Archives

Heavy Weight

What happens when to a spring if it's supporting a heavy weight?

I understand that it stretches further, but how could this occurance be calculated or explained? Is there a formula?
This is a picture of the spring and scenario I have in mind:

http://i40.tinypic.com/oilq0.jpg

In which a heavy weight would be attached to the end of the spring.

I'd really appreciate any help with this!

A spring's deformation dX is proportional to the force applied to or removed from the spring dF. And the constant of proportionality, k, is the so-called spring constant. So we have dF = k dX.

And there you are. Here's an example.

Assume k = 200 N/m is the spring constant. And there is no weight (no force) hanging from one end while the other end is affixed to a ceiling. So we have dF = 0 = k dX and thus dX = dF/k = 0/k = 0. So there is no deformation, the spring does not extend beyond its neutral length X.

Now add 100 N of weight to the hanging end and let go. We added dF = 100 N. So now we have dX = dF/k = 100/200 = 1/2 meters. And the spring has sprung, so to speak. It's now 1/2 meter extended beyond it neutral length. So if X = 2 meters when there is no weight (the neutral length), its length is now X + dX = 2 + 1/2 = 2.5 meters long with that 100 N weight attached.

OK then...let's attach another 100 N to the first one. We add 100 N; so we have dF = 100 N and the stretch, the deformation, is dX = dF/k = 100/200 = 1/2 m. Another half meter. So now the extended length is X + dX + dX = 2 + 1/2 + 1/2 = 3 meters with the two weights hanging on.

Works the other way, too. We can remove weights just as well.

Suppose we take away 50 N of weight. So now we have dF = -50 N, there are 50 Newtons less. In which case dX = dF/k = -50/200 = -1/4 meter. And now the length of the spring is:

X + dX + dX - dX = 2 + 1/2 + 1/2 - 1/4 = 2 3/4 meters.

Note. I use dF to emphasize this is a change in force, addition or subtraction, that causes a change in length dX.

Find Heavy Weight On eBay Below:

Walthers 932 10563 Great Northern Pullman Heavyweight 10 1 2 Sleeper HO
Walthers 932 10563 Great Northern Pullman Heavyweight 10 1 2 Sleeper HO
$46.73
Bachmann 13603 HO Scale 72 Heavyweight Combine Santa Fe 1524 Pullman Green
Bachmann 13603 HO Scale 72 Heavyweight Combine Santa Fe 1524 Pullman Green
$67.62
HO scale Athearn Santa Fe Ry heavyweight passenger car COACH CLERESTORY ROOF
HO scale Athearn Santa Fe Ry heavyweight passenger car COACH CLERESTORY ROOF
$8.00
Mantua Heavyweight 40 AAR Boxcar MStL Minneapolis St Louis KD couplers
Mantua Heavyweight 40 AAR Boxcar MStL Minneapolis St Louis KD couplers
$7.00
HO IHC HEAVY WEIGHT JAMES E STRATES SHOWS OBSERVATION CAR 49757 SHELL ONLY
HO IHC HEAVY WEIGHT JAMES E STRATES SHOWS OBSERVATION CAR 49757 SHELL ONLY
$8.98
HO IHC HEAVY WEIGHT JAMES E STRATES SHOWS BAGGAGE CAR 49754 SHELL ONLY
HO IHC HEAVY WEIGHT JAMES E STRATES SHOWS BAGGAGE CAR 49754 SHELL ONLY
$8.98
IHC Passenger Coach SANTA FE Heavyweight SAN VINCENTE ATSF w INTERIOR
IHC Passenger Coach SANTA FE Heavyweight SAN VINCENTE ATSF w INTERIOR
$19.96
IHC Passenger Baggage SANTA FE Heavyweight ATSF 3892 American Railway Express
IHC Passenger Baggage SANTA FE Heavyweight ATSF 3892 American Railway Express
$19.96
AHM RIVAROSSI PENNSYLVANIA RAILROADPRR HEAVYWEIGHT DINING CAR KNUCKLE COUPLERS
AHM RIVAROSSI PENNSYLVANIA RAILROADPRR HEAVYWEIGHT DINING CAR KNUCKLE COUPLERS
$8.00
WALTHERS PROTO 920 17052 PULLMAN 6 3 HEAVYWEIGHT SLEEPING CAR
WALTHERS PROTO 920 17052 PULLMAN 6 3 HEAVYWEIGHT SLEEPING CAR
$69.95
HO Scale ROYAL AMERICAN SHOWS 8 Car Circus Carnival Heavyweight Set IHC New
HO Scale ROYAL AMERICAN SHOWS 8 Car Circus Carnival Heavyweight Set IHC New
$199.92
Microscale Decal HO 87 383 ATSF Passenger Car Heavyweight Revised
Microscale Decal HO 87 383 ATSF Passenger Car Heavyweight Revised
$7.50
Microscale Decal HO 87 384 Pullman Passenger Car Heavyweight Sleeper Ass
Microscale Decal HO 87 384 Pullman Passenger Car Heavyweight Sleeper Ass
$7.50
Microscale HO Decals Santa Fe Pullman Heavyweight Sleeper Passenger Car 87 384
Microscale HO Decals Santa Fe Pullman Heavyweight Sleeper Passenger Car 87 384
$3.85
HO HEAVYWEIGHT SURGICAL UNIT COMBINE CAR US ARMY HOSPITAL WW II 89347
HO HEAVYWEIGHT SURGICAL UNIT COMBINE CAR US ARMY HOSPITAL WW II 89347
$24.98
IHC HO Scale Union Pacific Heavyweight Railway Post Office 2247 PN 49695 NIB
IHC HO Scale Union Pacific Heavyweight Railway Post Office 2247 PN 49695 NIB
$21.95
WALTHERS 932 10023 HEAVYWEIGHT 12 1 SLEEPER MAINTENANCE OF WAY MW  3003
WALTHERS 932 10023 HEAVYWEIGHT 12 1 SLEEPER MAINTENANCE OF WAY MW 3003
$55.99
WALTHERS 932 10173 HEAVYWEIGHT 36 SEAT DINER MAINTENANCE OF WAY MW  4001
WALTHERS 932 10173 HEAVYWEIGHT 36 SEAT DINER MAINTENANCE OF WAY MW 4001
$64.99
WALTHERS 932 10254 PULLMAN HEAVYWEIGHT 3 2 LOUNGE OBS  3959D PENNSYLVANIA PRR
WALTHERS 932 10254 PULLMAN HEAVYWEIGHT 3 2 LOUNGE OBS 3959D PENNSYLVANIA PRR
$109.99
WALTHERS 932 10263 PULLMAN HEAVYWEIGHT 3 2 LOUNGE OBS GREAT NORTHERN GN
WALTHERS 932 10263 PULLMAN HEAVYWEIGHT 3 2 LOUNGE OBS GREAT NORTHERN GN
$109.99
WALTHERS 932 10353 HEAVYWEIGHT CHAIR CAR SANTA FE TWO TONE GRAY
WALTHERS 932 10353 HEAVYWEIGHT CHAIR CAR SANTA FE TWO TONE GRAY
$109.99
WALTHERS TRAINLINE 931 785 60 HEAVYWEIGHT BAGGAGE CAR UNION PACIFIC UP 2237
WALTHERS TRAINLINE 931 785 60 HEAVYWEIGHT BAGGAGE CAR UNION PACIFIC UP 2237
$109.99
WALTHERS 931 789 TRAINLINE 60 HEAVYWEIGHT RPO SANTA FE  75
WALTHERS 931 789 TRAINLINE 60 HEAVYWEIGHT RPO SANTA FE 75
$84.99
WALTHERS 931 793 TRAINLINE 60 HEAVYWEIGHT RPO CNW CHICAGO  NORTHWESTERN  9432
WALTHERS 931 793 TRAINLINE 60 HEAVYWEIGHT RPO CNW CHICAGO NORTHWESTERN 9432
$79.99
IHC Premier Ho ACL Heavy Weight Diner Car with weights Sarasota 49003
IHC Premier Ho ACL Heavy Weight Diner Car with weights Sarasota 49003
$16.99
AHM Rivarossi Heavyweight Rio Grande 1351
AHM Rivarossi Heavyweight Rio Grande 1351
$11.85
HO SCALE MODEL POWER HEAVY WEIGHT EXXON CHEMICAL TANKER 8105 W BOX
HO SCALE MODEL POWER HEAVY WEIGHT EXXON CHEMICAL TANKER 8105 W BOX
$10.95
Union Pacific Two Tone Grey Heavy Weight Harriman Passenger Car Stripes 87 390
Union Pacific Two Tone Grey Heavy Weight Harriman Passenger Car Stripes 87 390
$5.95
Walthers full length heavyweight coach HO Scale Collectors Item
Walthers full length heavyweight coach HO Scale Collectors Item
$49.95
AHM IHC Rivarossi HO 1920s Heavyweight PRR Coach NIB
AHM IHC Rivarossi HO 1920s Heavyweight PRR Coach NIB
$20.00
Model Power HO Heavy Weight Conrail Caboose 98242
Model Power HO Heavy Weight Conrail Caboose 98242
$9.95
Model Power HO Heavy Weight Burlington Northern Caboose 98245
Model Power HO Heavy Weight Burlington Northern Caboose 98245
$9.95
Bachmann N Santa Fe Green 72 Heavyweight Coach With Lighted Interior 13751
Bachmann N Santa Fe Green 72 Heavyweight Coach With Lighted Interior 13751
$54.99
Walthers NIB Old Stock Pullman Heavyweight 14 Section 3958A 932 10204 HO Penn
Walthers NIB Old Stock Pullman Heavyweight 14 Section 3958A 932 10204 HO Penn
$47.48
Athearn HO Rio Grande Spanish Fork Canon Heavyweight Observation Car
Athearn HO Rio Grande Spanish Fork Canon Heavyweight Observation Car
$29.99
HO 31 IHC BLACKEND WHEEL SET 31 METAL WHEELS SET 4355 H36 IHC HEAVYWEIGHT
HO 31 IHC BLACKEND WHEEL SET 31 METAL WHEELS SET 4355 H36 IHC HEAVYWEIGHT
$48.98
HO IHC HEAVYWEIGHT SLEEPER 8 1 2 CAR ATLANTIC COAST LINE  49006
HO IHC HEAVYWEIGHT SLEEPER 8 1 2 CAR ATLANTIC COAST LINE 49006
$24.95
HO IHC HEAVYWEIGHT READING BAGGAGE CAR 49570  FREE SHIPPING
HO IHC HEAVYWEIGHT READING BAGGAGE CAR 49570 FREE SHIPPING
$24.98
Pecos River Brass HO scale Santa Fe heavyweight Chair Diner with AC 1518 15
Pecos River Brass HO scale Santa Fe heavyweight Chair Diner with AC 1518 15
$179.00
Illinois Central IC ACF 70 Heavyweight Baggage Car Custom
Illinois Central IC ACF 70 Heavyweight Baggage Car Custom
$30.00


Recently Purchased Heavy Weight:


ihc ho acl heavy weight 121 sleeper passenger car with weights, ihc ho acl heavy weight 812 sleeper passenger car with weights, athearn standard heavyweight coach baltimore and ohio paint new, n scale atlas baltimore amp; ohio bamp;o heavyweight passenger car combine, n scale atlas baltimore amp; ohio bamp;o heavyweight passenger car observation car, n scale atlas baltimore amp; ohio bamp;o heavyweight passenger car diner, ho scale great northern 6 heavyweight passenger car set, 1 ho kato heavy electric double track catenary tower kit less tension weight, ho ihc bamp;o baltimore and ohio lincoln memorial heavyweight pullman car, brass precision scale heavyweight pullman 12 section sleeper plan 3410 with air, ho athearn carstens 40th anniversary heavyweight baggage car railroad model craf, atlas heavyweight milwaukee road paired window coach, walthers heavyweight southern pacific solarium observation car, walthers heavyweight milwaukee road paired window coach, walthers heavyweight soo line 812 pullman, walthers heavyweight soo line acf baggage car, walthers heavyweight hw paired window coach 93210100 undecorated nib, nickel plate nkp heavyweight steel day coach ho athearn gently used c9, ho brass pennsylvania rr class d78cr heavyweight diner pre 47 coach yard mint, nickel plate nkp heavyweight baggage ho athearn new c9, nickel plate nkp heavyweight rpo ho athearn new c9, nickel plate nkp heavyweight steel day coach ho athearn preowned c7, ho scale ihc lot heavyweight atsf smoothside passenger cars , ho scale ihc lot of 4 heavyweight santa fe passenger cars , southern heavyweight diner dining car walthers classic rtr, southern pullman heavyweight 1012 plan3585 lot4728 walthers classic rtr decals, ho scale santa fe railroad heavyweight pullman echo lake bachmann spectrum, ho pennsylvania railroad p70 heavyweight coach kitalco modelsnibprr, brass suydam models 80 ft heavyweight pullman nr , ho rivarossi canadian national heavyweight diner 1265 with kd508 couplers, ho scale brass lambert 851 heavyweight combine passenger car h124, ho scale brass lambert 823 heavyweight diner passenger car h125, lot of6 mantua classics super heavyweight freight cars new in boxes , mantua classics super heavyweightho bamp;o water car new in box, athearn ho scale baltimore amp; ohio heavyweight rpo car 213 , 7 ihc long island lirr heavyweight passenger cars orange amp; grey ho used, ahm ihc rivarossi ho 1920s heavy weight bamp;o duplex sleeper ob exc, bachmann 13605 ho scale 72 heavyweight combine union pacific yellowgrayred, roundhouse rnd86499 ho heavyweight round roof coach spgrey 2124, roundhouse rnd86498 ho heavyweight round roof coach spgrey 2117, roundhouse rnd86497 ho heavyweight round roof coach spgrey 2093, roundhouse rnd86496 ho heavyweight round roof coachspttone grey2142, roundhouse rnd86495 ho heavyweight round roof coachspttone grey2129, roundhouse rnd86494 ho heavyweight round roof coachspttone grey2088, roundhouse rnd86493 ho heavyweight round roof coach spgreen 2156, roundhouse rnd86492 ho heavyweight round roof coach spgreen 2151, roundhouse rnd86491 ho heavyweight round roof coach spgreen 2122, roundhouse rnd86488 ho heavyweight diner up 3683, roundhouse rnd86487 ho heavyweight clerestory coach up 1233, roundhouse rnd86486 ho heavyweight round roof coach up 1322, roundhouse rnd86485 ho heavyweight baggage up 1391, roundhouse rnd86484 ho heavyweight rpo up 2057, roundhouse rnd86479 ho heavyweight round roof coach np 1321, roundhouse rnd86473 ho heavyweight clerestory coach el 1105, roundhouse rnd86472 ho heavyweight round roof coach el 1020, roundhouse rnd86470 ho heavyweight rpo el 690, roundhouse rnd86456 ho heavyweight rpo cn 7853, roundhouse rnd86455 ho heavyweight observation sf 1535, roundhouse rnd86454 ho heavyweight pullman sfhavasu, roundhouse rnd86453 ho heavyweight diner sf 1468, roundhouse rnd86452 ho heavyweight clerestory coach sf 3064, roundhouse rnd86451 ho heavyweight round roof coach sf 3005, roundhouse rnd86450 ho heavyweight baggage sf 292, roundhouse rnd86449 ho heavyweight rpo sf 128, ihc burlington heavyweight rpo, ho scale walthers 92017202 82 pullman heavyweight 121 sleeper, ho athearn 6 car heavyweight baltimore amp; ohio passenger cars all different, spectrum heavyweight great northern passenger car ho scale, bachmann 13705 hoscale 72 heavyweight coach union pacific 1115 yellowgrayred, new union 76 oil tanker ho scale 8121 union 76 model power heavy weight silver, ahm ihc rivarossi ho 1920s heavy weight pullman manhattan exc, champ decals ho brh232 nyc heavyweight pass wide gold leaf 190540 k146, champ decals ho brh236 nyc heavyweight pass narrow gold leaf 193240 k146, walthers classic heavyweight ho scale pullman 1012 plan3585 lot 4728, ho bachmann spectrum santa fe heavyweight coach road number 840, rivarossi heavyweight pullman rio grande, ho ihc 49141 burlington heavy weight coach 6166 passenger car



Comments are closed.