Question

3.29. Un peso W' se deja caer desde una altura h sobre un resorte de cons- tante k. Calcular (a) la máxima deformación del muelle, (b) la velocidad máxi- ma alcanzada por el peso. (c) Resolver los apartados a y b suponiendo h 0. FIG. P 3.29 Y P 3.30

Answer 1

a) Let maximum deformation is x then before release, Total energy of system = Potential energy of weight w = wx because h = 0 &after maximum deformation, this whole P.E. of w converts into potential energy of spring, since w comes to rest i.e. its velocity will becomes zero rightarrow 1/2 kx^2 = wx rightarrow x = 2w/k b) let maximum velocity of block is reached when deformation is y w_y = 1/2 w/g v^2 + 1/2 ky^2 or v^2 = 2gy - gk/w y^2 or v = (2gy - gk/w y^2)^1/2 for v to be maximum, dv/dy = 0 rightarrow [1/2 (2gy - gk/w y^2)^-1/2] times (2y - 2gk/w y) = 0 rightarrow y = w/k rightarrow v_max = (2g w/k - gk/w times w^2/k^2)^1/2 = squareroot gw/k