleration
Definition:
What does the sign of the acceleration signify?
What types of acceleration are there?
Questions
If acceleration is zero, what does this mean about
the motion of an object?
Is it possible for a racecar circling a track to have
zero acceleration?
Uniform (Constant) Acceleration
Equation:
SI unit:
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: 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?
Graphical Problem
What physical feature of the graph gives the
acceleration?
5/30/2013 3 Bertrand/Perkins
t
vA
B
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5/30/2013 4 Bertrand/Perkins
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Practice Problem: Determine the acceleration
from the graph.
Determine the displacement of the object from 0
to 4.0 seconds (using the graph above)
How would you describe the motion of this
particle?
Describe the motion
Draw Graphs for Stationary Particles
Draw Graphs for Constant Non-zero Velocity
Draw Graphs for Constant Non-zero Acceleration
Kinematic Equations
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?
5/30/2013 5 Bertrand/Perkins
t
x
t
v
t
a
t
x
t
v
t
a
t
x
t
v
t
a
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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 whileleaving ¼ of the runway remaining as a safety
margin?
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?
b) How fast would they be going if they
accelerated for an additional second at this rate?
c) Sketch approximate x-vs-t, v-vs-t and a-vs-t
graphs for this ride.
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.
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 thestopping distance, what is your speed?
c) How long does it take you to stop?
d) Draw x vs t, v vs t, and a vs t graphs for this.
Free Fall
Definition:
Acceleration due to Gravity:
5/30/2013 6 Bertrand/Perkins
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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?
b) what is the ball’s speed and velocity when it
strikes the ground at the base of the cliff?
c) sketch approximate x-vs-t, v-vs-t, a-vs-t
graphs for this situation.
Practice Problem: You throw a ball straightupward 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?
b) How high does the ball go?
c) What is the ball’s velocity when you catch it?
d) Sketch approximate x-vs-t, v-vs-t, a-vs-t
graphs for this situation.
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.
Acceleration is 9.8 m/s2
and directed
DOWN the entire time the object is 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
5.04.03.02.01.00t(s)
57.536.820.79.22.30x(m)
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 thecurve to determine the instantaneous velocity at all three
points.c) On a separate graph, draw a velocity vs time graphusing the instantaneous velocities you obtained in thestep above.d)From your velocity vs time graph, determine theacceleration of the car.
5/30/2013 7 Bertrand/Perkins
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Homework problem: S117-B2
Work this problem on a separate sheet of graph paper to turn in.
A world-class runner can complete a 100 m dash in about 10 s. Past studies have shownthat runners in such a race accelerate uniformly for a time t u and then run at constant
speed for the remainder of the race. A world-class runner is visiting your physics class.
You are to develop a procedure that will allow you to determine the uniform accelerationau and an approximate value of t u for the runner in a 100 m dash. By necessity your experiment will be done on a straight track and include your whole class of eleven
students.
(a) Indicate which of the following pieces of equipment, other than the runner and the
track, that your class will need to do the experiment. List the equipment you use
in your experiment on your graph paper.
_____ Stopwatches _____Tape measures _____Rulers _____Masking tape
_____Metersticks _____Starter’s pistol_____String _____Chalk
(b) Outline the procedure that you would use to determine au and t u , including a
labeled diagram of the experimental setup. Use symbols to identify carefully what
measurements you would make and include in your procedure how you would useeach piece of the equipment you checked in part (a).
(c) Outline the process of data analysis, including how you will identify the portionof the race that has uniform acceleration, and how you would calculate the
uniform acceleration. NOTE: TO EARN FULL CREDIT FOR THIS PART,
YOU MUST COME UP WITH A GRAPHICAL SOLUTION!
5/30/2013 8 Bertrand
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Homework problemCase 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.
Case 2: Ball B is projected vertically
upward from the foot of the cliff with an
initial speed of v o . Derive an expression
for the maximum height y max reached by
the ball.
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 v o from the foot of the cliff such
that Ball B will collide with Ball A. Derive
an expression for the amount of time thatwill elapse before they collide.
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 v o from the foot of the cliff
directly beneath ball A. Derive an
expression for how high above the groundthey will collide.
5/30/2013 9 Bertrand
B
h
vo
A
h