Question

Fifteen joules of work is done on object A, which is attached to an uncompressed spring, so that all the work done goes into compressing the spring.
Sixty joules of work is done on object B, which is attached to an uncompressed spring that is identical to the spring to which object A is attached; all the work done goes into compressing the spring.
How does the compression of the spring for object B compare to the compression of the spring for object A after this work is done?

• A. The compression of the spring for object B is four times as much as it is for object A
• B. The compression of the spring for object B is sixteen times as much as it is for object A
• C. The compression of the spring for object B is two times as much as it is for object A
• D. The compression of the spring for object B is less than two times as much as it is for object A (but not the same amount)
• E. The compression of the spring for object B is the same as it is for object A

Answer 1

Answer: (C)

The compression of the spring for object B is two times as much as it is for object A

The work done in compressing the spring is stored as the potential energy of spring , given by

$U=1/2k{x}^2$

where $x=$ compression of spring ,

$k=$ spring constant ,

for object A , potential energy =work done

$1/2k{x}_A^2=15$ ...................................eq1

for object B , potential energy =work done

$1/2k{x}_B^2=60$ ....................................eq2

dividing eq2 by eq1 ,

$x_B^2/x_A^2=60/15=4$

or $x_B/x_A=2$

or $x_B=2x_A$