Concept explainers
A cyclist is riding a bicycle at a speed of 20 mph on a horizontal road. The distance between the axles is 42 in., and the mass center of the cyclist and the bicycle is located 26 in. behind the front axle and 40 in. above the ground. If the cyclist applies the brakes only on the front wheel, determine the shortest distance in which he can stop without being thrown over the front wheel.
Find the shortest distance in which the cyclist can stop the cycle without being thrown over the front wheel.
Answer to Problem 16.153RP
The shortest distance is
Explanation of Solution
Given information:
The initial speed of the bicycle is
The distance between the axles is
The location of mass center of the cyclist and the bicycle is
Calculation:
Consider the acceleration due to gravity as
Sketch the system as shown in Figure 1.
The cyclist applies the brake only on the front wheel. Hence,
Show the free body diagram of the system as shown in Figure (2).
Refer to Figure 3.
Apply the Equilibrium of moment about B as shown below.
Substitute
The initial velocity
Calculate the distance
Substitute
Therefore, the shortest distance is
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