How is the Equilibrium Height of a Ball Determined Using Spring Constants?

[dance_sg]

Homework Statement

Two springs are set up on a table. The longer spring has a spring constant of 225 N/m and an initial length of 42.0 cm. The shorter spring has a spring constant of 675 N/m and an initial length of 28.0 cm. How far above the table is an 8.50-kg ball when it reaches its equilibrium position?

Homework Equations

f=-kx

The Attempt at a Solution

first change cm to m, then would i find the forces of each spring, add them up for find the total force, then use that and the 8.50 kg mass to find x?

 

[Feldoh]

Yes, the springs combined must be equal to the gravitational force.

 

[dance_sg]

how exactly do i use the force that i found to solve for x? because i don't know k

 

[Feldoh]

k is the spring constant -- you have two springs and you know both their spring constants.

 

[dance_sg]

o! so just add the two up.

 

[dance_sg]

does this look right to you then?
F=-kx
F=(-225N/m x 0.42m)+(675N/m x 0.28m)
F=-94.5 + -189N
F= -283.5N
X=f/-k
X=-283.5N / -900N/m
X= 0.315