Question

wt whl r whl dist | %grade (al Prob 1 Thevehicle weight excluding its four wheels is 380 lbs Each wheel has a weight of 20 lbs, a radius of 0.9 ft and radiusofeyration k-0.5 ft about the wheel's axle. Determine(a) therotational speed of the wheels in rpm after it has coasted down the 70 %grade a distance of 230 t starting from rest and (b)thetime in seconds to same Neglect friction and air resistance. 380 20 | 0.9 0.5 230 70 952.6315.123 score 30 value 30 TES YES

answer is in yellow just need to know how to arrive at the solution

Answer 1

Given that w_T = w_c + w_w = 380 + (20)(5) = 480 lb h = 230 sin 18^0 = 71.07 (Take theta = 18^0) v = 73.26 pg(Takle) mu = 0.5 ft I_w = m_w k^2 = 5/32.2 k^2 rightarrow 1 w.v/r 73.2/0.5 = 146.4 rod/s energy volume T_1 + v_1 - 2 = T_2 T_2 = v_1 - 2 = w_T h = 480 times 71.07 = 34113.616 ft T_2 = 4(1/2 I_w.w^2 + 1/2 mwv^2) + 1/2 mv^2 3413.6 = 4(1/2 times 5/32.2 k^2 + (146.4)^2 + 1/2 times 5/32.2 (73.2)^2) + 1/2 (380/32.2) times (73.2)^2 3413.6 = 232961k^2 + 31616.94 k = 5.17 \r\n v^2 = U^2 + 73.2^2 = 0 = 2 times 9 times 230 a = 11.83 ft/sec^2 v = 73.2 v = 0 5.230ft] v = U + at 78.2 = 0 + 1183 times t t = 6.18 sec