It takes a force of 19,000 lb to compress a spring from its free height of 15 in to its fully compressed height of 10 in. How much work does it take to compress the spring the first in? (a) 1900 in.−lb (b) 950 in.−lb (c) 3800 in.−lb (d) 190,000 in.−lb


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Question Number 125048 by bemath last updated on 08/Dec/20

$I t t a k e s a f o r c e o f 19, 000 l b t o$ $c o m p r e s s a s p r i n g f r o m i t s f r e e$ $h e i g h t o f 15 i n t o i t s f u l l y$ $c o m p r e s s e d h e i g h t o f 10 i n . H o w$ $m u c h w o r k d o e s i t t a k e t o$ $c o m p r e s s t h e s p r i n g t h e f i r s t i n ?$ $(a) 1900 i n . - l b$ $(b) 950 i n . - l b$ $(c) 3800 i n . - l b$ $(d) 190, 000 i n . - l b$
Commented by mr W last updated on 08/Dec/20

$W = \frac{1}{2} \times 1 \times (\frac{1}{10} \times 19000) = 950 i n . - l b$ $\Rightarrow a n s w e r (b)$
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