a slider crank mechanism is shown in the figure. find the distance between the wrist pin w and the…

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})