Question

Motion of block A (W-8051b) on the inclined surface is resisted by friction (Hk0.1 and a linear spring (K-25 lb/ft). If the block is released from rest #3. with the spring unstretched, determine a) The maximum displacement of the block from its rest position b) The velocity of the block when it is 15 ft from its rest position 30° c) The time required for the block to move 15 ft from its rest position

Answer 1

Using conservation of energy P.E_1 + K.E_1 = P.E_f + K.E_f + W_f m_g x sin theta - mu m_g x cos theta = 1/2 k x^2 805 times 32.2 times sin 30 x - 0.1 times 805 times 32.2 times cos 30 times x = 1/2 times 25 times x^2 therefore x^2 - 10705.75 x/12.5 = 0 x = 856.46 ft because x_max = 856.46 ft (b) Again conservation of energy 805 times 32.2 times 15 sin 30 - 0.1 times 805 times 32.2 times 15 cos 30 - 1/2 times 25 times 15^2 = 1/2 805 times v^2 196218.75 - 33672.36674 - 2812.5/0.5 times 805 times 2 = v^2 v = 19.921 ft/sec V = 19.921 ft/sec (c) sigma f_x = 0 - m_g sin theta - 2242.74 + 25 times 856 = 8059 a = 6208.76/805 implies a = 7.713 ft/sec^2 therefore using, S = ut + 1/2 at^2 squareroot 15 times 2/7.713 = t implies t = 1.972 sec