Answer:
2.08 J
Step-by-step explanation:
From Hook's law,
The expression for the work required to stretch a spring is given as,
W = 1/2ke²................... Equation 1
Where W = Work require to stretch the spring, k = spring constant of the spring, e = extension.
make k the subject of the equation
k = 2W/e²........................ Equation 2
Given: W = 2 Joules, e = 52-35 = 17 cm = 0.17 m
Substitute into equation 2
k = 2×2/(0.17²)
k = 138.41 N/m
First the work needed to stretch it to 45 cm
W = 1/2ke²
Where k = 138.41 N/m, e = 45-35 = 10 cm = 0.1 m
Substitute into equation above
W = 1/2(138.41)(0.1²)
W = 0.69205 J.
Also the work needed to stretch the spring to 55 cm
Given: e = 55-35 = 20 cm = 0.2 cm
W' = 1/2(138.41)(0.2²)
W' = 2.7682.
Hence the work needed to stretch the spring from 45 cm to 55 cm = 2.7682-0.69205 = 2.08 J