Answer:
the elastic potencial energy stored when the spring is compressed x=8 cm is K(x)= 0.048 J
Explanation:
since the work is related with the force through
W=∫F dx
for a spring of constant k :
F=k*x , where F= compression force, x= compression length
then for a compression from 0 until x
W=∫F dx = ∫ k*x dx = k ∫x dx =1/2*k*x² - 1/2*k*0² = V(x) - V(0)
since the work depends only on the final value of compression and not on the process 1/2*k*x² represents the elastic potential energy V stored in the spring, then
V(0) = 1/2*k*0² = 0
V(x) = 1/2*k*x²
when the spring is compressed x= 8 cm = 0.08m , the elastic potencial energy is
V (x) = 1/2*k*x² = 1/2 * 15 N/m* (0.08m)² = 0.048 J
