Question

A cylinder of mass m is free to slide in a vertical tube. The kinetic friction force between the cylinder and the walls of the tube has magnitude f. You attach the upper end of a lightweight vertical spring of force constant k to the cap at the top of the tube, and attach the lower end of the spring to the top of the cylinder. Initially the cylinder is at rest and the spring is relaxed. You then release the cylinder. What vertical distance will the cylinder descend before it comes momentarily to rest? Express your answer in terms of the variables m, f, and constants g, k.

Answer 1

Answer:

x = (mg-f)/k

Explanation:

there are three forces acting on cylinder in a tube, (1) force due to spring = -kx (2) force due to friction = f (3) force due to gravity.

we want to calculate an instant when all three forces acting on mass cancel and there is 0 net force  and cylinder momentiraly comes to stop.

let's write it in mathematics.

kx+f-mg=0 (kx is positive because it is upwards and that is how we have setup our coordinate axis in this problem).

solving for x gives.

x = (mg-f)/k.