Class 090914
Synopsis of what you should know to date, and the questions you need to get used to asking yourself:
At this point in your course everything you do is done in terms of the concept of an interval, using a few definitions (acceptable abbreviations for these definitions are included)
applied using a few principles
expressed in terms of some basic mathematics
When considering an interval you should ask the following questions:
If we represent the known information on a velocity vs. clock time trapezoid, that trapezoid has two altitudes, a width or base, a slope and an area. If we know any three of these quantities, we can figure out the rest.
If we consider the v0, vf, `dt trapezoid we get the equations of uniformly accelerated motion. If we consider the definitions of average velocity and average acceleration, we can verbally and/or algebraically work out the equations of uniformly accelerated motion. These equations allow us, if we know three of the quantities v0, vf, `dt, a and `ds, to find the other two.
At this stage of the course, a few students completely understand these representations, and a few more are well on their way to doing so. The majority of the class could, however, benefit from checking their work on any problem involving motion against this list. With practice the puzzle of uniformly accelerated motion will fit together. When it does, you will have a good foundation for the rest of the course.
You will be asked this week to apply these ideas to a series of problems and experiments, while we also continue to work with the idea of forces.
Brief Experiments
Rotating Strap
Rotate a strap on top of a die and see through how many degrees it rotates (within +- 10 degrees, which you can easily estimate) and how long it takes to coast to rest (accurate to within 1/4 of a cycle of the fastest pendulum you can reasonably observe).
Do this for at least five trials, with as great a range as possible of rotational displacements.
Report your raw data (including data sufficient to determine the length of your pendulum in centimeters) &&&&
Work out the average rate of change of rotational position (in degrees) with respect to clock time (in half-cycles of your pendulum). &&&&
UNNECESSARY ANSWER: On average, the system had an
average rate of acceleration of (40+23.1+21.3+31.7+20+22)/6= 26.4 degrees/half
cycle
Your preceding calculations are average accelerations.
Your last calculation was not requested and while harmless, you should
understand why it was unnecessary.
The reason is there is no point in averaging the average accelerations for a
series of different time intervals.
Atwood machine
Your instructor will operate the apparatus and tell you the displacement of the system, and the number of excess paperclips. You time it for each trial. The displacement of the system is 80 cm from start to stop.
Report your raw data (including data sufficient to determine the length of your pendulum in centimeters) &&&&
Work out the average rate of change of position (in cm) with respect to clock time (in half-cycles of your pendulum). &&&&
Ball down two ramps
Set up a two-ramp system, the first with a 'two-quarter' slope and the second with a 'one-domino' slope.
Time the system from release at the start of the first ramp to the end of the first ramp, determining the time interval as accurately as possible, using synchronization between your pendulum and the initial and final events for each interval.
Do the same for the interval from release at the start of the first ramp to the end of the second ramp.
Report your raw data (including data sufficient to determine the length of your pendulum in centimeters) &&&&
Good report:
Attempting to time the ball at the end of the first ramp as close as possible to the pendulum reaching equilibrium:
20 cm pendulum had 6 half cycles, not at equilibrium
25 cm pendulum had 5.5 half cycles, yes for equilibrium
Attemping to time the ball at the end of the second ramp as close as possible to the pendulum reaching equilibrium:
20 cm pendulum had 9 half cycles, not at equilibrium
25 cm pendulum had 9 half cycles, not at equilibrium
30 cm pendulum had 8 half cycles, not at equilibrium
15 cm pendulum had 10.5 half cycles, yes for equilibrium&&&&
Work out the average rate of change of position (in cm) with respect to clock time (in seconds) for the motion on each ramp. &&&&
Trial 1: rocAve= 12cm/.94 sec= 12.76 cm/s
Trial 2: rocAve=24cm/.8 sec= 30 cm/s
<h3>.94 s and .8 s are periods of the pendulum, not time intervals for motion down the ramp.
You know the period of the pendulum and the number of half-cycles for each ramp. So you can figure out the time it takes for that number of half-cycles, and that's the time down the ramp.</h3>17 cm/2s=8.5 cm/s
<h3>the ball on the ramp doesn't move 17 cm; it moves the length of the ramp
17 cm is the length of the pendulum, which determines the period of the pendulum but has nothing to do with how far the ball moves</h3>Work out the average rate of change of velocity (in cm/s) with respect to clock time (in seconds) for the motion on each ramp. &&&&
Hotwheels car
The hotwheels car will be passed along from one group to the next. Make at least one good observation of the displacement and time required in both the north and south directions.
Report raw data: &&&&
Indicate your choice of north or south as the positive direction, and stick with this choice for the rest of the analysis of this experiment: &&&&
Find acceleration for both trials: &&&&
Dropped object timed using pendulum
Drop an object to the floor at the same instant you release a pendulum whose equlibrium position is the wall.
Adjust the length of the pendulum and/or the height of the object until the pendulum reaches equlibrium at the same instant the ball reaches the floor.
Report your raw data, including pendulum length and distance to floor (including distance units): &&&&
Figure out the acceleration of the falling object in units of distance (using whatever distance unit you specified above) and clock time (measured in number of half-cycles): &&&&
Opposing springs
Repeat the opposing-rubber-band experiment using springs.
Report your raw data: &&&&
Report the average slopes between the points on your graph: &&&&
If you were to repeat the experiment, using three of the 'stretchier' springs instead of just one, with all three stretched between the same pair of paper clips, what do you think would be the slope of your graph? &&&&
terminology note: for future reference we will use the term 'parallel combination' to describe the three rubber bands in this question
If you were to repeat the experiment using three of the 'stretchier' springs (all identical to the first), this time forming a 'chain' of springs and paper clips, what do you think would be the slope of your graph? There are different ways of interpreting this question; as long as your answer applies to a 'chain', as described, and as long as you clearly describe what is being graphed, your answer will be acceptable (this of course doesn't imply that it will be correct): &&&&
terminology note: for future reference we will use the term 'series combination' to describe the three rubber bands in this question
We haven't yet defined force, energy and power, so you aren't yet expected to come up with rigorously correct answers to these questions. Just answer based on your current notions of what each of these terms means:
If each of the 'stretchier' springs starts at its equilibrium length and ends up stretched to a length 1 cm longer than its equilibrium length, then:
- Which do you think requires more force, the parallel or the series combination?
- Which do you think requires more energy, the parallel or the series combination?
- Which do you think requires more power, the parallel or the series combination?
Solving Equations of Motion
Solve the third equation of motion for a, explaining every step. &&&&
Solve the first equation of motion for `dt, explaining every step. &&&&
Solve the fourth equation of motion for `ds, explaining every step. &&&&
Solve the second equation of motion for v0, explaining every step. &&&&
Units calculations with symbolic expressions
Using SI units (meters and seconds) find the units of each of the following quantities, explaining every step of the algebra of the units:
a * `dt &&&&
1/2 a t^2 &&&&
(vf - v0) / `dt &&&&
2 a `ds &&&&
Identifying initial and final events and kinematic quantities
* Exercise 1: A ball is released from rest on a ramp of length 4 meters, and is timed from the instant it is released to the instant it reaches the end of the ramp. It requires 2 seconds to reach the end of the ramp.
What are the events that define the beginning and the end of the interval? &&&&
Write down on your paper the symbols v0, vf, a, `dt, `ds.
From the given information you know the values of three of the five quantities. What are the known quantities? &&&&
On your paper circle the symbols for the three quantities you know.
Now write down all four equations, and circle the symbols for the three quantities you know.
Write down an equation which includes all three symbols, and circle these symbols in the equation. Which equation did you write down, and which symbol was not circled? &&&&
Solve this equation for the non-circled variable and describe the steps necessary to do so. If your algebra is rusty you might find this challenging, but as before make your best attempt. &&&&
Having solved the equation as best you can, substitute the values of the three known quantities into that equation. Then simplify your expression to get the value of the unknown quantity. Again, do your best. &&&&
* Exercise 2: A ball is dropped from rest and falls 2 meters to the floor, accelerating at 10 m/s^2 during its fall.
What are the events that define the beginning and the end of the interval? &&&&
Write down on your paper the symbols v0, vf, a, `dt, `ds.
From the given information you know the values of three of the five quantities. What are the known quantities? &&&&
On your paper circle the symbols for the three quantities you know.
Now write down all four equations, and circle the symbols for the three quantities you know.
Write down the one equation which includes all three symbols, and circle these symbols in the equation. Which equation did you write down, and which symbol was not circled? &&&&
There are two equations which each contain three of the five symbols. Write down the other equation and circle the three known symbols in the equation. Which equation did you write down, and which symbol was not circled? &&&&
One of your equations has `dt as the 'uncircled' variable. You want to avoid that situation (though if you're ambitious you may give it a try). Solve the other equation for its non-circled variable (which should be vf) and describe the steps necessary to do so. If your algebra is rusty you might find this challenging, but as before make your best attempt. &&&&
Having solved the equation as best you can, substitute the values of the three known quantities into that equation. Then simplify your expression to get the value of the unknown quantity. Again, do your best. &&&&
Additional Exercises
* Exercise 3: A pendulum completes 90 cycles in a minute. A domino is 5 cm long.
There are four questions, with increasing difficulty. Based on typical performance of classes at this stage of the course, it is expected that most students will figure out the first one, while most students won't figure out the last (your instructor will of course be happy if the latter is an underestimate).
Here are the questions:
Homework:
Your label for this assignment:
ic_class_090914
Copy and paste this label into the form.
Report your results from today's class using the Submit Work Form. Answer the questions posed above.
Synopsis of what you should know to date, and the questions you need to get
used to asking yourself:vvvv
At this point in your course everything you do is done in terms of the concept
of an interval, using a few definitions
(acceptable abbreviations for these definitions are included)
• the definition of average rate of change (abbreviation: rocDef)
the change of A with respect to B
• the definition of average velocity (abbreviation: vAveDef)
the average rate of change of position with respect to clock time.
• the definition of average acceleration (abbreviation: aAveDef)
The average rate of change in velocity with respect to clock time.
• the definition of a graph trapezoid (abbreviation: trapDef)
applied using a few principles
• the principle that all quantities with units must always be expressed in terms
of units (abbreviation: unitsPrin)
• the principle that the change of a quantity on an interval is found by
subtracting its initial value on that interval
from its final value on that interval (abbreviation: changePrin)
expressed in terms of some basic mathematics
• basic arithmetic (including the arithmetic of fractions, and especially
multiplication and division of fractions)
• the basic rules of algebra (rudimentary factoring (mostly of monomials),
adding same quantity to both sides of
an equation, multiplying both sides by same quantity)
• very basic geometry, especially the geometry of a trapezoid (average altitude
at midpoint, average altitude
average of initial and final altitudes, equal-area rectangle, slope of a line
segment, area of a rectangle)
When considering an interval you should ask the following questions:
• What events define the beginning and end of the interval?
• What quantities are known at the beginning and end of the interval?
• Do we know the change in any quantity from the beginning to the end of the
interval?
• Which of the known quantities are rates of change, and if any are, what is the
definition of each rate of
change?
If we represent the known information on a velocity vs. clock time trapezoid,
that trapezoid has two altitudes, a width or
base, a slope and an area. If we know any three of these quantities, we can
figure out the rest.
• What are the units of each of these quantities?
• Do we know either, or both, of the quantities given by the 'graph altitudes'
of the trapezoid?
• Do we know the quantity given by the slope of the trapezoid?
• Do we know the quantity given by the width, base or 'run' of the trapezoid
(all three words refer to the same
quantity)?
• Do we know the quantity given by the altitude of the equal-area rectangle (the
same as the quantity
represented by the average altitude of the trapezoid)?
• In summary, do we know three of the five quantities, and if so how do we find
the other two?
If we consider the v0, vf, `dt trapezoid we get the equations of uniformly
accelerated motion. If we consider the
definitions of average velocity and average acceleration, we can verbally and/or
algebraically work out the equations of
uniformly accelerated motion. These equations allow us, if we know three of the
quantities v0, vf, `dt, a and `ds, to find
the other two.
• Of the five quantities v0, vf, `dt, a and `ds, which do we know?
• Which of the four equations of uniformly accelerated motion include three of
these five quantities (depending
on which three quantities we know, there might be one or two equations that
include all three)?
• For every equation which includes three of the five quantities, there is a
single unknown quantity. For each
such equation, what is that quantity?
• Using basic Algebra I, solve each such equation for the unknown quantity (you
may prefer to avoid solving
the third equation for `dt, since that equation is quadratic in `dt and the
solution might at this stage be confusing).
• Substitute your known values into the solved expression (including units with
every quantity) and simplify (this
includes the expressions for the units).
At this stage of the course, a few students completely understand these
representations, and a few more are well on their
way to doing so. The majority of the class could, however, benefit from checking
their work on any problem involving
motion against this list. With practice the puzzle of uniformly accelerated
motion will fit together. When it does, you will
have a good foundation for the rest of the course.
You will be asked this week to apply these ideas to a series of problems and
experiments, while we also continue to
work with the idea of forces.
Brief Experiments
Rotating Strap
Rotate a strap on top of a die and see through how many degrees it rotates
(within +- 10 degrees, which you can easily
estimate) and how long it takes to coast to rest (accurate to within 1/4 of a
cycle of the fastest pendulum you can
reasonably observe).
Do this for at least five trials, with as great a range as possible of
rotational displacements.
Report your raw data (including data sufficient to determine the length of your
pendulum in centimeters) &&&&
Strap rotation (in deg.) Pendulum count (in 1/2 cycles) (1/2 length of the book)
450 6
225 4
405 5
550 8
225 4
Work out the average rate of change of rotational position (in degrees) with
respect to clock time (in half-cycles of your
pendulum). &&&&
Ave rate of rotational position = 550 – 225 = 325 clock time is over 4 half
cycle interval 325 deg/4 half cyc 31 ¼
deg/half cycle
Atwood machine
Your instructor will operate the apparatus and tell you the displacement of the
system, and the number of excess
paperclips. You time it for each trial. The displacement of the system is 80 cm
from start to stop.
Report your raw data (including data sufficient to determine the length of your
pendulum in centimeters) &&&&
Pendulum count (1/2 cycles) (length of phy book)
14
14
9
Work out the average rate of change of position (in cm) with respect to clock
time (in half-cycles of your pendulum).
&&&&
Change in position is 80 cm clock time is 14 – 9 = 5 ½ cyc 80/ 5 = 16 cm/half
cycle
Ball down two ramps
Set up a two-ramp system, the first with a 'two-quarter' slope and the second
with a 'one-domino' slope.
Time the system from release at the start of the first ramp to the end of the
first ramp, determining the time interval as
accurately as possible, using synchronization between your pendulum and the
initial and final events for each interval.
Do the same for the interval from release at the start of the first ramp to the
end of the second ramp.
Report your raw data (including data sufficient to determine the length of your
pendulum in centimeters) &&&&
Ramp pendulum count (length varies) seconds
1 3 ½, ½ cyc (22 cm) .938
2 7 ½, ½ cyc (16 cm) .8
Find the time spent on each ramp, seconds, using the approximate formula
• period = .2 sqrt(length).
&&&&
.2 sqrt(22)=.2 (4.69) = .938 sec
.2 sqrt(16)= .2 (4) = .8 sec
<h3>These are the periods of the pendulum. If I read your data correctly, it
takes 3.5 half-cycles of one pendulum to
travel down one ramp and 7.5 half cycles of another pendulum to travel down both
ramps.
To .938 s and .8 s are not time interval associated with this motion, but rather
period of the pendulums used to measure
the motion. </h3>
Work out the average rate of change of position (in cm) with respect to clock
time (in seconds) for the motion on each
ramp. &&&&
22cm – 16cm = 6 cm .938sec - .8sec = .138 sec 6 cm / .138 sec. = 43.47 cm/s
<h3>These are the lengths of the pendulum. Nothing is moving along the
pendulum.</h3>
Work out the average rate of change of velocity (in cm/s) with respect to clock
time (in seconds) for the motion on each
ramp. &&&&
43.47 cm/s / .138 s = 315.06 cm/s ^2
Hotwheels car
The hotwheels car will be passed along from one group to the next. Make at least
one good observation of the di
splacement and time required in both the north and south directions.
Report raw data: &&&&
N to S S to N
3 half cycles 4 half cycles (length of pendulum is ½ the book)
22.5 cm 25 cm
Indicate your choice of north or south as the positive direction, and stick with
this choice for the rest of the analysis of this
experiment: &&&&
North was toward the snack bar.
Find acceleration for both trials: &&&&
N to S
Rate of change position wrt clock time = 22.5 cm/ 3 half cyc = 7.3 cm/half cyc =
Vel
Rate of change of vel wrt clock time = 7.3 cm/half cyc / 3 half cyc = 2.43 cm/
half cyc^2
S to N
Rate of change position wrt clock time= 25 cm/ 4 half cyc = 6 ¼ cm/half cyc =
Vel
Rate of change of vel wrt clock time = 6 ¼ cm/half cyc / 4 half cyc = 1 5/8
cm/half cyc^2
<h3>Good, except that you used vAve / `dt rather than `dv / `dt to calculate
accelerations.</h3>
Dropped object timed using pendulum
Drop an object to the floor at the same instant you release a pendulum whose
equlibrium position is the wall.
Adjust the length of the pendulum and/or the height of the object until the
pendulum reaches equlibrium at the same instant
the ball reaches the floor.
Report your raw data, including pendulum length and distance to floor (including
distance units): &&&&
Distance the dime was dropped = 40 cm
Pendulum = 27 cm
Pendulum and dime from wall = 14 cm
Figure out the acceleration of the falling object in units of distance (using
whatever distance unit you specified above) and
clock time (measured in number of half-cycles): &&&&
40 cm / 1/2 half cycle, vel = 80 cm/half cycle
80 cm/halfcyc / ½ halfcycle = 160 cm/halfcyc^2
Opposing springs
Repeat the opposing-rubber-band experiment using springs.
Report your raw data: &&&&
Small Large
0 cm to 10 cm 13 cm to 35 cm
0 cm to 7 ½ cm 12 cm to 28 cm
0 cm to 5 ½ cm 8 ½ cm to 22 ½ cm
Report the average slopes between the points on your graph: &&&&
Change in y over change in x 22 cm/10 cm = 11/5
16cm/ 7.5cm= 16/7.5
14cm/5.5cm= 14/5.5
<h3>You appear to be dividing y values by x values, rather than dividing change
in y value by change in x value.
Your graph would consist of three points, with two line segments between them.
So there would be two slopes, not
three.</h3>
If you were to repeat the experiment, using three of the 'stretchier' springs
instead of just one, with all three stretched
between the same pair of paper clips, what do you think would be the slope of
your graph? &&&&
A lot closer to 1 probably less than one or even negative
terminology note: for future reference we will use the term 'parallel
combination' to describe the three rubber bands in this
question
If you were to repeat the experiment using three of the 'stretchier' springs
(all identical to the first), this time forming a
'chain' of springs and paper clips, what do you think would be the slope of your
graph? There are different ways of
interpreting this question; as long as your answer applies to a 'chain', as
described, and as long as you clearly describe
what is being graphed, your answer will be acceptable (this of course doesn't
imply that it will be correct): &&&&
The slope would be 1 give or take a little
terminology note: for future reference we will use the term 'series combination'
to describe the three rubber bands in this
question
We haven't yet defined force, energy and power, so you aren't yet expected to
come up with rigorously correct answers
to these questions. Just answer based on your current notions of what each of
these terms means:
If each of the 'stretchier' springs starts at its equilibrium length and ends up
stretched to a length 1 cm longer than its
equilibrium length, then:
• Which do you think requires more force, the parallel or the series
combination?
series
• Which do you think requires more energy, the parallel or the series
combination?
parallel
• Which do you think requires more power, the parallel or the series
combination?
parallel
Solving Equations of Motion
Solve the third equation of motion for a, explaining every step. &&&&
`ds = v0 `dt + .5 a `dt^2
‘ds – (v0 ‘dt) = .5a’dt^2 subtract v0 `dt from both sides
(‘ds – (v0’dt))/ .5 ‘dt^2 = a divide by .5 ‘dt^2 leaving only the a quanity
Solve the first equation of motion for `dt, explaining every step. &&&&
`ds = (vf + v0) / 2 * `dt
‘ds / ((vf + v0) / 2) = ‘dt divide by (vf + v0) / 2 leaving only the ‘dt
Solve the fourth equation of motion for `ds, explaining every step. &&&&
vf^2 = v0^2 + 2 a `ds
vf^2 - v0^2 = 2a ‘ds subtract v0^2 from both sides
vf^2 - v0^2 / 2a = ‘ds divide by 2a leaving ‘ds
Solve the second equation of motion for v0, explaining every step. &&&&
a_ave = (vf - v0) / `dt
a * ‘dt = (vf – vo) multiply by ‘dt
a* ‘dt – vf = -v0 subtract vf from both sides
-( a* ‘dt – vf) = v0 Multiply by -1 to get a positive answer
Units calculations with symbolic expressions
Using SI units (meters and seconds) find the units of each of the following
quantities, explaining every step of the algebra
of the units:
a * `dt &&&&
here we are multiplying a and ‘dt, so a(‘dt) a is m/sec^2 ‘dt is sec so the
answer is m/sec
1/2 a t^2 &&&&
½ does not have units, a = m/sec^2, t= sec m/sec^2 * sec^2 = m
(vf - v0) / `dt &&&&
Vel has the same units = m/sec, ‘dt = sec m/sec/sec =m/sec^2
2 a `ds &&&&
a = m/sec^2, ds=m, m/sec^2 * m = m^2/ sec^2
Identifying initial and final events and kinematic quantities
* Exercise 1: A ball is released from rest on a ramp of length 4 meters, and is
timed from the instant it is released to the
instant it reaches the end of the ramp. It requires 2 seconds to reach the end
of the ramp.
What are the events that define the beginning and the end of the interval? &&&&
The release of the ball is the start, when it reaches the end of the ramp is the
end.
Write down on your paper the symbols v0, vf, a, `dt, `ds.
From the given information you know the values of three of the five quantities.
What are the known quantities? &&&&
‘ds, v0, ‘dt
On your paper circle the symbols for the three quantities you know.
Now write down all four equations, and circle the symbols for the three
quantities you know.
Write down an equation which includes all three symbols, and circle these
symbols in the equation. Which equation did
you write down, and which symbol was not circled? &&&&
`ds = (vf + v0) / 2 * `dt vf is not circled
Solve this equation for the non-circled variable and describe the steps
necessary to do so. If your algebra is rusty you
might find this challenging, but as before make your best attempt. &&&&
`ds = (vf + v0) / 2 * `dt
‘ds/‘dt = (vf + v0) / 2 Divide by ‘dt
2(‘ds/‘dt) = (vf + v0) Mult by 2
2(‘ds/‘dt) – v0 = vf Subt by v0
Having solved the equation as best you can, substitute the values of the three
known quantities into that equation. Then
simplify your expression to get the value of the unknown quantity. Again, do
your best. &&&&
2(4m/2sec) – 0 = vf
4 m/sec = vf
* Exercise 2: A ball is dropped from rest and falls 2 meters to the floor,
accelerating at 10 m/s^2 during its fall.
What are the events that define the beginning and the end of the interval? &&&&
Beginning dropping of the ball, ending when it hits the floor
Write down on your paper the symbols v0, vf, a, `dt, `ds.
From the given information you know the values of three of the five quantities.
What are the known quantities? &&&&
v0, ‘ds, a
On your paper circle the symbols for the three quantities you know.
Now write down all four equations, and circle the symbols for the three
quantities you know.
Write down the one equation which includes all three symbols, and circle these
symbols in the equation. Which equation
did you write down, and which symbol was not circled? &&&&
vf^2 = v0^2 + 2 a `ds vf
There are two equations which each contain three of the five symbols. Write down
the other equation and circle the three
known symbols in the equation. Which equation did you write down, and which
symbol was not circled? &&&&
`ds = v0 `dt + .5 a `dt^2 ‘dt
One of your equations has `dt as the 'uncircled' variable. You want to avoid
that situation (though if you're ambitious you
may give it a try). Solve the other equation for its non-circled variable (which
should be vf) and describe the steps
necessary to do so. If your algebra is rusty you might find this challenging,
but as before make your best attempt.
&&&&
vf^2 = v0^2 + 2 a `ds
vf = sqrt (v0^2 + 2 a `ds)
Having solved the equation as best you can, substitute the values of the three
known quantities into that equation. Then
simplify your expression to get the value of the unknown quantity. Again, do
your best. &&&&
vf = sqrt (v0^2 + 2 a `ds)
vf = sqrt (0 ^2 + 2(10 m/sec^2) (2 m)
vf = 40 m^2/sec^2
<h3>Good up to here, but
vf = sqrt(40 m^2/sec^2).</h3>
Additional Exercises
* Exercise 3: A pendulum completes 90 cycles in a minute. A domino is 5 cm long.
There are four questions, with increasing difficulty. Based on typical
performance of classes at this stage of the course, it is
expected that most students will figure out the first one, while most students
won't figure out the last (your instructor will of
course be happy if the latter is an underestimate).
Here are the questions:
• If an object travels through a displacement of 7 dominoes in 5 half-cycles,
then what is its average velocity in
cm/s? &&&&
Change in position = 35 cm, clock time= 180/ 60 * 5/x, x= 5/3 sec
35 cm / 5/3 sec = 21 cm/sec
• If that object started from rest and accelerated uniformly, what was its
average acceleration in cm/s^2?
&&&&
21 cm/sec / 5/3 sec = 63/5 cm/ sec^2
<h3>`dv / `dt, not vAve / `dt</h3>
• From observations, the average velocity of the ball is estimated to be 9
dominoes per half-cycle. What is its
average velocity in cm/sec? &&&&
Change in position = 45 cm, change in clock time = 1/3 sec
45 cm/ 1/3sec =135 cm/sec
• Its acceleration is observed to be 5 dominoes / (half-cycle)^2. What is its
acceleration in cm/s^2? &&&&
25cm/1/3 sec^2 = 75cm/sec^2
<h3>The change in clock time would be squared. Otherwise very good.</h3>
`gr54