Question

A rider on a high speed bike leans at angle of 57° to the horizontal on a horizontal curved road of radius 100 m. Two possible speed rated accidents in this situation are: (1) skidding (sliding) off the way or (2) rolling over or tumbling down. Analyze the force diagram representative of the dynamics of the system and then determine The safest speed to prevent accident (2): V = km/h Calculate the maximum coefficient of friction to ensure safety at the speed calculated above: = You are required contribute your informed opinion to two other students discussing the safety of the bike with respect to the mass of the bike/biker system. If me = 200 kg, and m) = 182 kg and they are both taking a curve of the same radius above under different friction conditions (coefficient of friction has been modified to js = 0.49) Calculate the safest speed for Bike A: Ve= km/h and Bike B: 1) = km/h The angle each bike leans with to the horizontal under the new conditions is . for Bike A and O for Bike B

please help

Answer 1

This is a very nice question. I have solved it fully for your complete understanding.

solm: AN Mv2 r ots f ng

The 4 Forces acting on the bike+ rider are : 1. Mg downwards from Centre of Gravity. 2. N upwards from the point of contact. 3. f= MN Friction radially inwards from point of contact. 4. MV7r Centrifugal force radially outward from centre of gravity. 1, out worlds. To prevent sliding Mv3 s R - 2 (f=pal mmg). s M - of mong MR.g To prevent Rolling => < over, MW/R bsinsts 2 Mo = 0 Mv² h sino boos Q = & Coss7° mg x hi R of the sinsi yg selftassat V - Rg lots Cots7° > V= 100 x 9.81 x Cot 57
t
→ V = 25:29 m/s. = 91199 bambur Am From He 0:65 2 ma=200 mb=182 M 0:49. from Em Max. Velocity depend on Man. Does not V4 A meg Namax 0:49 X100 x 9.8) > Vmax = 21.92m/s. > Va=Nb 78.9 km/tr Am From Er Mv2 h sino h loso Muz mg h Rgh. Rgh Jono = -3 v2 (AMRg Mega => tamo 8:49

. OA OB = 63.99 Am A. force for Centrifugal 200 x12 *(2192)2 FCA M4.62 R 100 >> FCA 960.97 N we com see both are almost Sonne, Frictional force for A. 0:49 x 200X9.81 f MN MMA mang The small because defference is f = 961.38 w of hounding of values in calculation. B. Centrifugal force for B 182 x(21.92)? ra fool MB. R 100 N Farb = 874.5 An frictional force for B fB = MN = MMB 0:49 x 182 x 9.87 maga fB = 879.8 an

hope the solution is clear and it helps your understanding. ??. Best wishes.