What is the spring's length and constant in Hooke's law with buoyancy force?

[vinamas]

Homework Statement

A ball with a mass of 250 g and a volume of 126 cm^3 is hung vertically to a spring the springs length becomes 0.690 m.Then the ball is slowly submerged in water with a density of 1000 kg /m^3 then the spring's length becomes 0.620 m.

Find Buoyancy force of the water on the ball

What was the spring's original length

What is the constant (k) of the spring

Homework Equations

F=K(Lf-Li)
Fb=Fg-Wapp
Fb=density x volume x gravity

The Attempt at a Solution

I attempted to solve it by creating a the following system of equations
0.250 x 9.81 = K(0.690-Li) and 0.250 x 9.81 - 1000 x 126^-6 x 9.81 = K(0.620-Li)
Every time I solve it I get that K=17.65 and Li= 0.551 m
The answer sheet says that K=20.6 and Li = 0.561
Please help I suspect that my mistake is in the second equation but am not too sure

 

[Chestermiller]

Homework Statement

A ball with a mass of 250 g and a volume of 126 cm^3 is hung vertically to a spring the springs length becomes 0.690 m.Then the ball is slowly submerged in water with a density of 1000 kg /m^3 then the spring's length becomes 0.620 m.

Find Buoyancy force of the water on the ball

What was the spring's original length

What is the constant (k) of the spring

Homework Equations

F=K(Lf-Li)
Fb=Fg-Wapp
Fb=density x volume x gravity

The Attempt at a Solution

I attempted to solve it by creating a the following system of equations
0.250 x 9.81 = K(0.690-Li) and 0.250 x 9.81 - 1000 x 126^-6 x 9.81 = K(0.620-Li)
Every time I solve it I get that K=17.65 and Li= 0.551 m
The answer sheet says that K=20.6 and Li = 0.561
Please help I suspect that my mistake is in the second equation but am not too sure

I obtain your equations and your answers.

 

[vinamas]

Thanks!