QQjectives for Chapter 10 - Energy. Work and SimPlg Machines Student Targets 403. I can identify kinetic energy as a function of velocity. 2. An object that has kinetic energy must be a. moving b. falling c. pretty d. elevated
e. at rest
A. Must be moving. It COULD be falling, but it MUST be moving. 3. Which gives the correct relationship for kinetic energy? a. KE = mv c. KE = mv/2 2 b. KE = mv2 d. KE = mv /2
D. 4. An object that has kinetic energy must have (A) acceleration. B) a force applied to maintain it. C) momentum. D) none of the above C momentum (if it has mass and velocity, it also has to have momentum.) Y, mY"> 0 then mv >0.
404. I can calculate gravitational potential energy' and kinetic energy. 5. What's the KE of a 100,000kg spaceship orbiting at 8,000m/s? a)4x1013j b)3.2x10'2j c)4x10Bj (0.5)(100,000kg)(8000m/s)2
= 3.2 x 1012J
406. I can identify that energy is transferred between different forms. 7. An arrow in a bow has 70 J of potential energy. Assuming no loss of energy due to heat or poor accounting procedures, how much kinetic energy will the arrow have after its shot and traveling in air? a.140J b.70J c.50J d.35J e.OJ B. All of the energy would turn into kinetic energy. Work will produce energy. Energy can do work. 1/ := 6.1'-~ W02.l flON~"~ .e,ow =: AU: 407. I can solve problems using conservation of mechanical energy.
-y.J
'10r :.
70r
408. I can apply the mathematical definition of work as the product of Force and displacement. 10. How much net work is done by gravity on a rock that weighs 50 N that you carry horizontally across a 10 mroom? a.500J E. No Work
b.500W
c.10J
d.5J
~ ~
~~
-.yr;. j
0=96° lO.5 ?()~:::O
:e-.
W=Fdcos 9 Since the weight acts at 270° and the displacement downward cannot move a rock horizontally by itself.
is at 0° 9 is 90°.
cos 90° = O. Gravity acting
11. It takes a net work of 40 J to push a box of physics papers 4 meters across a floor. Assuming the push is in the same direction as the box moved, what is the magnitude of the net force on the box of physics papers? a. 4 N b. 10 N c. 40 N d. 160 N e. none of these B.
W=Fdcos9
= F = Wid (cos 9) = 40J 14m cosoo = 10N
When there is an angle between the force and the displacement, W = F d cos9.
12. T/F
True. You have to take into account the angle between the force and the displacement. forces won't cause a displacement.
Some
13. Clarice has a mass of 78 kg and climbs the schools stairs in 23.0 seconds. The school stairwell contains 41 stairs that are 18 em tall each. How much work against gravity did Clarice do climbing up the stairs? a. 5641 J b. 576 J c.564127J d. 245 J e. 764 J a.
W=Fd(cos
9) = mgd (cosO) = (78kg)(9.80m/s2)(41stairs)(0.18m/stair)
409. I can identify situations
of net positive work, negative
= 5641J
work, zero work.
14. When friction slows down a ball, friction is doing: a) Positive Work b) Negative work c zero work b) Work would be negative. Friction always opposes displacement is 180°. The cos 180°= -1. Work from friction
motion, so the angle between force and is negative.
410. I can identify work as a change in energy. 15. The amount of potential energy possessed by an elevated object is equal to A) the B) the C) the D) the E) the
distance it is lifted. work done in lifting it. force needed to lift it. value of the acceleration due to gravity. power used to lift it. B) Energy comes from work.
OPRF Physics Custom
The work you do turns into energy.
Objectives
Note: any objectives involving calculation of one variable imply the calculation of any other variable in the equation. depending on the given information. 10/11.1 16.
Calculate power. How much power is required to do 100 J of work on a 35 kg object in 2 seconds? a. 17.5 W b. 3500 W c. 200 W d. 50 W e. 100 W d. P =
Wit = 100J/2s = SOW
17. Power equals work multiplied by time. a. True b. False False.
Power = work divided
by time.
10.4 State SI units for work, energy,
spring constant,
and power.
21. The unit of energy is the watt. a. True b. False b. False,
The unit is the joule.
22. The unit of power is the watt. a. True b. False A. True:
1J/1s = 1W
23. The unit of work is the Joule. a. True b. False A.
True.
11.5 Calculate answers for hypothetical energy scenarios you double the velocity, what happens to the energy. etc)
using the idea of proportionality.
(e.g .. if
24. If you lift two loads of equal weight up one story, how much work do you do compared to lifting just one load up one story? A) Four times as much 8) One quarter as much C) Twice as much 0) One half as much E) The same amount This depends on the interpretation. If you say you carry two loads up one flight vs. carrying two loads at once up the stairs, the answer is E. W=Fd cos 8.
the
Another way students interpreted the question that each load was the same weight. If each load is the same weight, taking two loads is double the force. In this case, two loads would be twice the work. The answer would be C. 25. If Nellie Newton pushes an object with three times the force for twice the distance, she does A) three times the work. 8) six times the work. C) four times the work. 0) the same work.
F2 = 3F,
d2=2d,
W2=F2d2={3F,)(2d,)
= 6W, Answer:
(B)
26. How much farther will a car traveling at 200 km/s skid than the same car traveling at 100 km/s?
r;,
'w'~('.",tt.",,~AY£ ••'
A) The same distance 8) Five times as far C) Half as far 0) Four times as far E) Twice as far ...0) There is four times the energy, so the skid would be four times the distance. 27. If a student pushes an object with twice the force for twice the distance, she does a. the same work b. twice the work c. four times the work d. eight times the work F2 = 2F,
d2=2d,
W2=F2d2={2F,)(2d,)
= 4W, Answer:
c.
28. How much MORE kinetic energy will a car traveling at 100 km/hr have then the same car traveling at 50 km/hr? a. five times as much b. four times as much c. twice as much d. the same e. half as much b. four times KE1
= % m~ = % m (50m/s)2 = 1250m
KE2
= % m (100m/s)2
= 5000m
Mechanical advantage
Calculate the mechanical advantage of a lever that moves a 12.000N object O.20m when a person applies a force of 91ON over a distance of 3.00m. Calculate the ideal mechanical advantage for the system. Calculate the efficiency of the system.
= =
= =
= =
MA F,/F. 12,000N/910N 13 IMA deld, 3.00m/0.20m 15 e MAtiMA x 100 13/15 x 100
=
=
= 88%
A student takes the following data for a spring. Find the work done on the spring and the spring constant. Displacement
0.0
0.0
0.3 0.5
137.5 275.0
0.8 1.0
412.5 550.0
1.3 1.5
687.5
1.8 2.0
2.3 2.5 2.8 3.0
Slope= spring constant = 550N/m
Force
825.0 962.5 1100.0 1237.5 1375.0 1512.5 1650.0
Slope = (y,-y,)/(x,-x,)
= (1375N - 550N)/(2.5m -l.Om)
= 550 N/m
W = area under graph = )I, bh =)1,(3.0m)(1650N) 2475J
Force vs. Displacement 3000.0 2500.0 2000.0 1500.0 1000.0 500.0 0.0 0.0
1.0
k = 550N/m W
= % (J.Om)(1650N) = 2475J
2.0
3.0
4.0
5.0
6.0
A student takes the following data for a spring. Find the work done on the spring and the spring constant. Force
Displacement
0.0
0.0
0.3
137.5
0.5
275.0
0.8
412.5
1.0
550.0
1.3
687.5
1.5 1.8 2.0
825.0 1100.0
2.3
1237.5
2.5 2.8
1375.0
3.0
1650.0
962.5
1512.5
Work Done by.a Constant Force Choose from the following list:
2) Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do. A) Joel does 75% more work than Jerry. ~ B) Joel does 50% more work than Jerry.1J C.( ~ C) Je(~ 0 more work than Joel. <:0) Neither of them do an wor.
=--f
Answer: 0 Diff 2 3) You lift a 50. N physics book up in the air a distance of 1 m, at a constant velocity of 0.5 m/s. The work done by gravity is A) +50 J.
)-
J. -50 J
~
c9=-ltJO'
roo
E) +100 J
Answer: C Diff: 2
~J,
W::
F.J= tJ
C()~B
::{PN )l f J~Of.{86~
'{-50!)
ttl
4) Matthew pulls his little sister Sarah in a sled on an icy surface (assume no friction), with a force of 60.0 newtons at an angle of 37.0° upward from the horizontal. If he pulls her a distance of 12.0 m, the work he does is A) 0.333 kJ
~!W E) 185 J
Answer: C Diff: 2
F=-ftjAJ
9-=-376
:: l6NYJ2"')~3:1:J
d =-(2.M. /.~ -?
( ~:57rJ~
q
7) An auto is coasting on a level road. It weighs 10. kN. How much work is done by gravity as it moves horizontally 150. meters? Answer: zero (displacement is perpendicular to the force) Diff: 2 8) If there is no motion, can work be done on a system? A) yes, provided an outside force is applied B) yes, since motion is only relative .9J1n-since.a.sy.sl 'c is not movin has no kinetic energy ~ecause of the way work is defined \
r
w -I-.J
Answer: D Diff:1 Choose from the following list: (a) friction (b) J/s (c) dyne.cm (d) N-m (e) 550 ft.lb/s (f) mgy (g) 1/2 mv2 (h) dimensionless (i) N/m U) 3.6 MJ (k) ft.lb (I) -kx (m) weight (n) ft.lb/s
iJ - 1
9) Match joule to one of the choices above. AnswE>N-~ Diff: 1
_
~
F(N) 5
o
5
x (m)
10
6) The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown on the graph above. How much work did the squirrel do during that 10. s?
b.l~:~ 25.J .
E) zero
"OeL
e
AW<
i b~ Y.(jCW) w)
~fJ :::2~3 -
e
_
Answer: C Diff: 2 7) The force that a squirrel exerts on a nut it has found is observed over a 10. second interval, as shown on the graph above. What was the average power exerted by the squirrel? A) zero B) 1.3 W ~
D)L:21iiI E) 5.0 W
Answer: C Diff: 2
9) Consider a 0.002 gram mass hung from a spring. When an additional 15. kg is added, the equilibrium position changes by 20. cm. (a) What is the spring constant? (b) How much work is done on the spring? Difficult - Draw graph (c) If 30. kg are added, by how much will the equilibrium position change?
Answer: (a) 0.74 x 103 N/m (b) 15. J (c) 40. cm Diff:3
11) When you lift a 12. ounce (3N) beverage can from the table top to your mouth, you do approximately how much work? A) 1 Calorie d.=tJ/ B) 1 Wall C)1 1 Joule COJ erg
F::-3N
3M.
VI:: f.J e :: @j.J'fE.3JY\ks.O)
Answer: 0 Oiff:2
~6fiJ
13) You throw a ball straight up. Compare the sign of the work done by gravity w . with the sign of the work done by gravity while it goes dow~ A.) Work up is -, and the work down is -. L~ B) Work up is +, and the work down is +. it .1 ..gwor~
up
IS -,
l5)wort< Up Is +,
r
a~;1c/~::O~ t::K
crown IS +. down IS-,
")
t
~"
I
a
Answer: C Oiff:2
e ~ISo"
e =0'
Work Done by a Variable Force
1) A 10. kg mass, hung onto a spring, causes the spring to stretch 2.0 cm. The spring constant is A 5.0 N/cm B 49 N/cm It: ~ C) 0,20 N cm 0) 20. N/m 2.'1",::6,021'1'\ E) 0.0020 N/cm
~~161(~F; J~
Answer' B Oiff:2 .
@
J: r:--
F
-;}
'f
J~
([OII'j~.8~"L):: 18N
_ o0I-J la
-
---
-
0, 02.~1-
5) The~r
UQ
l{'DO NJ/II
r the curve, on a Force vs. position (F-x) graph, represents work. I B)-e . lency. F Ofll,cv" I{
Answer: A Oiff 1
Ia",
I
dr-
l(71c
If)
8) The resultant force you exert while pressing a key on the keyboard of your new computer, for a 1.0-s period, is plaited on the graph, shown.
x(m)
-5 How m~ch zero
did you do during this 1-s interval?
.J C) -25. J D) 12.5 J E) 22. J Answer: A Diff: 2 10) Daisy (a) (b) (c)
'G.:' ffI!J.-QO/~.e~:J~ 9!1.! d
raises 10.kgto a heightof2.5 meters in 2.0 seconds. How much work did she do? How much power was expended? = "I. If she raises it in 1.0s rather than 2.0s, how do the work and power change?
z.S-
w,-::W •.
-
(b,2 I
7..0}.
11) Consider a plot of the applied force (F) vs, of the curve would be
ISP
uN
M 2-.S''''_~OJ()j
-c L '-f S
3 vJ ":Sil\.Le
0~
jl
'r;
~..
-
2.P\~Pt
<
t- .. 2,0.,< ,\rJ--FJ..fJco16
p~V ,,'Z-'tS-r
Answer: (a) 0.25 kJ (b) 0.13 kW (c) same work but power doubles Diff:3 'i 7
e
_
~
4t:{ Pt("~
acement (x) for an ideal elastic spring. The slope
~:::: ~g~:~fo~~~~~a~pring constant. C) the acceleration of gravity. D) the reciprocal of the acceleration of gravity. Answer: A Diff:2 The Work-Energy
Theorem:
Kinetic Energy
1) A driver, traveling at 22. mis, slows down her 1500. kg car to stop for a red light. What work is done by the friction force against the wheels"\[. .. -VI :.u1J "Of ~ 0 M '" l~d'1
Ak e
5
Answer: 3.6 x 10 Joules Diff:2
'I,.,r- Kef - t: G l . " 1. /'II. 1Y"" z. I-
1
--z /V1V,
.~
G lIS-OOk~(O"t%-[~i~l~l2"r.J] (3 61
60u ~
Choose from the following list: (a) (b) (c) (d) (e) (f)
friction J/s dyne-cm N.m 550 ft.lb/s
mv2 (h ens ion less (i) N/m OJ 3.6 MJ (k) ft-Ib (I) -kx (m) weight (n) ft-Ib/s 2) Match kinetic energy to one of choices above. 2
Answer: (g) 1/2 mv Oiff: 1
3) The work energy theorem says A) the net work done is equal to the initial kinetic energy less the final energy. B) the net work done plus the final kinetic energy is the initial kinetic energy. the ne w one-ptus"tl1eTr'iITlalKmetlc energy IS e Inal me ICener 0) the net wor 1m la kinetic energy IS e Ina me IC energy. E) final kinetic energy plus the net work done is the initial kinetic energy.
\r "~It. 6
Answer: C o iff: 2
' " VI =: j( C f - K C( V+ K(,~ ~ff <=-
4) Car J moves twice as fast as car K, and car J has ha fthe-mass-of-ca-rK
lJ
J, compared to car K is ~
r
= 2lJ K.
i'v'I
- l M
~-'Z.-K.
~
g)42et~a1~e. E) 1 to 2.
({) ~
MJl.)J
~ ':
~G~
_
\( !(~rt\,<-}..2iJ~)2_ .!..I -i--
\
-2..
\'t\t
The kinetic energy of car
1JL
Answer: B Oiff: 2
, M <.. V'"
<-
B
5) If both the mass and the velocity of a ball are tripled, the kinetic energy is increased by a factor of
31\, '; 1\\....
A) 18.
Su, =
\)2
B) 81.
C) 6.
&!Y Answer: E
Oiff: 2
~'
iQrr.,'j)"roJL t
,
(\'I, 7), ">.
6) Is more work required to increase a car's speed from rest to 30 mph, or from 50 mph to 60 mph?
1\
Answer: 50 to 60 mph Oiff:2
1-\
~t:: ..:. M 1) ~ 2.. t-
7) Kinetic energy is proportional to speed. Answer: FALSE Oiff: 1
~ W\
iJ"'\ V 2.. -
IT IS-pl'l>par-'hIOMiJ; IIt-o~o.,.~.M.••.1 \-llS
-..!.
~
M -V' 1-
("
[V~\.,- V,,'j 1
30
01. :. ------~-
~6qL_g)1-
too :~~
~ liDO i~") - -
9) A truck weighs twice as much as a c~~ g at twice the speed of the car. Which statement is true about the truck's kinetic energy (KE) compared to that of the car? A) The truck has 4 times the KE of the car. tt. T'_- 2./VI." 1/ .". -1 l. B) All that can be said is that the truck has more KE. ..., I 2.. I'U - -uM 1) C The truck has twice t r. V-r ':- Vc.. 0) The tru _s times the KE of the r. 1".. 1I Z E) The truck has times the KE of the car. I fl\r 'U 2Ll.
J2
Answer: 0 Oiff:2 Choose from the following list: (a) friction (b) J/s (c) dyne-cm (d) N-m (e) 550 ft.lb/s (f) mgy (g) 1/2 mv2 h . ensionless i) N/m J (k) ft-Ib (I) -kx (m) weight (n) ft-Ib/s
3) Match spring constant to one of the choices above. Answer: (i) N/m Oiff: 1
la:, Ji
~:
J.f,.
JC?vc..J r r..(2 •.•..
r\.1);;-"
'7
Me.. V", L~ ~
t) ~c.. V';?-
(I1l;.
t
8) On the accompanying diagram of a pendulum, at wha~ the kinetic energy maximum? ~
I(~~~ M -U 1..
C) C
Answer: A Diff: 2
-
13) On a plot of F vs. x, what represents the work done by the force F? A) the slope of the curve B en th a C the under the curve D) the pro aXlmum force times the maximum x E) the maximum F times minimum x Answer: C Diff: 2 9) A "machine" multiplies (increases) A) time. B) energy. C
f('
--::::.-
re
tJbth~'3CalA ~vw"\~\J
Answer: D Diff: 1
I.IScrl
Ot'
eJ.t~
J or powtV.
10) You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions? \ 2c.Ai auld have skidde 4tiilies fartheC) ":;' 1) -8) IrwouICDtave-skiddecr~5 Far. eC) It would have skidded.J2 times farther. T D) It is impossible to tell from the information given. 'IVfN~
M
K
\"
11 E :::
Answer: A Diff: 2
I"'n
I : ~~
2...1), : V~ :
L.
14) A 4-kg mass moving with speed 2 mIs, and a 2-kg mass moving with a speed of 4 mIs, are gliding over a horizontal frictionless surface. Both objects encounter the same horizontal force, which directly opposes their motion, and are brought to rest by it. Which statement correctly describes the situation? A) Both masses travel the same distance before stopping. B) The 2-kg mass travels twice as far as the 4-kg mass before stopping. C) The 2-kg mass travels farther, but not necessarily twice as far. 0) The 4-kg mass travels twice as far as the 2-kg mass before stopping. E) The 4-kg mass loses more kinetic energy than the 2-kg mass. Answer: B Oiff: 2 23) A container of water is lifted vertically 3.0~en weight is 30. N, how much work was done? u.lil A)0.18kJ B) 45 J 0
90~
::>
t &=0" oil .i I
No work was done. . -O.J~ kJ -
~
Answer: 0 Oiff2 Power
retur
F:~1I.9.,
to its original position. If the total tJw;J J
..,
d
"f. •.• I pUJI'
&:(e6~
V ~WoP 'lJ;_ ~ ~D",£l;;{'o;O~+~)~) ••,,~ -:: 9 OJ 4 t 90 J~( (1)
Choose from the following list: (a) friction (b) J/s (c) dyne-cm (d) N-m (e) 550 ft-Ib/s (f) mgy 9)1/2 2 Imensionle ~(i) m U) 3.6 MJ (k) ft-Ib (I) -kx (m) weight (n) ft-Ib/s 2) Match efficiency to one of the choices above. Answer: (h) dimensionless Oiff: 1 3) Match watt to one of the choices above. Answer: (b) J/s Oiff: 1
J~fvW\-doll :.- &t'rM~
leu Lit f-tt,,)
~ ~'4lf leJ..S
e:: :;".
L I CR-~w)
JiMe •..~lblt'e-Si(va 1"-t0
7) Compared to yesterday, you did 3 times the work in one-third the time. To do so, your power output must have been "7 A) the same as yesterday's power output. V L'2 I B) one-third of yesterday's power output. IJ\ IC) 3 times yesterday's ower output. ~ 1 ~.:, U-Yl .9. s yes er ay sower ou f\ ~ -
-VI r 3 \J A ".!-
r At
D- .J!-
r-
t'T
r ':!£.-
C) '"",,me, y",'ecay', POW"o"P'1. Answer:
f.
0
0
'~h
,
6,t
Q
I
j
.<\
'::
V.
At
Diff: 2
q~.
~ W,
~
At
l\
I
::-
7
,
13) A roofer lifts supplies a height of 20. m with a hand-operated winch. How long would it take him to lift a 200. kg load, if the winch has an efficiency of 90%, and the rate at which the winch can do work is600W?
J.=20",
Answer: 73. seconds Diff: 2 V;:: V. I.
if
p= '0000
P=-YJ.\:.
"T
••
'{\J •
F<~= fcx>t:))U.&I'lI.l') = 1.',80AJ e=-'16;" r\\1't 1J,. TriP. "" ~\JJ 4. t.? -. t t-~~F;oL ""
M.-::200~ f
(.
• -
.~
~
-
e
0 '
~t~fJb",) ~ \;;~ ~~v
" I"
..1-_
4
15) Water flows over a waterfall 20.mn'rgh, at the rate of 4.0 x 10 kg/s. If this water powers an electric generator with a 40% efficiency, how many watts_of electric power can be supplied?
et ~ WM, ~~ t VJ.~efJJ,~poura~~
Answer: 3.1 MW Diff:2
'-t. 0 X/t> ~Kj/c
p", J[ t
~ ~~ 1,J,n
F~
"'::1
6,0)7Gl rtff Wb~,\
-=-
3'1 ~), e.W,,, :: @,({Jf!i.fJ{/OS'0)f
_
o¥.y'
tv;;
18) Lisa runs up 4 f1ifftlts of stairs in 22. ~econds. She weigh~510. Newtons. If each fllgtlrrises 310.cm: F:~\OI\J of •• !J1O~\J.l~I' ~~\I.l..!!:J.-\ /2. II (a) What was her work? '=- 2..2.~ '1''J~ 'j ~ loacI 0\.1 (b) What average power (watts) was required during the 22. s? .•. / _ I
t.
J :: ,
W
Answer: (a) 6.32 kJ (b) 287. watts Diff:3
=-
"&-!. ~
FJ cO,($-
(a) ""(5(OAJQZ,lfM
Lb)
p.:;r..
<3: O.
::
t :32.05
= 2.8 7 W
b~
19) A cyclist does work at the rate of 500.w while riding. With how much averag~*~rizonta does the wheel push when she is traveling at 10. m/s? Answer: 50. N Diff:2
P :: f -0
f-- J:- _- S"O -u
I
P
F;; 7.
:-SZV 'oJ
A~swer: 3.7 kW Dlff: 2
'" 2{)
e '.,] \r/:"
/ ~ "'/~ Iv.
c _ '-j -
w> \Tr (
-
'.'¥-t
,.Ir /\ I-
(,J.
.:>
rgy when he runs up a ~
_
Mj @--''jfl.8~'J.:Jb8'';6=0'
t "-t:> 0 S
I
C
e..
M:: (PO
r,J ~;::IJ e cJlwJ
~.::.':!£.::
(O'i/ .::. !.S
I<,j',%3
21) Assuming muscles are 20% efficient, at what rate is a 60. kg boy using e flight of stairs 10.m high, in 8.0 s?
V
'Sb€;fJ
0/11
6,~
()
Difficult 8) A brick and a pebble fall from the roof of an apartment building under construction. At some point the brick is moving at a speed of 3.0 mls and the pebble's speed is 5.0 m/s. If both objects have the same kin . what is the ratio of the brick's mass to the rock's mass? A 25 to 9.0 B . 0 . C) 5.0 to 3.0 D) 12.5 to 3.0 E) 12.5 to 4.5 Answer: A Diff: 2
