A block of mass m = 3 kg pressed against a spring compressing it by an amount x

Question

A block of mass m = 3 kg pressed against a spring compressing it by an amount x = 0 4 m. The block is then released from rest and moves along a frictionless track AB and then around the frictionless loop-the-loop, of radius R = 0.6 m, as shown in the adjacent Figure The spring constant is k = 750 Figure is not drawn to scale Find me speed of the block at C at the top of the loop-the-loop. Find the radial acceleration of the block at point C at the top of the loop-the-loop. After going around me loop-the-loop me block moves along the portion BD of the track where there is friction and finally leaves the track at point 0 moving straight upward Find H the maximum height reached by me block if the magnitude of the work done by friction between points B and D is W= 15 0J first your answers in terms of any or all of the variables m, k, x, R, W and g (acceleration to gravity), and then their numerical values.

Explanation / Answer

energy balance 1/2 kx^2 = 2*mgR + 0.5*mv^2 v = (kx^2/m + 4gR)^0.5 v = 7.97 m/s radial force = 0.5mv^2/R -mg radial accl = 0.5v^2/R -g Arad = 0.5*7.97^2/0.6 -9.8 = 43.13 m/s^2 (upwards) energy balance 0.5kx^2 = mgh + W 0.5*750*0.4^2 = 3*9.8*h + 15 h = 1.53 m

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