Question

A metal cylinder of mass m = 5 kg with a coaxial hole is sliding horizontally on a metal rod. A spring with spring constant ? = 500 N/m is attached to the cylinder. The other end of the spring is attached on a table at a vertical distance of ℎ = 0.3 m below the cylinder. The spring has an equilibrium length of ?0 = 0.5 m.

a) Draw a free-body diagram of the cylinder

b) Show that the horizontal force from the spring on the cylinder is: ?? = −?? (1 − (?0 /sqrt(?^2 + ℎ^2 ))

c) Show that the vertical component of the spring force acting on the cylinder is: ?? = −?ℎ (1 − (?0 /sqrt(?^2 + ℎ ^2 )))

d) What is the normal force from the rod acting on the cylinder when the spring is at its natural equilibrium length?

e) Show that the normal force ?(?) from the rod acting on the cylinder as a function of position ? is: ? = ?ℎ (1 − (?0 /sqrt(?^2 + ℎ^2)) + ??. Discuss the direction of the normal force.

Answer 1