Question

Question 2 (15 marks total) It is a rainy day at the Tour de France (a famous bicycle race). In this stage of the race, there is a sprint finish. With about 100 m to go, the cyclists increases their speed from about 60 km/hr to 70 km/hr in a manner of seconds. The resulting acceleration is 0.6 m/s for the cyclist shown. Given the cyclist weighs 63 kg, the bike weighs 7 kg, us = 0.6, U = 0.5 and the geometry in the figure, will the rear tire slip? What is the normal force acting on each wheel? Assume that the centre of mass system (cyclist and bike) acts at G which remains at the height shown throughout the sprint. Assume the wheels have negligible mass. 1.2 m +0.4 m + 0.6 m For the problem above, answer the following questions: a) State the knowns, unknowns and assumptions for this question. (1 mark) b) Draw the free body diagram(s) required to solve the problem; include all external forces. (6 marks) c) Write the equations necessary to solve the problem. Be sure to number them clearly. DO NOT SOLVE! If necessary, provide additional details in writing about the process required to complete the solution. (8 marks)

Answer 1

(a) knowns : - weight of systemi Acer of the system i-e Moving Force. Unknowns: - Reactions at the tyres Friction force at the tyres Assumptions - No Air and water drag due to air and rain water (b) Free Body Diagram xma Gt Centre of gravity of System N,,N₂ Normal reactions at tyres fit tz fist, → Friction forces Ni ng 2 at tyres. In the Cycle, rear wheel is driving wheel that's why friction force is forward to make the Cycle move forward while, in the front wheel pushing effect due to rear driven and friction force is backward to avoid slipping.

(c) Efa=0 f - f = Ma - 1 Efy=0 Ni+N₂ = Mg - (11) EMG=0 N, 20.4+ fx 12 - Nx0.6- fx12=0 (111) EMA=0 ma x12 + Mg x 0.4 – N2X1 = 0 - (iv) we have 4- Unknown and 4 equations. These can be solved to get the values. Note : - we cannot writte friction force as f = Us Ni ? tiniting friction force or f = els N₂ , maximum friction force. In our case, we don't know the friction force is maximum or not. so, f, & MSN, and f & Us N₂ Also, as there is to any slipping between tyres and road. So, ft MkN, and ft N. we will get the values off and fn by solving above equations.
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