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= Your friend has joined the e-vehicle movement by outfitting their road bike with an electric motor on the front hub. Their bike has wheel base of length L = 3.75 ft. The combined center of gravity of the bike-rider system height h 3 ft and equidistant to each wheel. The total weight of the bike and rider is w = 240lb. The motor outputs a torque of, M = 100 ft-lb. The wheels have a radius of L/3 ft. If the rider does not pedal assist, the bike is advertized to be able to travel 15mph on flat level ground. However your friend reports that on steep hills, the front tire will sometimes slip rather than maintain traction. Assume the contact point with the ground has a coefficient of static friction of g 0.67 and kinetic friction k 0.45. - = At an angle of 0 degrees, what is the maximum friction force availabe at the front wheel? number (rtol=0.01, atol=1e-05) N What is the maximum incline the bike can climb assuming no pedal assist? Assume the location of the combined cg remains the same. The bike is a machine (frame) but keep in mind the front wheel is not rigidly attached (it is free to rotate!), so any point moment applied to the front wheel is not transfered to the frame. Fol = number (rtol=0.01, atol=1e-05) What angle of inclide will cause the rider's combined center of gravity cause the bike tip backwards? Otip number (rtol=0.01, atol=1e-05) Omin T

= Your friend has joined the e-vehicle movement by outfitting their road bike with an electric motor on the front hub. Their bike has wheel base of length L = 3.75 ft. The combined center of gravity of the bike-rider system height h 3 ft and equidistant to each wheel. The total weight of the bike and rider is w = 240lb. The motor outputs a torque of, M = 100 ft-lb. The wheels have a radius of L/3 ft. If the rider does not pedal assist, the bike is advertized to be able to travel 15mph on flat level ground. However your friend reports that on steep hills, the front tire will sometimes slip rather than maintain traction. Assume the contact point with the ground has a coefficient of static friction of g 0.67 and kinetic friction k 0.45. - = At an angle of 0 degrees, what is the maximum friction force availabe at the front wheel? number (rtol=0.01, atol=1e-05) N What is the maximum incline the bike can climb assuming no pedal assist? Assume the location of the combined cg remains the same. The bike is a machine (frame) but keep in mind the front wheel is not rigidly attached (it is free to rotate!), so any point moment applied to the front wheel is not transfered to the frame. Fol = number (rtol=0.01, atol=1e-05) What angle of inclide will cause the rider's combined center of gravity cause the bike tip backwards? Otip number (rtol=0.01, atol=1e-05) Omin T

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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h M W AVY NAVY
Transcribed Image Text:h M W AVY NAVY
Your friend has joined the e-vehicle movement by outfitting their road bike with an electric motor on the front hub. Their bike has wheel base of length L = 3.75 ft. The combined center of gravity of the bike-rider system height h = 3 ft and equidistant to each wheel. The total weight of the bike and rider is w = 2401b. The motor outputs a torque of, M = 100 ft-lb. The wheels have a radius of L/3 ft. If the rider does not pedal assist, the bike is advertized to be able to travel 15mph on flat level ground. However your friend reports that on steep hills, the front tire will sometimes slip rather than maintain traction. Assume the contact point with the ground has a coefficient of static friction of µ = 0.67 and kinetic friction μ = 0.45. At an angle of 0 degrees, what is the maximum friction force availabe at the front wheel? Fol number (rtol-0.01, atol=1e-05) N What is the maximum incline the bike can climb assuming no pedal assist? Assume the location of the combined cg remains the same. The bike is a machine (frame) but keep in mind the front wheel is not rigidly attached (it is free to rotate!), so any point moment applied to the front wheel is not transfered to the frame. = Omin number (rtol-0.01, atol=1e-05) What angle of inclide will cause the rider's combined center of gravity cause the bike tip backwards? Otip= number (rtol=0.01, atol=1e-05) Assuming now that the rider has the leg-strength to hold the bike on any incline (torque at the rear wheel matches the component of the weight along the slope). What is the steepest angle that the motor can continue to assist without slipping if we assume that the motor has only binary (on or off) control? - i.e. what is the angle at which attempting to apply the motor torque at the front wheel causes slipping? N.B. the solution does not have an algebraic form and will need a numerical method to find! Omaz= number (rtol=0.01, atol=1e-05) €
Transcribed Image Text:Your friend has joined the e-vehicle movement by outfitting their road bike with an electric motor on the front hub. Their bike has wheel base of length L = 3.75 ft. The combined center of gravity of the bike-rider system height h = 3 ft and equidistant to each wheel. The total weight of the bike and rider is w = 2401b. The motor outputs a torque of, M = 100 ft-lb. The wheels have a radius of L/3 ft. If the rider does not pedal assist, the bike is advertized to be able to travel 15mph on flat level ground. However your friend reports that on steep hills, the front tire will sometimes slip rather than maintain traction. Assume the contact point with the ground has a coefficient of static friction of µ = 0.67 and kinetic friction μ = 0.45. At an angle of 0 degrees, what is the maximum friction force availabe at the front wheel? Fol number (rtol-0.01, atol=1e-05) N What is the maximum incline the bike can climb assuming no pedal assist? Assume the location of the combined cg remains the same. The bike is a machine (frame) but keep in mind the front wheel is not rigidly attached (it is free to rotate!), so any point moment applied to the front wheel is not transfered to the frame. = Omin number (rtol-0.01, atol=1e-05) What angle of inclide will cause the rider's combined center of gravity cause the bike tip backwards? Otip= number (rtol=0.01, atol=1e-05) Assuming now that the rider has the leg-strength to hold the bike on any incline (torque at the rear wheel matches the component of the weight along the slope). What is the steepest angle that the motor can continue to assist without slipping if we assume that the motor has only binary (on or off) control? - i.e. what is the angle at which attempting to apply the motor torque at the front wheel causes slipping? N.B. the solution does not have an algebraic form and will need a numerical method to find! Omaz= number (rtol=0.01, atol=1e-05) €
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