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 know in $\triangle CPW$: $CP = 10.4$ cm, $PW = 28.7$ cm, $\angle CPW = 180^\circ - 25.2^\circ = 154.8^\circ$

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:

$$\begin{align*} CW^2 &= 10.4^2 + 28.7^2 - 2 \cdot 10.4 \cdot 28.7 \cdot \cos(154.8^\circ)\\ &= 108.16 + 823.69 - 606.16 \cdot (-0.904)\\ &= 931.85 + 547.97\\ &= 1479.82 \end{align*}$$

Step3: Solve for CW

Take square root and round:
$CW = \sqrt{1479.82} \approx 38.5$

Answer:

38.5