Question

a slider crank mechanism is shown in the figure. find the distance between the wrist pin w and the connecting rod center c. the distance between the wrist pin w and the connecting rod center c is cm. (round to one decimal place as needed.)

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines states that for a triangle with sides \(a\), \(b\), \(c\) and the angle \(\theta\) opposite to side \(c\), \(c^{2}=a^{2}+b^{2}-2ab\cos\theta\).
In \(\triangle CPW\), let \(a = 11.7\), \(b=28.8\), \(\theta = 24.2^{\circ}\). We want to find the length of \(CW\) (let \(CW = x\)).
So, \(x^{2}=11.7^{2}+28.8^{2}-2\times11.7\times28.8\times\cos(24.2^{\circ})\).
First, calculate \(11.7^{2}=136.89\), \(28.8^{2}=829.44\).
Then, \(\cos(24.2^{\circ})\approx0.912\).
\(2\times11.7\times28.8\times0.912=(2\times11.7\times28.8)\times0.912 = 678.72\times0.912 = 619.09264\).
\(136.89 + 829.44-619.09264=347.23736\).

Step2: Solve for \(x\)

Take the square - root of \(347.23736\). \(x=\sqrt{347.23736}\approx18.6\).

Answer:

\(18.6\)