Engineering Spring Deformation: Potential Energy Balance Incorrect?

[MomentumBJ]

Homework Statement

In this problem, a block that slides over an inclined plane reaches a spring at the bottom and compresses it.

Relevant Equations

In the energy balance T1 + V1 = T2 + V2, where:

T1 = (1/2)m*v1^2
V1g = m*g*h1
V1e = k*e1^2 = (1/2)*(30x10^3)( 0.050 )^2 = 37.5 J <--- compressed spring

T2 = (1/2)m*v2^2
V2g = mgh2
V2e = (1/2)*k*e2^2 =(1/2)*(30x10^3)(0.050 +x )^2 = 37.5 +1500*x + 15000*x^2

^----- again compressed


Thanks !

In the initial position the spring is previously compressed, then the block adds a force, and the spring is again deformed. I think the energy balance is incorrect; the potential energy of the spring is repeated.

 

[Lnewqban]

Welcome!

Could you provide a diagram for this problem?
The spring can only accumulate energy (as it gets compressed) and return it back into the system (as it returns to its original length).

 

[MomentumBJ]

Thanks Lnewqban !, is the problem 13.68 form Beer and Jhonston. I misunderstood the question of the problem, the problem ask for additional compress, I got the complete deformation, there is not repeated term Thanks again.