The cutting arm of the paper cutter is pinned about a fixed axis at O , and its angle rela...

The cutting arm of the paper cutter is pinned about a fixed axis at O , and its angle relative to the horizontal is measured by ϕ .A linear elastic torsional spring at O with constant kt keeps the arm from falling when not in use. Model the cutting arm as a uniform slender bar of length L = 20 in. and weight W = 2.5 lb. Neglect friction in the pin at O.

Determine the value of the torsional spring constant kt so that when the cutting arm is released from rest at ϕi = 70°, it reaches ϕf = 15° with zero angular speed. Assume that the torsional spring is undeformed when ϕ = 90°.

Figure P7.47