Se
ec 7.6
Work
A. Before Cllass Video
o Example
es
What are the
e work units o
of measureme
ent? 1. W
orce * Distancce. Find the w
work done in llifting a 15 lbs of books offf the floor 2. If the force iss constant, then Work = Fo
to tthe top of a taable which is 4 feet high. A force of 3 x 2  4 x  2 pounds actts on a particlle which is loccated a distan
nce from tthe origin. Ho
ow much 3. A
work is done in moving it from x  1 to x  3 ? 1
Dessiré Taylor Math 12
242 4. A 15 foot rope is lifted from the ground into the air by pulling it at constant a speed. The rope weighs 1.5 lbs/ft. How much work was done lifting the rope 15 feet? 5. A 7 lb bucket of water is lifted from the ground into the air by pulling 15 feet of rope at constant a speed. The rope weighs 1.5 lbs/ft. How much work was done lifting the bucket and rope? 2
Desiré Taylor Math 1242 B. Work Don
ne by Lifting
Unnits: Wo
ork = Force
e x Distancce Force = Masss x Accelerration Foorce Work English E
Poound (lb) Metric M
Neewton (N)*
Foot‐po
ound (ft‐lb)
Newton‐meter (N‐m) or Joule (J) * N
Newton = 9.88 kg
Exaamples: 1.) How much w
work is done in lifting a 60 kg object 3 m
m up? 2.) How much w
work is done in lifting a 60 lb object 5 ftt up? 3.) Jessica McClure became famous at the
e age of 18 m
months after ffalling into a w
well in the baackyard of herr home in Texas on Occtober 14, 198
87. Between tthat day and October 16, rrescuers worked for 58 ho
ours to free "B
Baby Jessica" from
m the eight‐in
nch‐wide welll casing 22 fee
et below the ground. If aa rescue workker pulled Jesssica from the well usin
ng a rope with
h weight 3 lb//ft, and assum
ming that Jesssica weighed 25 lb, how m
much work waas done in pulling Jessica and the ro
ope out of the
e well. 3
Dessiré Taylor Math 12
242 4.) A 2 lb. buckett is lifted from the top of a 10
0 ft. tall buildin
ng by a cable a t constant a sp
peed. The cable weighs 0.1 lb./ft. a. How much work is needed tto lift the buckket and rope frrom the groundd to the top off the building? b. How much work is needed tto lift the buckket and rope frrom the groundd half way up tthe building (frrom 0 ft. to 5 ftt.)? c. How much work is needed tto lift the buckket and rope th
he rest of the w
way to the top of the buildingg (from 5 ft. to
o 10 ft.)? 4
Dessiré Taylor Math 12
242 C. Work Don
ne by Springs
FSpring = k Ho
ooke’s Law
w: F  kx ↓ Force
e •
↓
Spring Con
nstant xx ↓
↓ D istance Sttretched
B
Wo
ork: W   kx dx where A = the pooint stretched from and B == the point sttretched to A
Adjjustments Nattural Length: Remember tto make an ad
djustment forr the natural length of a sp
pring where aappropriate. Uniits: Since the
e units for forcce and work aare both base
ed on lengthss in feet or meeters, we havve to convert any other units (such as cm
m or inch) to ffeet or meterr before starting any calcu lations. eter  100 cm
m
member, me
Rem
 x cm
m
x
x
metter , similarlyy, ft  12 in  x in  ft 12
100
Exaamples: 1.) (Type 1: Forrce given, Wo
ork asked) A force of 40 N
N is required tto hold a sprin
ng that has beeen stretched
d from its natural position of 10 cm
m to a length o
of 15 cm. How
w much workk is done in sttretching the spring from 1
15 cm to 18 cm? 5
Dessiré Taylor Math 12
242 Exaamples: 2.) (Type 2: Wo
ork given, Wo
ork/Force askked) 7 Joules of work is reqquired to streetch a spring ffrom its natural length of 20 cm to 50 cm. uch work is do
one in stretch
hing the sprin
ng from 25 cm
m to 35 cm? a. How mu
b. How farr beyond its natural length will a force o
of 25 N stretcch the spring?? 6
Dessiré Taylor Math 12
242 D. Work Don
ne by Pum
mping
Waater Density =
= 1000
kg
m3 

Waater Weight = Water Density x Gravity =
= 1000
Sincce Newton = kg  
kgg
m
 9.8 2   9800 2 2
3  
m   s 
m s kg  m
N
, Water Weight =
= 9800 3
2
m
s
Waater Weigh
ht: 
Metricc Units: 98800
N
m 3 
EEnglish Unitts: 62.5
lbb
ft 3
A Cylind
drical shaped tank is locateed 5 ft undergground. If thee tank is complettely full of waater, how mucch work is req
quired to pum
mp all of the water out of the tankk to ground leevel? Because
e of the propeerties of wateer pressure, the distance that the water is being pumpeed (lifted) willl be the distaance from thee surface of the wate
er to the locaation it is pum
mped to. How
wever, during the process of pump
ping, the wateer level will go down, and hence the disstance will continuo
ously change . So, to fin
nd the total aamount of wo
ork done, we will find the w
work done in pumpingg one “slice” of water out of the tank, aand then add
d up all of the slices. Consider a slice madee at a random
m height y. The worrk done in pu mping out this slice can bee calculated b
by: WSLICE = Fo
orce • Distancce And we know that Foorce = Volumee of the Slice • Water Weiight, so WSLICE = Volume • W
Water Weight • Distance
Since the slice has a ccylindrical shaape,  Volume of thhe Slice =  Water Weighht =  Distance watter is lifted = 7
Dessiré Taylor Math 12
242 WSLICE = Volume • Water Weight • Distance WTOTAL = 8
Desiré Taylor Math 1242 Exaamples: 1.) An inverted cone shaped tank has dim
mensions: heiight C = 12m,, radius A = etely full, find
d the work done in pumpinng all the 4m. If the taank is comple
water out off the tank to aa level of B = 3m above the top of the ttank. 9
Dessiré Taylor Math 12
242 Rulle for Pumpiing: B

General Tank: W    Area of Slice  Watter Weight   C  y  dy A
B

Water Weightt   C  y  dyy
Tank with a circularr cross sectio
on: W    Radius off Tank   W
2
A
Where o A is the “bottom
m level” of w
water to be rremoved o B is the “top levvel” of waterr to be remo
oved o C is the level that water is p
pumped to 2.) A trough shaaped tank hass dimensions: height a = 4
4ft, b = 8ft, hh = 12ft and c = 20ft. If the tank is completely full, find the work done inn pumping all the water out of the taank, over the side of the taank. 10
Dessiré Taylor Math 12
242 3.) A hemispherical shaped ttank has dime
ensions: r = 1
10m. If the taank is completely ffull, find the w
work done in pumping all the water ou t of the tank, to a distance of 2m above the to
op of the tankk. 11
Dessiré Taylor Math 12
242 4.) A tank in the shape of a triangular priism (see figurre) has the fo llowing dimensions: Height B = 1
15m, Length C
C = 20m, and Width D = 100 m. The tank is ffilled to the to
op with water. Find the w
work required to pump all of the waater out of tan
nk to a heightt A = 5m abovve the top of the tank. 12
Dessiré Taylor Math 12
242 5.) A tank in the shape of a cylinder on itts side (see figgure) has the following dim
mensions: He
eight H = 15m
m and Radius R = 5m. The tank is filled to the top with watter. Find the w
work required to pump alll of the e top of the taank. water out off a hole in the
13
Dessiré Taylor 242 Math 12