Answer:
The maximum compression of the spring is 0.154 m
Explanation:
From the energy theorem, we have that the net work equals the change in kinetic energy. If x is the vertical height that the block slides when compressed by a spring, we have to:
m*g*(d + x)*sin*(30°) - 0.5*k*x^2 = 0
This equation equals zero because there is no change in block speed. Replacing values:
5*9.8*(1.3+x)*0.5 = 0.5*3000*x^2
24.5*(1.3+x) = 1500*x^2
1500*x^2 - 24.5*x - 31.9 = 0
solving this quadratic equation we have that x = 0.154 m