The machine shown is used for compacting powder. Collar C slides on plunger AB and is driv...

The machine shown is used for compacting powder. Collar C slides on plunger AB and is driven by a motor (not shown in the sketch) so that it has the oscillatory vertical motion δ = (10mm)(sin πt) where t is time in seconds. Plunger AB weighs 4N and is pressed against the powder by the spring whose end is driven by the motion of collar C. The spring has stiffness k =0.1 N/mm and 100 mm unstretched length. Assume there is no friction in the system (other than friction between individual grains of powder), and assume the motion of C is slow enough that there are no dynamic effects. Determine the largest and smallest forces the plunger applies to the powder over a full cycle of motion of C if

(a) The powder column is at its initial height h = 110 mm.

(b) The powder column is at its compacted height h = 80 mm.

Figure P3.38