Hooke's law states that it takes a force equal to kΔx is required to stretch a sorting a distance Δx beyond its rest length.
A) determine a formula in terms of k & Δx that represents the amount of work required to stretch a spring to a distance Δx. Hint: since the force is constant, you must use the formula Work=average force x distance
B) calculate how much energy is stored within a spring that has a spring constant of 80.0N/m and is stretched to a length of 0.35m
A)
W=∫F•dx=-∫kx•dx (limits ↓0↑x) =kx²/2
or
ΔW=F•Δx =-kx •Δx,
W=ΣΔW= Σ(-kx•Δx)=
=- kx Σ{(0-x)/2}= kx²/2
B)
W= kx²/2=80•0.35/2 =14 J
A) To determine the amount of work required to stretch a spring to a distance Δx, we can use the formula for work: Work = Force x Distance.
Since Hooke's law states that the force required to stretch a spring to a distance Δx is equal to kΔx, we can substitute this into the formula for work:
Work = (kΔx) x Δx
Simplifying this expression, we get:
Work = k(Δx)^2
Therefore, the formula in terms of k and Δx that represents the amount of work required to stretch a spring to a distance Δx is given by Work = k(Δx)^2.
B) To calculate the energy stored within a spring with a spring constant of 80.0 N/m and stretched to a length of 0.35 m, we can use the formula for energy stored in a spring:
Energy = (1/2)k(Δx)^2
Given that k = 80.0 N/m and Δx = 0.35 m, we can substitute these values into the formula:
Energy = (1/2) x 80.0 N/m x (0.35 m)^2
Calculating this expression, we find:
Energy = 4.9 J
Therefore, the energy stored within the spring is 4.9 Joules.