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 \boxed{} cm. (round to one decimal place as needed.)

Explanation:

Step1: Identify triangle sides/angle

We have triangle \(CPW\) with \(CP = 10.5\ \text{cm}\), \(PW = 27.6\ \text{cm}\), and \(\angle CPW = 180^\circ - 24.7^\circ = 155.3^\circ\) (supplementary angle).

Step2: Apply Law of Cosines

Law of Cosines: \(CW^2 = CP^2 + PW^2 - 2 \cdot CP \cdot PW \cdot \cos(\angle CPW)\)
Substitute values:

$$\begin{align*} CW^2 &= 10.5^2 + 27.6^2 - 2 \cdot 10.5 \cdot 27.6 \cdot \cos(155.3^\circ)\\ &= 110.25 + 761.76 - 579.6 \cdot (-0.9093)\\ &= 872.01 + 527.03\\ &= 1399.04 \end{align*}$$

Step3: Solve for CW

Take square root of \(CW^2\):
\(CW = \sqrt{1399.04}\)

Answer:

\(37.4\ \text{cm}\)