How Do You Calculate the Spring Constant with Kinetic Friction Involved?

[fender5791]

A .18 kg block sits against a horizontal spring. A 22 N force is applied by a hand and the spring is compressed .18 m. There is a coefficient of kinetic friction between the table and block of .3. Once the spring is compressed, the force holds the block in place without motion. What is k (spring constant)?

Would k = 22 N / .18 m or would k = (22N + friction force) / .18 m? When it's in the compressed state, tendency of motion is toward equilibrium, so do you calculate it with the force applied and friction both acting against the motion of the spring or just the force applied since it's still? No static friction coefficient was given, so I'm confused.

The problem before had us do a free-body diagram for the object in the compressed state, and I thought that both the force applied and friction would be acting against it, even though static friction wasn't given, so I did

Fspring = -kx = (Fapplied + uFn) and got 125 N/m

any ideas if this is correct?

 

[ehild]

As static friction was not given, draw the free body diagram when the block moves. The block moves on the effect of a constant force (22 N), and the friction acts again the motion, together with the spring force. The block will accelerate first, then decelerate and stops at the end, after 0.18 m.

Write the equation of motion and solve it, or apply the work-energy theorem.

ehild