Question

You are loading a toy dart gun, which has two settings, the more powerful with the spring compressed twice as far as the lower setting. If it takes 5.0 J of work to compress the dart gun to the lower setting, how much work does it take for the higher setting?

A. 20 J
B. 10 J
C. 2.5 J
D. 40 J

Answer 1

option A

Step-by-step explanation:

given,

compression for lower setting = x

work done to compress in lower setting = 5 J

compression in higher setting, x' = 2 x

work done in higher setting = ?

Work done in compression of spring at lower setting

`W = (1)/(2)kx^2`

`5 = (1)/(2)kx^2`............(1)

Work done in compression of spring at higher setting

`W' = (1)/(2)kx'^2`

`W'= (1)/(2)k(2x)^2`

`W'= 4* (1)/(2)kx^2`

`W'= 4* W`

from equation (1)

`W'= 4* 5`

W' = 20 J

Work take for the higher setting is equal to 20 J

Hence, the correct answer is option A