Question

1. a bike crank mechanism is shown in the figure. find the distance between the pedal pin ( p ) and the connecting rod center ( c ).

the distance between the pedal pin ( p ) and the connecting rod center ( c ) is ( square mathrm{cm} ). (round to ten decimal places as needed.)

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Here, \(a = 15.7\), \(b = 20.8\), and \(C = 16.7^{\circ}\).

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Step2: Calculate each term

First, calculate \((15.7)^{2}=246.49\), \((20.8)^{2} = 432.64\). Then, \(\cos(16.7^{\circ})\approx0.958\).

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Step3: Find \(c^{2}\)

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Step4: Find \(c\)

Take the square - root of \(c^{2}\). \(c=\sqrt{53.34}\approx7.3\)

Answer:

\(7.3\)