Design problem Need clear answer please!! ENGR 2030 Engineering Dynamics Design

Question

Design problem
Need clear answer please!! ENGR 2030 Engineering Dynamics Design Problem Set 1 Due Monday, February 12 Instructions: Below are several design problems which are intended to give you the opportunity to apply the dynamics principles we have learned about to real-world situations. Choose one of the problems that you would like to solve. You may do the problem individually, or work with a partner. Your answers should be done on engineering computation paper and include all necessary information, assumptions and diagrams. Attach print-outs of any reference material, (besides the textbook), that you rely on for your analysis. Be thorough in your answers and show all of your work. Remember, if I can't read it or follow it, you don't get credit for it.

Explanation / Answer

for the given scenario of the bike problem
let the cente ro fmass of the bike + rider be at height h from the ground
let maximum acceleration be a
then
maximum torque at maximum accelration = T
now, radius of tyre = R
then from force balance friction force = f
then
also, distance of the hind tyre from the center of mass, horizontally be t

T - f*R = Ia/R
also

for the forward tyre not to lift
mg*t > f*R
hence
mg*t - m*a*(h - R) > (T - Ia/R)

aslo, from force balance
f = m*a ( where m is mass of bike + rider)
hence
T = Ia/R + m*a*R
hence
mg*t - m*a*(h - R) > ( m*a*R)
g*t > a(R + h - R)
g*t > a*R
a < gt/R

for a typical bike
t = 1 m
R = 0.5 m
hence
a < 4.9 m/s

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