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

Answer:

option A

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

$W = \dfrac{1}{2}kx^2$

$5 = \dfrac{1}{2}kx^2$............(1)

Work done in compression of spring at higher setting

$W' = \dfrac{1}{2}kx'^2$

$W'= \dfrac{1}{2}k(2x)^2$

$W'= 4\times \dfrac{1}{2}kx^2$

$W'= 4\times W$

from equation (1)

$W'= 4\times 5$

    W' = 20 J

Work take for the higher setting is equal to 20 J

Hence, the correct answer is option A