Download Energy AP 1 Packet Answers

Name'
Unit 5 Energy
Big Idea I: Objects and systems have properties such as mass and charge. Systems may have internal structure.
Essential Knowledge
structure.
I Proficient
I.A.I: A system is an object or a collection of objects. Objects are treated as having no internal
a. A collection ofpatticles in which internal interactions change little or not at all, or in which changes in these
interactions are irrelevant to the Question addressed, can be treated as an obiect.
Bi~ Idea 4: Inleractions between svstems can result in chan~es in those svstems.
Learning Objective (4.C.1.I):
Essential Knowledge 4.C.1: The
The student is able to calculate the total energy ofa system and justi!)' the
energy of a system includes its
kinetic energy. potential energy, and
microscopic internal energy.
Examples should include
mathematical routines used in the calculation of component types of energy within the
system whose sum is the total energy.
Learning
gravitational potential energy,
elastic potential energy, and kinetic
Objective
(4.C.1.2):
The student is able to predict changes in the total energy of a system due to changes in
position and speed of objects or frictional interactions within the system.
energy.
Essential Knowledge 4.C.2: Mechanical energy (the sum
Learning Objective (4.C.2.1):
The student is able to make predictions about the changes in
of kinetic and potential energy) is transferred into or out of
a system when an external force is exelted on a system such
the mechanical energy of a system when a component of an
that a component of the force is parallel to its displacement.
extemal force acts parallel or antiparallel to the direction of the
disolacement of the center of mass.
Learning Objective (4.C.2.2):
The student is able to apply the concepts of Conservation of
The process through which the energy is trans felTed is
called work.
a. If the force is constant during a given displacement, then
the work done is the product of the displacement and the
component of the force parallel or antiparallel to the
displacement.
b. Work (change in energy) can be found from the area
under a graph of the magnitude of the force component
parallel to the displacement versus displacement
Energy and the Work-Energy theorem to detennine
qualitatively and/or quantitatively
that work done on a two-
object system in linear Illation will change the kinetic energy
of the center of mass of the system, the potential energy of the
systems, and/or the internal energy of the system
Biu Idea 5: Chant!es that occur as a result of interactions are constrained by conservation laws.
Learning Objective (5.B.I.I):
Essential Knowledge 5.B.I:
The student is able to set up a representation or model showing that a single object can
-:Iassically, an object can only
only have kinetic energy and use information about that object to calculate its kinetic
Jtave kinetic energy since
potential energy requires an
interaction between two or more
enerqv.
objects.
The student is able to translate between a representation ofa single object, which can only
have kinetic energy, and a system that includes the object, wJlich may have both kinetic
and Dotential eneroies.
Learning
Objective (5.B.1.2):
internal structure can have potential energy.
Potential energy exists within a system if the
Learning Objective (5.B.3.1):
The student is able to describe and make qualitative and/or quantitative
predictions about evelyday examples of systems with internal potential
objects within that system interact with
ener~y.
Essential
Knowledge 5.8.3: A system with
conservative forces.
a. The work done by a conservative force is
Learning Objeetive (5.B.3.2):
The student is able to make quantitative calculations of the internal potential
ener<'.v of a svstem from a description or diaoram of that system.
independent of the path taken. The work
description is used for forces external to the
Learning Objective (5.B.3.3):
system. Potential energy is used when the
The student is able to apply mathematical reasoning to create a description
forces are intemai interactions between patts
of the internal potential energy ofa system from a description or diagram of
of the system.
the objects and interactions in that svstem.
Learning Objective (5.1l.4.1):
Essential Knowledge 5.B.4: The intemal energy of a system includes
The student is able to describe and make predictions
the kinetic energy of the objects that make up the system and the
about the internal energy of systems
potential energy of the configuration of the objects that make up the
system.
a. Since energy is constant in a closed system, changes in a system's
potential energy can result in changes to the system's kinetic energy.
b. The changes in potential and kinetic energies in a system may be
fUlther constrained by the construction of the system.
'.ssential Knowledge
.8.5: Energy can be
transferred by an
external force exerted on
an object or system that
Learning
Objective
--
(5.B.4.2):
The student is able to calculate changes in kinetic
energy and potential energy of a system, using
information from representations of that system.
Learning Objective (5.B.5.1):
The student is able to design an experiment and analyze data to exam ine llOW a force exelted on
an object or system does work on the object or svstem as it moves throuoh a distance
Learning Objective (5.B.5.2):
The student is able to desion an experiment and analyze ~raphical data in which intemretations of
1
Unit 5. Energy
Name:
moves the object or
system through a
distance; this energy
transfer is called work.
Energy transfer in
mechanical or electrical
systems may occur at
different rates. Power is
defined as the rate of
energy transfer into, out
of, or within a system.
Essential «nowledge
5.0.1: In a collision
between objects, linear
momentum is conserved.
In an elastic collision,
kinetic energy is the
a. In a closed system. the
linear momentum is
constant throughout the
collision.
kinetic energy after an
elastic collision is the
same as the kinetic
energy before the
collision.
done on an object or system from infonnation about a force exerted on the object or system
I
throuoh a distance.
Learning Objective (5.8.5.4):
I
The student is able to make claims about the interaction between a system and its environment in
which the environment exer1s a fored on the system, thus doing work 011 the system and changing
the energv of the svstem (kinetic enetgv plus potential enemv).
Learning Objective (5.B.5.5):
I
The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object
or system from information about a force excited on the object or system throue:ha distance.
Learning Objective (5.0.1.1):
I
The student is able to make qualitati~e predictions about natural phenomena based on
conservation of linear momentum and restoration of kinetic energy in elastic collisions
Learning Objective (5.0.1.2):
The student is able to apply the princIples of conservation of momentum and restoration of kinetic
I
same before and after.
b. In a closed system, the
the area under a force-distance curve are needed to detennine the work done on or by the object or
svstem.
I
Learning Objective (5.B.5.3):
I
The student is able to predict and calculate from graphical data the energy transfer to or work
energy to reconcile a situation that appears to be isolated and elastic, but in which data indicate
that linear momentum and kinetic energy are not the same after the interaction. by refining a
scientific question to identifY interactions that have not been considered. Students will be
expected to solve qualitatively and/or quantitatively for one-dimensional situations and only
qualitatively in two-dimensional situations.
I
Learning Objective (5.0.1.3):
I
The student is able to apply mathematical routines appropriately to problems involving elastic
collisions in one dimension andjustitY the selection of those mathematical routines based on
conservation of momentum and restor~tion of kinetic energy.
.
Learning Objective (5.0.1.4):
I
The student is able to design an experimental test of an application of the principle of the
conservation of linear momentum, predict an outcome of the experiment using the principle,
analyze data generated by that experiment whose uncertainties are expressed numerically, and
evaluate the match between the prediction and the outcome
Learning
Objective (5.0.1.5):
I
The student is able to classify a given collision situation as
elastic or inelastic. justi fy the selection' of conservation of linear momentum and restoration of
kinetic energy as the appropriate principles for analyzing an elastic collisioll. solve for missing
variables, and calculate their values.
Essential Knowledge
5.0.2: In a collision
between objects, linear
momentum is conserved.
In an inelastic collision,
kinetic energy is not the
same before and after the
collision.
a. In a closed system, the
linear momentum is
constant throughout the
collision.
b. in a closed system, the
kinetic energy after an
inelastic collision is
different from the kinetic
energy before the
collision.
I
Learning
Objective (5.0.2.1):
I
The student is able to qualitatively predict. in tenns of linear momentum and kinetic energy. how
the outcome of a collision between two' objects changes depending on whether the collision is
elastic or inelastic.
I
Learning Objective (5.0.2.2):
I
The student is able to plan data collection sU<llegies to test the
law ofconscrvation of momentum in a two-object collision that is elastic or inelastic and analyze
the resulting data graphically.
I
Learning
I
Objective (5.0.2.3):
The student is able to apply the conservation of linear momentum to a closed system of objects
involved in an inelastic collision to predict the change in kinetic encrgy.
Learning
Objective (5.0.2.4):
I
The student is able to analyze data that verifY conservation of momentum in collisions with and
without an extemal friction force.
I
Learning
Objective (5.0.2.5):
I
The student is able to classify a given collision situation as
elastic or inclastic. justify the selection
conservation of linear momentum as the appropriate
solution method for 3n inelastic collisiod, recognize that there is a common final velocity for the
colliding objects in the totally inelastic cttse, solve for missing variables, and calculate their
values.
I
of
2
Energy and Work Chapter Reading Assignment
Directions:
Read sections 10.2 starting on page 298 - 10.8 and 10.10 (skip rotational kinetic energy) in chapter 10.
As you read answer all Stop to Think questions (Check your answers on page 332) and work through all example
problems.
1.
Below is a list of what you need to take away from your reading.
Define/Know
a.
The six forms of energy
b.
Work
c.
Mechanical energy and its forms
d.
The SI unit for Work and Energy
e.
Kinetic energy: definition, symbol, units
f.
gravitational potential energy: definition, symbol, units
g.
elastic potential energy: definition, symbol, units
h.
what type of energy is generated
i.
Power: definition, the three equations to calculate, units
from friction
2. Explain:
a.
How energy is transferred
into or out of a system
b.
The law of conservation
of energy for an isolated system
c.
The law of conservation
of mechanical energy and what conditions must be met for mechanical energy to
be conserved
d.
What component
of force produces work and when work is positive, negative and zero.
e.
What happens to the energy of a system when positive work is done (see figure 10.7)
f.
What happens to the energy of a system when negative work is done (see conceptual example 10.2)
g.
The condition in which a force does no work and give some examples.
h.
Why the hikers in figure 10.19 have the same change in potential energy even though they took different
routes.
i.
Why, in example 10.6, conservation of energy is used to calculate speed at the bottom of the slide and
not kinematics.
3.
Be able to:
a.
calculate kinetic energy and potential energy
b.
calculate work in terms of force and distance
c.
calculate work by determining the change in mechanical energy of a system
d.
to identify the types of forces present at different locations/moment
e.
use conservation
of time in a problem
of mechanical energy to calculate speed of an object that starts at some initial height
(ex. be able to solve example 10.9)
3
Work and Energy Problems
1.
What are the two primary processes by which energy can be transferred
2.
Identify the energy transformations
negligible. (e.g. K --+U,--+ E'h)
from the environment
to a system?
in each of the following process, unless stated consider air resistance to be
a. A ball is dropped from atop a tall building
u.~-..f:b. A ball is dropped from atop a tall building (consider air resistance)
I
U~-¥--tt+h
c. A helicopter
rises from the ground at constant seed
bG\'v-ern
~
lAfj
d. An arrow is shot from a bow and stops in the ce ter of its target.
t -- S-t\-.
tA s -
e. A pole vaulter runs, plants his pole, and vaults up over the bar.
k --lAs --YU,
3.
I
Identify the energy transfers that occur in each of the following processes (e.g. W--+ K)
a. You pick up a book from the floor and place it oh a table.
W-Uj
b. You roll a bowling ball.
w - \<
4.
'An object experiences a force while undergOing the displacement shown. Is the work done
positive (+), negative (-), or zero (O)?
y
1
e '10
a.
b.
Sign of W "" _.... _~. ____
d.
F
S'Ign 0 fW-- _
_..
r
Sign ofW
e.
-
'4JY;:
d
,/
d
_------
...
F
Sign of W =
E7 .::'- q of)
.,..
Sign ofW ""
7-
f.
.0
Sign of W ""
4
Work and Energy Problems
5.
Each of the diagrams below shows a displacement vector for an objcct. Draw ami label a forcc
vector that will do work on the object with the sign indicated.
u.
\J
b.
..lo
c.
.. f"
II' > 0
d
-------
",'
-.-
-
.. .. -.
-
IV~O
IV < 0
[--_ ..
_---_ ..
I
6.
7.
A 0.2 kg plastic Calt and a 20 kg lead Calt both roll without friction on a horizontal surface.
Equal forces are used to push both carts forward a distance of~,
starting fTomrest. After
traveling 1 ro, is the kinetic energy of the plastic Calt greater than, less than, or equal to the
kinetic energy of the lead cart? Explain.
-
For each situation described below:
Drawa before and after diagram (like figures 10.8 and 10.12 in your textbook)
Identify ALLforces acting on the object
Determine if the work done by each of these forces is positive (+), negative (-), or zero (0).
Make a table beside the figure showing EVERYforce and the sign of its work.
a. An elevator mov~¥ward.
qJ"
f\\W
~
b. An ~~
I!>~
move~~ward.
-S1 -
-
d
~Rtf ~:
~y(e
c. Yo slide down a ste~p hill.
""
N
N
Bj
t-1
/ Il"l A force of 25.0 N is applied s
V
much work was done?J
w- ~~
a
o:~
kg mass o£
__C(\qY\
q.WOfl:: _
-
J
0
-:
frictionless surface a distance of 20.0 meters. How
-----,
\S?o ~j
V'J; (J-S) (~Q)::-
5
r:--,fi..
I
Work and Energy Problems
c-
ti'lA
force of 120 Nis applied to the front of a sled at an angle of 28.0' above the horizon~11o
Vdistance
of 165 meters. How much work was done by the applied force?
as to pull the sled a
W:: fd c.O~e -=(\1..0lO~2.~)t \ (;'5 J -::~\
--1-4-~1.-.4-0--'1
J
much work would be required to lift a 12.0 kg mass up onto a table 1.15 meters high at constant speed?
~ow
V"-=
~A
t=: d :::~'2.') ( q.Y') \. \ CS
-= \ 1'3'?1.
0"
barge is being pulled along a canal by two cables being pulled as shown to the right. The
-
e
Vtension
in each cable i$ T =14,000 N and each cable is being pulled at an angle = 18.0' relative
to the direction of motion as 5hown. How much work will be done in pulling this barge a
distance of 3.0 kilometers?
w::;.~
\
(IL.tDOO)(C-O~
\~1]C1D:i){.} ,C1 no"
V
~ 109.2 kg crate
is pulled up a rough incline with an initial speed of 1.2 m/s. A pulling force of 105 N is applied parallel
the surface of the incline, which is at an angle of 21.8' to the horizontal. The coefficient of kinetic friction is 0.32
and the crate is pulled a distance of 7.3 m.
U'
a) How much work is done upon the crate by the force of gravity?
w"'f"d
= SJxd
:::(Cj.Z)l'1.r)'9iY")'2.\S(7.3):::
\ W
I
-= -'Z.l-f '-\ .'-t J ]
-I
b) How much work is done upon the crate by the force of friction?
\N::::+=""et -::
fet::: ~'b'2)(Cj,2JCq.r)(COS2\.,",)(,.'O}=
IN =-\ q ~ . '5 \J]
r
c) How much work is none upon the crate by the force of the puller?
'N:::
f="d =
~
c\ .=-
Q 0 S) t,. 3)::
to
to. <;
-r )
d) Find the change in kinetic energy of the crate. (make sure you calculate the net work)
w=tJ'K
vv::: -'2Y4.'i -
\Cj~.5 -f"llPloS
"b'2.v.eo3""
_
e) Find the speed of the crate after it is pulled 7.3 m.
'l-
V -=l\
2"::
~.Y3'i\
6
Work and Energy Problems
Kinetic Energy:
13. Can kinetic energy ever be negative? Give a plausible reason for you answer without making use of any formulas.
\)\) '\\- ,S
J
0-- ~(JA).OJ<'
qy.a#l.kl
m/s. What is the kinetic energy of this car?
14. A car, which has a mass of 1250 kg is moving with a velocity of 26.0
:i. vY\V
'K -::
1.-
:i (12'50)(
::
B
2(,) 'l.
J
22SDC
15. a. If a particles speed increases by a factor of three, by what factor does its kinetic energy change?
V
t-
-=-
2.I YY\v.,1-
1
l"J,7.
1:.
\'V\
-
~
-= ~
b, Particle A has half the mass and eight times the kinetic ener y..of-patti
N\A
0;
1'-" = iYV\,. Vii?.
it"\~
¥.~-;:. r-r-.e,V(3;,"l.-'
0('
<iS~.•.-::
;,(tI¥"l6)Yp,'v
~~-; g'~~
I;}
./. t (/vI:."
119)
Vf- -:.'" "o-\:
JIlPV5
:\' -="t """g y'1A
m.6'I ~'2.-:: L
On the axes below. draw graphs of the kinetic energy of
a. A 1000 kg car that unifonnly accelerates from 0 to 20
0<6
VA'l.
_
"l-
~
mls in 20 s.
It, ye,
b. A 1000 kg car moving at 20 mls that brakes to a halt \'!~J
!,uli.~de~I"-re.tW!}ill. 4 s.
- y {l.
1):>'" 0 \ ~'\- c. A 1000 kg car that drives once around a 40-m-diarnetcr circle at a speed onO hils.
0::'
Calculate K at several times, plot the points, and draw a smooth curve between thelll,~
a.
I
250,000 ----1-
/'.
~"i<\}'~.:~::::
'-\ Ie
~
~
.~
t\''''
('
~
00
'-'
\
j
,
.-i.j?[11
C.
K(J)
j---:.:_
iiI
t
~
,
(1/4--: --,
250.000-,:-;----';---200,000
::':.r-"_.I -~-'
' -.',~~----;-' ..-
'''?,ooo ~~,ooo -.--
~~~~*
~J-"\
b.
K (J)
50,0001-'---
;
250,ooo----T--r---;
200.000
5
1
7.'(1'000')('2.0)
10
'l-
'5
;
(ui)
-
'I
::',:'
:
0
IN
02
20
I
=c"", [:'=~JI=I,=
.
50.000-I
i-I-i-
i....
I
O.
~
-;: (\OJO)
K(J)
"1,.1
1(5)
02468
oJ
::..'l-Ct>,"OO
</."
17. A ball, which has a mass of 2.40 kg., Is dropped from the top of a building 96,O,meterstall;
a. How long will it take for this ball to reach the ground?
~ 9 -t'2.
qlu= .!..(cU;)t <.
q LR ::
b. What will btthe
rj\ ~v-.. ::
'iLR -= -t "1.
/'"
::
I CUi '1
4.'1
~
velocity of the ball just as it reaches the ground?
-i V'<f.
Lq.~)lq (.,) ::
v' 'l.
( 1. )
OJ YD. '6'=- ~
~ V '2..
'l.
V"l.-=- I % ~,
(;i)
• (.,
o
c. What will be the kinetic energy of the ball just as it reaches the ground?
\
\(-="i.VV\.V
'l.-
¥: -= ;'('2.'--l)(4~.3g-)4
=
iI2.'i)(,~rl.lD)
=~'L5\?~
d. How much work would be needed to lift this ball back up to the top of thelJi(ding
~Vp."1-'
Y'Ve, -= Vt-.
=iW\~ VIf>1- J
L-/
16.
. What is the speed ratio VJ_V;...B?
__
l
1
o
at a constant speed?
7
Work and Energy Problems
Potential Energy - Gravitational and Elastie
18.
Below we see a I kg object that is initially 1m above the ground alld rises to a height of 2 IlL
Anjay and Brittany e.1ehmeasure its position but lise a different coordinate system to do so.
Fill in the table to show the initial and final gravitational potential energies and t;, Ug as
measured by Anjay and Brittany.
\.Ad =: W\ ~ Y\
Anj:JY
~------
Ends hen::
~---
S13mhtlc
2m
Uriwmy
Anjay
o
Brittany
-0 ..
19. A 5.0 kg mass is initially sitting on the floor when it is lifted onto a table 1.15 meters high at a constant speed
a. How much work will be done in lifting this mass onto the table?
W::::6U~::
VY\~\t\
=
(s)(eVl)(\.\S) -=
@'C".6~J" (
b. What will be the gravitational potential energy of this mass, relative to the floor, once it is placed on the table?
c. What was the initial gravitational potential energy, relative to the floor, of this mass while sitting on the floor?
LAc;}i
=@
20. A crate, which has a mass of 48.0 kg., is sitting at rest at the bottom of a icietionless inclined plane which 2.85
meters long and whieh meets the horizontal at an angle of 31.5'. A force F is applied so as to push the crate up this
incline at a constant speed.
a. What is the magojtl.!£le of the force F required to push the crate to the top of the incline at a constant speed?
"2.~::.0
=-
fP
0
fp-~Il:::()
f'q,o tlJ 1) (q'.V)f;;n '].5)
0
1"-'1~ '"
J
N
~
~
b. How much work will be done in pushing the crate to the top of the incline?
w =+=""d
=('2)1v)(7..¥6)
-;;\lDO.S:r
1
c. What is the height of this incline?
1-.~
~y~?
8
Work and Energy Problems
21.
Rank in order, from most to least, the aIllount of clastic potential energy ([1,,), to (Us)4 stored in
each of tl1tjse slfings.
LAs:'" - ~
.1.
1
I ,/
A '2
1-.,....
"S-- ~(2 "'"\A
lAS-: '2 r-'""
11\
n
k
W~1
z[\/\/Nl ~M
J
.1.
lu 12-)
p '"
k
~
rv\f\I)
Sln:lchcd
Sll'~tched d
Slrclchcdd
C(lmprcsscdd
'"S:. Z 0" )
II
-Z
2tl
Explanation:
l;l~
=~~
~1-
,
:
22.
Ct"Owyf'.(
dJ
,,';
A heavy object is releascd from rest at position 1 abovc a spring.
It falls and contacts the spring at position 2. The spring achieves
maximum compression at position 3. Fill in ti,e table below to
indicate whether each of the quantities are +, -, or 0 during the
intervals 1-,)2,2-,)3, and 1-,)3.
1-,)2
,"x
.---_ .. _----._--
2-,)3
--2
--3
1->3
,,,- .-----------
-
r.-----.--- ...
- ....
0
ij_ .._--_._._._
+ ..--_. - ..----- Ir----.---.
;-_ .._.
,,
i,
,
!
D
-
.
;
-t
!
t
23. A dart gun is manufactured with a spring whose relaxed length of 0.228 m. If the spring constant is 52.0 N/m, how
much elastic potential energy is stored in the spring when it is compressed to a length of 0.143 m?
\A~:: ~~~'l-:: ~ (52') (. \y~ - ..'2.~~)
'1-:
l" \9 .JJ
1.lI (~"~ .•. -::
24. A screen door is manufactured with a spring whose relaxed length of 0.556 m. If the spring constant is 46.0 N/m,
how much elastic potential energy is stored in the spring when it is stretched to a length of 0.886 m?
25. A force of F = 35.0 N is applied to a spring and as a result the spring stretches a distance
a. What is the spring constant for this spring?
-F= ¥:x
~= ~
_
=: ~I~
=\2- ~LN/yY\
1
0e:
12.0:0i)
~--
C~
~
(I'V\) ..
b. How much energy will be stored in this spring?
9
Work and Energy Problems
26. A spring, which has a spring constant k, is hung from the ceiling as shown to the right. A mass
m = 3.00 kg is added to the end of the spring and is then slowly lowered until equilibrium is reached.
At this point the bottom of the mass has been lowered a distance of h = 52.0 em.
a. What is the magnitude of the force being exerted by the spring when the system reaches
eq~Ii~~m~
b.
= f9 = YV\0
(iq .4 tv
:: C~')(eL&,) =
What is the spring constant of this spring?
-:;;to'
-==-_-~
~ __
1'1.~-=f.:(-~)
~=-~';( =)
]
-.
=il¥: = 6~.5*\
2~-----~-How much energy is stored in the spring when equilibrium is reached?
c.
~ (£;(p.1D)(.152')1-
U.S::: ~ ~'f.1.
==(l,(P4-j"
j
Conservation of Energy
27. What is meant by an isolated system?
A ~
~
v.9\0A
~~.
~U'S
"A\\
-txtev~
V\o
cu-!
in~~
{trrc.e5
(Y\~
014).
28. Identify an appropriate system for applying conservation of energy to each of the following:
a. A spring is used to launch a ball into the air.
'5?n",~ + 'oill
b.
e~("~
A spring is used to push a car on an air track.
S
c.
f;lY1i'\~ ~
C"""
A spring is used to slide a block across a table where it stops.
S?"i"d
d.
-t
-t
\olc4 .., \- ojj~
A car moving on a frictionless surface collides with a spring and rebounds at essentially the same speed
with which it hit the spring.
?>pvi1 ~ c..
29.
. Three
balls of equ:l1mass are fued simultaneously with equal speeds
from the same height above the ground. Ball 1 is fIred straight up,
Ball 2 is fired straight down, and Ball 3 is fIred horizontally. Rank in
order, from largest to smallest, their speeds VI> V2, and V3 as they hit
the ground.
.
V:-~\/1.-- ~'V~'-
i-O~d~r:
Explanation:
S~
-..----
?c:>J'Y\ \(\~ir...~,
U& ~ ~
I('fG\Dvh\l~
Iall
f
~.~
BaH 3
B,II2
~
-l'\)~
~.
10
Work and Energy Problems
. Below arc shown three frictionless tracks. A block is released from rest at the position shown
on the left. To which point does the block make it on the right before reversing direction and
sliding back? Point B is the same height as the starting position.
30.
-A
B
c
MukC$ it to _.~
M:llr:csitlo
M3kcs it to
...
31. A spring gun' shoots out a plastic ball at speed vo' The spring is then compressed
first shot.
Go ~
a. ,By what factor is the spring's potential energy increased?
'I 1..
\ ¥- 'f..
v_ c.. '1;-~.
-; I
if
ll)-
V'S ~
~~v
b.
"2-
U
-=-j
e
twice the distance it was on the
2 '2. = ••JL
"2
By want factor is the ball's launch speed increased? Explain.
G//
\).S :::")~
1:) \.As-= ~
~
1-- ~
~
0< y..
.
:: ¥-
2
\I:::
32. A spring is mounted horizontally as shown to the right. A crate, which has a mass of 8.5 kg is pressed against the
spring with a force of 350 N. As a result the spring is compressed a distance of 82.0 cm. The mass is then released
and is allowed to slide along the horizontal, frictionless surface.
F.
m,.<~'''11 0
a. What is the spring constant of this spring?
~ ~JlR~
K~
fi ~~
::~~1.M.~
-'} \
=
=
.'
mi.
=.,.="'
..
.=
..
b. How much elastic potential energy will be stored in the spring?
LA ~ '" ~ ¥-'"
1. -,:
i lW2 ~ . ls')( • rz.)
S-y-j
\-~-"'3-.
L
"::-\
o d. What will be the kinetic energy of this crate after it has left the spring?
O)'('-~
\(:: i\'Y\ V ~ -:: Lh ~ ~_4'3.
S .y ]
~
e. What will be the velocity of the crate after it has left the spring?
If. -:::~ W'\V '1.
::- ')
.
\
l-t~.s-=
i(~''Q\f
1-
l~(,.q=l<t.<;)y
Suppose now that there is friction between the crate and the horizontal surfa
an t at t e coe icient of kinetic
friction between the crate and the surface is f.l = 0.65. As a result the crate slows down until it stops.
f. What will be the magnitude of the frictional force acting on the crate as it slides across the surface~.
~
,... c;.. - I••..
r;)("'.~) ~
('l
(
""N=''J-\...'!
S)(::jAI'-N:: ~vS)(n.?)=~.ISN
r;;;
'iS~.?>
+""..
\
X.
S'f.~
g. How much work will be done on the crate by the frictional force from the time the crate is released until ~e mass
stops?
(/
o - V-t:,.'S ::\-:IC\4'3.,:> :r J
W -= I)~ -= Kf - f-.l
--=e_-----,
h. How far will the mass slide before it comes to a halt?
\I~ :-
n
0 \01c. ~
0:>eW1 to
0...
boX
Col\Af'\.e-k
~y.
1.. .lhm \
11
Work and Energy Problems
33. A 2.45 kg rock is dropped from the top of a 15.5 m vertical cliff.
a.
What is the potential energy of the rock relative to the base of the cliff before it is dropped?
\.A~::yY\~
b.
=
::: (1.46)(CV15)(IS.5)
,312.15J'J
What is the kinetic energy of the rock just before it hits the ground below?
~i.=
U~:: \0(
'E~ ~
\"'1.2-.1.50" \
:=
What is the veiocity of the rock at a point 5.00 m above the base of the cliff?
c.
Un i :: LlQ(oo;)
T
d.
~
¥-
u.~~UxS)
=) \(::-
(]
-:::
~~(~'v\
J ~{rJ\V'2..
How much total energy does the rock have half way down.
\1JWJ. ~
~
\'v\Q sci...nu
_ .K)(CS-15.5)=
~lP~
\
v'7.=: 2(I02.q)
1
Y'2.
~ -=
11-\.~5 ~ 1
')12. \'.)S )
34. A roller coaster is at the top o~; 75.0 m hill. It rolls down th~ hill o~ very low friction wheels and climbs up to the
top of a 45.0 m hill. Find: (a) the speed of the thing at the bottom of the first hill
•••.
;=,!>
~2"LjS'
K
-=
u.~r;)
rf~"c:j) -=
i1-v
1 35
1..
(b) its speed at the top of the second hill.
.- E
f _ U "I
T jc:.
U.'(1S)~(S)
= ~ ",'7.
(.;'\
\ ,,-::
.L ""'-
'l..
) -t L..'T'''.
(Ci.Q){1<;) -:: (cH)l1-/5) +~ '2-
~
~~(l"') -=
E'\ -
,,'1..=
(9.'6')liS) = ~ y'l..
Q'CCj If
\r
\1-110
':b'ij.3]J
't"l4 :::~v'2..
y"-=
1';'5::I.'jl-/I-t.\V'1.
.
V:::2t...tlD.
35. A roller coaster starts at some height that you do not Imow. It goes down this hill and the
s up a second hill
that is 28.5 m above the first drop at a speed of 22.5 m/s. $0 how high was the initial hill?
.
1>
\
.,..c,~
.l-
-:;...
-(jl.
>./.\.
n" ')
1"
+\(..
l.Ar,.-U,.
3l'L,(.,»)
-
1. I'y'.
-= I'y...~
"l.fh='2.,Q.'3-+2'5,1':2
e;, 1>2.'-1'3
~:...--;:-:-;-~::-~\
Jq.q;y-.""
-:z.
('2?,.S -\ 2.
V
'1'1~l?h .,,(CI.S') (n.S)-r -;.{'Z"2..S)
I'f.~h-
~s
36. A roller coaster sits at the
height of 86.0 meters, the
at the bottom of the hill.
a. What is the gravitational
coaster while at the top
lA} ~ ~\-ui
\ h - S~. 3'0 m J
top of a hill and is preparing to enter a loop.the-Icop as sfiown to the right. The hill has a
loop has a radius of 22.0 meters and the roller coaster has a mass of 525 kg. Assume h=O
.
~'otentjai energy of the roller
of the hill?
~ (?'2.'S) (9.8')( ~\;)
=
L-jy 'lHl 0 :s
b. What will be the velocity of the roller coaster when it
-::: k.1?
.
V'l.-;.~~,8'').LP
1.
reaches point c?
~
:::= .\. YY\ 'l'
\\00\..
\
f::: '41.i~1
H4;'-11D= ~(t51.'5),j2
c. What will be the velocity of the roller coaster when it
reaches point A? ~ 1-j1. 41D
5~-:::.
b+
~::
j4'i2'il0::
'1.
•. -4:(<::>25)"
1:z.\,.~ro + 1..<"/2.5"'''
VL
= ~1.'5)Cq'~l
Y4)
LA.1'" l' 'f(
=-
=
)5 2.3. 2
-=
7..'6'.7
. 1.llIo'1D
1.V2.SV'1.~
IV
d. What WIllbe the velOCity of the roller coaster when It reaches point B?
lAa.; -:: U.
-~.
44'2"l10
~6
::
t\<
/,,'44L410~
\
1.._)
l':51.coX"l.~)l"L2) -I =1,(61.'5)" -i
'Z ]
-z.
\\1>\qD+'2.lJil.5V
,'l.'\?'rO-='2.c,,1..5v1. ~.
\{1..-= \
l..S'-f,'.t
---..
vn.l
C?S.~ s
5
..
2
Work and Energy Problems
...
37. A pendulum is pulled backward, and is released from a position 30-cm above the lowest point of its
path. How fast will the 250-g penduium be traveling when it reaches the lowest point in its swing?
.......~
.
\\,:. .~"('f\
.
.....•..,
fY':' . "2.6¥-j
V-;. '7
o
•
30.e{'
~:: q.~,%~
38. In order to thwart burglars, a clever child ties paint cans to 3.0-m long strings, and hangs them from the stairway of
his house. If the 8-kg can of paint is released at an angle of 35", how fast will it be traveling when it hits the burglar
in th face? (assume that the burglar is standing at the lowest point of the can's swing).
\(-::3(053'0'
\\-:'3-)(
)C=: 'l.y'61
~l'
y\
-=
17-)C
-=-"3 _1..Y'01
bL::'
rJ." '\
f::
y., -:. J.. M" "1-
'O"2.'~
2C'1,'lf;S't) .•. i"
:i"
S .'2.'h :.
Y\ -:. , 6't l'Y\
39.
v ~~ lo.S"lS'4
4
'2-
A small cube of mass III slides back and forth in a frictionless,
hemispherical bowl of radius R. Suppose the cube is released at
angle 0 . What is the cube's speed at the bottom of the bowl?
a. Begin by drawing a before-and-after visual ovcrview. Let the
cube's initial position and speed be Yi and Vi' Use a similar
notation for the final position and speed.
i.- ..---------- ..- - ..-- ---.
'b. At the WIlla
.. '. I"POSItIon,arc CI:t'[ lcr Ki Ot. (Ug )i zero.? If so,
. we.
hi 'h? --~
v
tA5
c. At the final position, are either Kr or (Ugh zero? If SO,which? ... -
'L--
C)
.
-==-.0
d. Write the conservation of energy equations in terms of position and speed variables, omitting any
terms that are zero.
e. Substitute into your expression in d above the appropriate expression of y in terms of Rand
'i. -:::Q.c..OH7
&
~
x.
J
Vf ::. 2. 9 (Q-
O-CQ) \Er
J
1,.'2'5~
e.
I
hi
13
Power Problems
40. A 100-kg cheetah moves from rest to 30 m/s in 4 s. What is the power?
.,,!:J- -:: ¥:f -~~
f-::: ~
b-\:
b-\:
_ {(IOO')(;;O) -
6lv
"2-
:\:(100)(0)
-:;;
Y
-
?:: 45DOO
Lt
41. A 48.0 kg telephone repairperson climbs up one of them power pole deals. She is carrying 7.85 kg of tools and
things. If she generates 0.765 hp, how much time does it take her to climb the 3.20 m tall pole? (1 hp=746 W)
P::: ~::
0.Uq
5,o.lJl - U'3f -~L
-::"/
t>-t
()J.;.
=) 6,O.~'1-=et'i/"-t"S5::x."1.~)(i.2)
..
b t;.
\'*
.11,5 ~)C 1YII~ -: '51c>.(p"1' W
D-\:.
'51o.1I9 --:::n 5\ .45\.,
-==) l::*.,::: 11'5\ .t..t'C1o
6-1::-
'S'o.lI'j
~
\ !::>t:;:::
1> ,en
S' \
42. I left a 150W bulb on for 2.5 hours. Determine how much electricity I used. In this case the electricity (electrical
energy)iSbcing changed into 'fffaT and Iight...that's the ~~e!
w')
ts O\",-e
{) w
r -= -:b1. .0 YW' 'i: .., ,,00 S
-==)
ItOO -
fo.....
w
- '1000
\;3IQ b)DC) 0
.:r
oy
-= 9000 s
\ :~Sx.\oI.oJ
\ Vw
43. A1QQY:! motor is being used to lift shingles at a constant velocity to the top of a roof. If one pack of shingles has a
28 kg mass, determine the velocity that the pack will be raised at. Ifthe shingles are being raised at a constant
v~then
---)~
(PY\~+ct..r+
the net force acting on the pack is?
-8 cL \ -;:: f"" V
\oN::
+-"0
V~1
\/-=
tf:
-fb"lc-e
¥\'\il~
IJ-.>
\1,(V\Q,ffi 'oU:
v.eloc:l~ -= . 0 ~t
~~
~~v'
')PO -:: li~)l';H)\f
~O'O -:: ~.4
----
Li
'2."14.\
'J.,~.
V*
If
'J -::;,3~
14
Energy and Collisions
44. Explain the difference between an elastic collision and an inelastic collision?
e\mtiC
(J)\\\~UV\~:
~
\~\o.~\ic.
~ ~~
C-oY'~vec1.
0J'e
~l~
C&'-¥exVed.(e4
C,()\\\'6)(SV\~:
~W"Y\
is
45. Can the objects bounce off each other in an iNelastic collision? Explain, include an example in your explanallon. \ tiS.
'r. \t rv:-;
ru
clt'bf
Ioill ~
~
it cloesYl't r-t~
fA.
'0ov-.K\(.£S off tw ~
\t\Q.,i
~koN
I
'15t>~
~j
yY\~
\t\.)
'oo...-U
~
-Th t"'vu b~
'v\{JW-{
\"
b-e.--e..v> \a~-r-.
46. Consider a perfectly elastic collision in which a moving ball 1 strikes an initially stationary Ball 2.
a.
b.
1- ~
Underwhat
circumstances,
Under what circumstances,
~ . bo.»
c.
if any, will Balli come to a stop?
if any, will Balli recoil backwards?
1...- ~5
Under what circumstances,
-1r
~.
Vwvve.}\,u c:a,~
00..»
CA-
\OU'"~
~
\O~
~
CA. '?>fV\.o.J.1u-
::1..
ocU
if any, will Balli continue moving forward?
1.., h.C\..)
+-
Wcun kJ
~
1m
1
2 kg=",
\.
1"'0&" 0.003 kg
\I~\ .•"O~
Before Collision
5
Immediately After Collision
47. A 2-kilogram block initially hangs at rest at the end of two I-meter strings of negligible mass as shown on the left
diagram above. A 0.003-kilogram bullet, moving horizontally with a speed of J 000 meters per second, strikes the
block and becomes embedded in it. After the collision, the bullet! block combination swings upward, but does not
rotate.
a. Calculate the speed v of the bullet! block combination just after the collision.
~'o.u-
f\
= Qf
1'I\'o'l'ci,
::~."
/'
'l"
~OO<')(\COO)":!
(.oc~;-'2.)""f
~ of ':: \.1+ '\~.
b.
Calculate the ratio of the initial kinetic energy of the bullet to Ie metlc energy
immediately after the collision.
'1.
~::
~+
c.
\(l~
=-
%tY"V\l»(Vt)'\)_
¥-f('o-tbl)
p=Mv'
"3 -:: . ?.. .00<' "f
~'o\) \{~ ~
~f!n'l>+yY\.•••
~
_
'It
0 1"
0
~(5t>3)(IOOO); ~
~.OIl~}(
\. c;)
Calculate the maximum vertical height above the initial rest position reached by the bullet/block combination.
t; l ::t.+
k{r>.J"'~\) ~ ~
J
/
=i (Me + yY\~\) "f"'1.
{(1..
O()~
')0. <;)"'1.
-;>
lrt'\\?-I"Y"'.'O\) <j"
1. .00)) lqs) ~
'=.
(
1.1':=
J \q . 1i'7, ""-'_
~
-\k(;;
'1
J
AY\ -::-:Ti l"\J
t
15
Energy and Collisions
U,3;-= ~ ""
T
"I
'f.'\~0
j-
,!
, .•.. :.,.;:
. :'
48. A small block of mass M is released 11"0111 rest at the top of the curved fi'ictionless ramp shown above. The block
slides down the ramp and is moving with a speed 3.5vQ when it collides with a larger block of mass 105M at rest at
the bottom of the incline. The larger block moves to the right at a speed 2vn immediately after the collision. Express
your answers to the following questions in ten~s gft!Je giyeJ~ quantities and fundamental constants. (~~-LY'7.A(Y'\~ \
(a) Determine the height h of the ramp from which the small block was released.
o..n5"W~)
bL -= tf
~
tA~l :: \<.f
rf~h--;;lrf.
/
t
-=
""-r ~
(~.r;yS'_
'l. ~
-V~
h ~~.~) - ~)
\I'l.
(b) Determine the speed of the small block after the collision.
~VJ)(
'P i. :: p+
I)AC"'.c?Vo)
~
-;.15 YO - '3 YO
tj.. Yf ~(\.t;ty\j(1.Vl))
::
"3.t;Vo :: Yf +(1. S)("2. Vo)
~.C:;VO :: Y.f -t '?:IV\)
.c;yo
J
d'N ~~30
(c) The larger block slides a distance D before coming to rest. Determine the value ofth£ coefficient of kinetic
_ J/riction II between the larger block and the surface on which it slides.
~\
\V\ (ooe ~
:;.::; •.G""
'il"f
0 {)
r
:: 0 - 1. (V5M ll'lVt))
!I'O
1.__L ••••
:f'",Da=
:i. Vo
.- J '2- •.
'L .
1.
}tJ<::: _~
\
F~d'<~3
S.
4V.'
~~)(~)O- 1-~ ~(
-~~t)::
_
= _1 ( I.~"""'IILtvo '1.')
_:r.
'1-.
¥-~- ¥:L
~~~
~#
_( D
I W:: /:)'(.
.•/~""
)
1.~~
~~
--
-=
(d) Indicate whether the collisiQl!.between the two blocks is elastic or r.;Pirltic. Justi
f-'~::F.f
..e)~'e.- ~
\
l.-VV\VL
7
'2. .
I
:: '2. rvwf
"2.
,-:',
+ ~\.::>'IVf
1-
~(?'5VoY -= M(."vo y- +--t(V;~)(1.VS
1"2.7.5Vo"-;;
• 2-5Vo'l.. 1"
vl/o"
11.. 2SVo 7..
~~
i
LP.'25Vo '2.
16
Energy and Collisions
~---------r------Ii
@I",.
.---- J---------~,T0V
Immcdiillcly Aflcr
Large Sphere
Slrikcs Fluor
Before
Release
49. A small and a large sphere, of mass M and 3M respectively, are arranged as shown on the left side of the figure
above. The spheres are then simultaneously dropped from rest. When the large sphere strikes the floor, the
spheres have fallen a height H. Assume air resistance is negligible. Express all answers in terms of M, H, and
fundamental constants, as appropriate.
(a) Derive an expressjan for the speed
Sl -::;
€-r
U~3'"
Immediately
-=
Vb
with which the large sphere strikes the floor.
/" ~~~
2~ """'
-=
~-;l'\ .----/
with identical speed
collision, the small sphere moves upward with speed
Derive an equation
.~
.
~~
~ ~,.J-'
that relates
'0.
Vb,
Vs
Vb
Vb and
J "Lr
collides head-on with
at that instant. Immediately
and the large sphere has speed
after the
V, •
(ce-tU~flfYV)
vs, and v,.
r )f\'Il
,Vb - Vb -:: ~YL + Vs
+~ . -.:: ?~"",t f'Mf
"'"
-=l-;7'l(V2}
1, V'o:: -;lo) +
\1
..
-\-~)VS
= O.
from part (b) to determine
Vs
the speed of the small sphere in terms of
~\VS:::
iVb
J
Vb'
\
J
the collision is elastic. Justify your answer using your results from parts (b) and (c).
¥:;~ -= ¥-fY""
ij.(?:Jrf)v'O 1- + ~ lrriY'o'l- -.:. !L "'f (vs
\(.i '3VV\ -t
.
3 V'O 1- + Vb 'l- -=- tbV'O) 'J-
/'
t/
~ p\~ in
Determine
~V\.. -\'Vs
V,
2.VIo:: 't,VL +VS
Indicate whether
:"::-=
•. T
In this particular situation
(c) Use your relationship
(e)
V::'
~
?e- -= Pf
~? ~lVb)
(d)
V 1-
after striking the floor, the large sphere is moving upward with speed
the small sphere, which is movin(j downward
(b)
-: ~~y'l.
\.-\
-=- L-\V
Vb?-
v-;
:o'2.v", ~
\0'1-
oJo<:NC
the height h that the small sphere rises all'ove its lowest position, in terms of the origin
~
c.. ~ :'\
~~<?'"tO.
10 _
eight H.
t; l :::
t;:f
3\'Y\~W-t ~H -::
\YI~h11,M
17
Energy and Collisions
I
50. A bullet of mass m is moving horizontally with speed
Vo
x-~~I
,
when it hits a block of mass 100m that is at rest on a
horizontal frictionless table, as shown above. The surface of the table is a height h above the floor. After the
impact the bullet and the block slide off the table and hit the floor a distance x from the edge of the table. Derive
expressions for the following quantities in terms of m, h, vo, and appropriate constants:
a.
the speed of the block as it leaves the table
b.
c.
the distance x
~wM(}Jk~
XI. :;
'I.e-=.
Y:i. -t V:\;
0 +{~
Suppose thnhe-butter-PaS'fu
d.
State whether the time required for the block to reach the floor from the edge of the table would now be greater,
less, or the same. Justify your answer.
~~
~p
e.
QLt
~
~V1}
State whether the distance x for the block would now be greater, less, or the same. Justify your answer.
JN
~q
btc~
fu~~
k2e
~
VV,0G0ry, ~ -HAe ljDcK-
b.et~v- cf!u - oJ- ~
~
'f
k-e ~o.J{skveeL
JHu
18
Just a Few More Energy Problems .....
A
___________________________
:_i:~_______________
~
51. A roller coaster ride at an amusement park lifts a car of mass 700 kg to point A at a height of90 m above the lowest
point on the track, as shown above. The car stalts from rest at point A, rolls with negligible friction down the incline
and follows the track around a loop of radius 20 m. Point B, the highest point on the loop, is at a height of 50 m
above the lowest point on the track.
a.
Indicate on the figure the point P at which the maximum speed ofthe car is attained.
b.
Calculate the value
c. Calculate the speed
VB
I'm,,'
of this maximum speed.
of the car at point B.
1:6
'2.
rf~ -= Mrr.6 + ~ry\V
ti- -=
\
'2.
1--V
::: ~'12.
V1- {2.) l 0'17---)
L&[. ~)(cro)-:: (q. y) (q 6) -t i V 2C6'~'2. -;: L-J q 0
-t
:i
V '2
d Now suppose that friction is not negligible. How could the loop be modified to maintain the same speed at the top of
the loop as found in (b)? Justify your answer.
.
rw
lOl7P
V'aciA,Vt-S ole
v:rov
1vvJlf
et \A6
Y~
o.k
(VL0Yt"
~
Ud
6
spv.-cLl
pe5'lAt
olR CH o.-s-€
~~~
rV1o- ~
-}1;u
Vo..a~
Car
mGYf
19
Just a Few More Energy Problems .....
5
4 '
Force
3
(N)
6
8
10
12
14
16
18 20
22
Displacemenl em)
52. A 0.20 kg object moves along a straight line. The net force acting on the object varies with the object's displacement
as shown in the graph. The object starts fi'om rest at displacement x = 0 and time t = 0 and is displaced a distance of
20 m. Determine each oCthe following.
a. The acceleration of the palticle wI~
di~p~rent
x is 6 m.
fW,6
0- :: ~
b.
ir
_ ~
- •Z
__~
~ (Iv ::
1--0
9<t-
J
The time taken for the object to be displaced the first 12 m.
'if =
x.~f
Vet- .•.iet+?
12 -:: 6 of 0
-t
i (1.
-t;
0")
G
t::fl
2..0
-z.
). ($
J
c. The amount of work done by the net force in displacing the object the first 12 m.
W C/Y1c-
:::
l
td o-r
~~~
~(~
\tV =['-I)(I'2.)
d.
oY
J" \
The speed of the object at displacement x = 12 m.
W -;. [) j:
V -z.. :::
Li ~ :: ~ (VW,1Lj'1; -::
e.
l-f(
l.-f ~
[,!~niJ
~(.'L)v'l.
The final speed of the object at displacement x = 20 m.
o-~w
4~
.t-
i (Y,)l2o-I"2-}
~'(Y\v-z..
"t--
V-=-
\.pYo
~(.'2-)v'Z-
1--t~-t11R
Lii
~
ft
0S.3~
-::;
~(2)V'L
20
Work & Change in Energy
1. Work and Heat
2. a. Ug -tK b. Ug -t K+ Eth
3. a. W -t Ug
b. W -t K
4. a. +
b. +
c. +
d. -
5.
IV,
0
6.
f.-
e.O
IV<O
Ie. <.. '10
c.
'"
> "10'
i
77
.V'
w""o
~
Cbv'\1t
0
P
""J
b.
~
CO"':!
e. K-t Us -tUg
~
"'JtF
a.
c. Echem -t Ug d. Us -tK-tEth
~\e
= 10.
Equal because W = change in Ksince the both start at rest they both have the same K (but their velocities are
different!)
7.
FI
~l
c. Youslidcd 0wn:l:\lccp hill.
F
Ikr",~~~_
~
\os
.>
~
f~ 0:-
A(1<N"'
8.
o
VI
22. K: +, ., 0 Ug: -, -, - Us: 0, +, +
500 J
9.
1.74xl0
4
23. 0.19 J
J
24. 2.5 J
25. a. 292 N/m b. 0.252 J
10. 135 J
7
11. 7.99 x 10 J
12. a. 244.4 J b. 611 J c. 766.5 J
26. a. 29.4 N
d.8.34 m/s
work and change the energy of a system or
14. 4.23 x 105 J
where heat cant be transfered
15. a. 9x b. 4
b.
:: ---i-...
-:t=L~-;:
150.000
...j. -,
lOO.lX()
~_I
__! -
50.00)
--'.
"
o
"!
4I
J
2.SO,OOOl"
200,000
.•
•
.
150.000
..
-
.
C.
250.00>
"'
200.000'
--t __ ,__ .J...
'I ._.r---l--tI
:
I
"1-
100.000
--,-+--
of.
o
lSO,OOO
-!1---T
'(1)
I
2.
)
4
28. a. spring + ball + earth
K(I)
I
-t- -j_ ... t•
50,000'
1(1)
OSIOiS20
KO)
100.000 .'-1
.--r-l.
---i---: -
l--..f.:
.
+ block + table d. spring + car
--t-'~"-;--I-
----l-f
-r----{-'-
so.ooo .o. '
o
2.
I
.68
29. all speeds equal (why?)
30. B, B, B
J._-iI
I(~)
31. a. 4 times
b. 2 times (Us-tK=4 and Kcx:v')
b. 143.5 J c. 143.5 J
e. 5.81 m/sec
a. 4.42 sec b. 43.4 m/sec
c. 2258 J d. 2258 J
18. Anjay: 9.8, 19.6, 9.8J Brittany: 0, 9.8, 9.8 J
19. a. 56 J b. 56 J c. 0 J
20. a. 246 N b. 701 J c. 1.49 m d. 701 J
21. 4>3>2=1
b. spring + car c. spring
I
I
32. a. 427 N/m
17.
into or out of
the system.
16.
K(J)
c. 7.65 J
27. A system with no external forces that could do
13. no just concerned with motion not direction
a.
b 56.6 N/m
d. 143.5 J
f. 54.2 N g. 143.5 J h. 2.65 m
33. a. 372 J b. 372 J c. 14.3 m/s d. 372 J
34. a. 38 m/s
b. 24 m/s
35.54 m
36. a. 4.42x105 J
c. 28.7 m/s
b. 41.05 m/s
d. 35.4 m/s
21
Work & Change in Energy
37. 2.42
m/s
38. 3.25 m/s
39. b. K, c. Ug, d. (2gy,)" e. [2g(R-Rcose)"
40.11.2 kW
41. 3.1 s
42. 1.35x106 J
43. 0.73 mis, Fn"
=0
44. elastic energy and momentum is conserved, in inelastic only momentum is conserved.
45. yes
46. a. equal masses b. Ball 2 has larger mass c. Ball 2 has smaller mass
47. a) 1.5 mis, b)667:1 c) O.11m
48. a. 6.125v/lg
49. a. (2gH)"
b. 0.5 va
b.
2Vb
= 3 VL + v,
c. 2 v/
I gOd.
c. 2 Vb = V,
Inelastic'
d. yes
e.4H
50. a) va/lOl b) -50mvo'/lOl c) (vo/101J(2h/g)" d)same e) less
51. a) at lowest point on track at bottom of first hill b) 42 mis, c) 28 m/s d) lower height of loop or decrease its
radius.
52. a) 20 m/s2, b) 1.1 s, c) 48 J, d) 21.9 mis, e) 25 m/s
22