Work = Force * Distance Work = 5 * 6 = 30 Foot Pounds.
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Work = Force * Work = Force * Distance Distance Work = 5 * 6 = 30 Foot Work = 5 * 6 = 30 Foot Pounds Pounds
Transcript of Work = Force * Distance Work = 5 * 6 = 30 Foot Pounds.
Work = Force * DistanceWork = Force * Distance
Work = 5 * 6 = 30 Foot PoundsWork = 5 * 6 = 30 Foot Pounds
Work = Force * DistanceWork = Force * Distance
Work = Force * DistanceWork = Force * Distance
Work = Force * DistanceWork = Force * Distance
How much work in ft-pounds is done How much work in ft-pounds is done lifting a 25 pound ball 8 feet?lifting a 25 pound ball 8 feet?
200.0200.0
0.10.1
A spring of natural lengthA spring of natural length
Hooke’s Law F(x) = kxHooke’s Law F(x) = kx
Tom McLean hung his 54# Tom McLean hung his 54# back pack on the scale at the back pack on the scale at the
Appalachin Trail and the Appalachin Trail and the spring stretched ¾ of an inch.spring stretched ¾ of an inch.
F(x) = kxF(x) = kx
54 = 0.75k54 = 0.75k
216/3 = k #/in216/3 = k #/in
F(x) = 72 xF(x) = 72 x
It takes Bruce McLean a force It takes Bruce McLean a force of 40 pounds to compress his of 40 pounds to compress his garage door spring ¼ inch.garage door spring ¼ inch.
F(x) = kxF(x) = kx
40 = 0.25 k40 = 0.25 k
160 = k #/in160 = k #/in
F(x) = 160xF(x) = 160x
If it takes 3 # to hold the spring If it takes 3 # to hold the spring two feet beyond its natural lengthtwo feet beyond its natural length
F(x) = kxF(x) = kx
F(2) = k2 = 3F(2) = k2 = 3
K = 3/2 thus F(x) = 3/2 xK = 3/2 thus F(x) = 3/2 x
The spring constant is 1.5.The spring constant is 1.5.
How much work was done in How much work was done in pulling the first spring to two pulling the first spring to two
feet beyond its natural length?feet beyond its natural length?
Work is the area of the green region.Work is the area of the green region.
222
00
3 3|
2 2 2
xW xdx
( )b
a
W F x dx
F=20 # keeps a spring 4 feet beyond F=20 # keeps a spring 4 feet beyond its natural length. Find k if F(x) = kxits natural length. Find k if F(x) = kx
5.05.0
0.10.1
With k=5, how much work if With k=5, how much work if stretched from natural length to 6 stretched from natural length to 6
feet beyond natural length?feet beyond natural length?A.A. 30 ft-lbs30 ft-lbs
B.B. 60 ft-lbs60 ft-lbs
C.C. 90 ft-lbs90 ft-lbs
How much work is done in pulling How much work is done in pulling the first spring two additional feet?the first spring two additional feet?
Work is the green area.Work is the green area.
244
22
3 3|
2 2 2
xW xdx
20# needed to stretch 4 ft. How 20# needed to stretch 4 ft. How much work to pull it another 4 ft?much work to pull it another 4 ft?
120.0120.0
0.10.1
Work = Force * DistanceWork = Force * Distance
Force = 9.8 * 5 = 49 NewtonsForce = 9.8 * 5 = 49 Newtons
Work = 9.8 * 5 * 0.6 = 29.4 Newton-Meters Work = 9.8 * 5 * 0.6 = 29.4 Newton-Meters (Joules)(Joules)
Work = Force * DistanceWork = Force * Distance
How much work is done if a force How much work is done if a force of 49 N is lifted 6 meters?of 49 N is lifted 6 meters?
W = 49 * 6 = 294 JoulesW = 49 * 6 = 294 Joules
If it takes 3 N to hold the spring 1.8 If it takes 3 N to hold the spring 1.8 meters beyond its natural lengthmeters beyond its natural length
F(x) = kxF(x) = kx
F(1.8) = 1.8k = 3F(1.8) = 1.8k = 3
K = 5/3 thus F(x) = 5/3 xK = 5/3 thus F(x) = 5/3 x
The spring constant is 5/3.The spring constant is 5/3.
How much work is done in pulling How much work is done in pulling that spring 1.8 additional meters?that spring 1.8 additional meters?
Work is the area that is green.Work is the area that is green.
How much work is done in pulling How much work is done in pulling that spring 1.8 additional meters?that spring 1.8 additional meters?
23.63.6
1.81.8
5 5|
3 3 2
xW xdx
23.6 2 2
1.8
5 5| [3.6 1.8 ]
3 2 6
x
55.4*1.8 27*0.3 8.16
joules
If Tom’s pack weighed 54 – 0.01x If Tom’s pack weighed 54 – 0.01x and Tom weighed 160 – 0.01x + and Tom weighed 160 – 0.01x +
200/x200/x1.11.1, how much work did he do , how much work did he do in walking the 2178 miles?in walking the 2178 miles?
Trip starts at x=10 and finishes Trip starts at x=10 and finishes when x = 2188 miles.when x = 2188 miles.
2188 1.1
10214 0.02 200x x dx
Mile PoundsMile Pounds2188 1.1
10214 0.02 200x x dx
4 N holds a spring 0.2 meters beyond 4 N holds a spring 0.2 meters beyond its natural length. Find k in F = kx.its natural length. Find k in F = kx.
20.020.0
0.10.1
Find the work in stretching that same Find the work in stretching that same spring from ½ meter to 1 meter.spring from ½ meter to 1 meter.
7.57.5
0.10.120F x
Find the work in emptying a Find the work in emptying a swimming pool filled with water.swimming pool filled with water.
Thin slabs of waterThin slabs of water
must be lifted x feet.must be lifted x feet.
Each slab weighsEach slab weighs
62.43*20*40 62.43*20*40 x for 5’x for 5’
62.43*20*8*(10-x) 62.43*20*8*(10-x) xx
(y-0)/(x-10)=40/-5(y-0)/(x-10)=40/-5
The The weightweight of one of one cubiccubic foot of foot of waterwater is is 7.48052 gallons per cubic foot times 8.3453 7.48052 gallons per cubic foot times 8.3453 pounds per gallonpounds per gallon, which equals , which equals 62.42718356 62.42718356 poundspounds of of water per cubicwater per cubic foot. foot.
Find the work in emptying a Find the work in emptying a swimming pool filled with water.swimming pool filled with water.
Thin slabs of waterThin slabs of water
must be lifted x feetmust be lifted x feet
Each slab weighsEach slab weighs
62.43*20*40 62.43*20*40 x for 5’x for 5’
62.43*20*8*(10-x) 62.43*20*8*(10-x) xx
5
1
0
62.43*800 xW dx 10
2
5
62.43*160 (10 )W x dxx
