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CBSE Class 11-science Answered

springs A and B are identical except that A is stiffer than B .in which spring is more work expended if 1)they are streched by the same amount 2) they are streched by the same force?
Asked by ana2003mika | 26 Feb, 2020, 08:24: PM
answered-by-expert Expert Answer
If WA is workdone by spring-A, then we have, WA = (1/2)kA xA2 .....................(1)
 
where kA is spring constant of spring-A
 
If WB is workdone by spring-B, then we have, WB = (1/2)kB xB2 .....................(2)
 
where kB is spring constant of spring-B
 
Both springs are stretched by same extent, then we have,  xA = xB ....................(3)
 
since spring-A is stiffer than spring-B, kA > kB  ....................(4)
 
Hence we get from (1), (2) , (3) and (4) ,   we get ,  WA > WB
 
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force FA applied to spring-A ,  FA = kA xA ...........................(5)
 
force FB applied to spring-B ,  FB = kB xB ...........................(6)
 
If both springs are stretched by same force, then FA = FB ..................(7)
 
Since kA > kB , using eqns.(5), (6) and (7), we get xA < xB  ....................(8)
 
 
Hence workdone by spring-A, WA = (1/2) kA xA2 = (1/2) FA xA  ...............(9)
 
Hence workdone by spring-B, WB = (1/2) kB xB2 = (1/2) FB xB ..................(1)
 
now using eqn.(7), (8), (9) and (10), we get  WA > WB
 
 
 
 
Answered by Thiyagarajan K | 26 Feb, 2020, 09:59: PM

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