A block is hanged from spring in a cage. Elongation in spring is $x_{1} = 42 mm$ and $x_{2} = 32 mm$ when cage moves up and down respectively with same acceleration. What is the elongation (in mm) in spring when the cage move horizontally with same acceleration.
(Elongation) $x_{1} = 42 mm$
$x_{2} = 32 mm$

Question

A block is hanged from spring in a cage. Elongation in spring is $x_{1} = 42 mm$ and $x_{2} = 32 mm$ when cage moves up and down respectively with same acceleration. What is the elongation (in mm) in spring when the cage move horizontally with same acceleration.

(Elongation) $x_{1} = 42 mm$

$x_{2} = 32 mm$

TestHub · Accepted Answer

Cage accelerating up: k x 1 ​ = m ( g + a ) ; down: k x 2 ​ = m ( g − a ) a g ​ = x 1 ​ − x 2 ​ x 1 ​ + x 2 ​ ​ = 7 , so g = 7 a and x 1 ​ = k 8 ma ​ = 4 2 ​ mm Horizontal acceleration: effective gravity g 2 + a 2 ​ = 5 2 ​ a x = k 5 2 ​ ma ​ = 8 5 2 ​ ​ × 4 2 ​ = 5 mm

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