Best solution? for work done on a spring.

[Tyrannosaurus_]

Homework Statement

GIVEN: Force constant (k) = 170N/m. Displaced 10cm (0.1m) from equilibrium position.
REQUIRED: Find the work done on the spring.

Homework Equations

Solution 1 uses: W = ΔE, & (elastic energy} E_e = 0.5(k)x², where k is the constant, and x is displacement from equilibrium position.

Solution 2 uses: W = F(Δd), & (elastic/spring force} F_e = kx, where k is the constant, and x is the displacement from the equilibrium position.

The Attempt at a Solution

Please evaluate these solutions & choose the best. Please tell me why. Please correct my misunderstandings. Thanks!

SOLUTION 1.
w = ΔE
w = E_efinal - E_einitial
w = 0.5(k)x_final² - 0 {because initial the spring is at the eq. position.)
w = 0.5(170N/m)(0.1m)²
w = 0.85J

SOLUTION 2.
w = F(Δd)
w = F_e(Δd)
w = kx(Δd)
w = (170N/m)(0.1m)(0.1m)
w = 1.7J


Which solution is better, and why? (It's obvious why the values are different.)
Please help me understand why/where these approaches are best. (I understand calculus, but I need to understand these concepts, before I use calculus to evaluate.)

 

[mfb]

The second method is wrong, F is not constant during the displacement.

 

[Tyrannosaurus_]

Thanks very much! ! !

Is there a resource you can point me to that explains why the force is not constant? Or, can you tell me why?

I'm not trying to be difficult, I just want to understand. I really want to be an engineer.

 

[mfb]

Is there a resource you can point me to that explains why the force is not constant? Or, can you tell me why?

Just check how you calculated the force at 10cm excitation. What is the force at an excitation of 5cm?

 

[Saketh#]

(elastic/spring force} Fe = kx, displacement x varies.Hence force is not constant