Question

suppose that 6 j of work is needed to stretch a spring from its natural length of 32 cm to a length of 48 cm. (a) how much work is needed to stretch the spring from 40 cm to 44 cm?

Answer 1

1.575 J

Step-by-step explanation:

Given:

W₁ = 6 J

x₁ = 48 cm = 0.48 m

x₀ = 32 cm = 0.32 m

x₂ = 40 cm = 0.4 m

x₃ = 44 cm = 0.44 m

W₁ =
`(1)/(2)`k(x₁² - x₀²)

6 =
`(1)/(2)`k(0.48² - 0.32²)

k = 6 × 2 ÷ 0.128

= 93.75 J/m²

W₂ =
`(1)/(2)`k(x₃² - x₂²)

=
`(1)/(2)`(93.75)(0.44² - 0.4²)

= 1.575 J