Rigid-Body Work and Energy - Example Problem 8.5-5

 

The braking system on a new concept bicycle is being tested. Both wheels of the bike have a diameter of 26 inches and weigh 1 lb. Most of that weight is concentrated on the circumference of each wheel. The bike frame weighs 2 lb and the rider weighs 140 lb. The braking system has the ability to apply a 10 lb-ft moment to each wheel when engaged. If the bike is traveling at 25 mph, what is the minimum stopping distance? You may assume that the wheels are rolling without slip.

 

 

Given:

• r = 13 in
• W_W = 1 lb
• W_F = 2 lb
• W_R = 140 lb
• M_f = 10 lb-ft
• v₁ = 25 mph = 36.7 ft/s
• v₂ = 0
• state 1 = when the system's speed is 25 mph
• state 2 = when the system comes to rest

 

Find:

• d

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

What is the angular speed of the wheels at state 1?

 

ω₁ = rad/s