Determine the Length of the Crankshaft AB


Determine the Length of the Crankshaft AB by first formulating a Cartesian position vector from A to B and then determining its magnitude.

Determine the Length of the Crankshaft AB

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

Let us first write the Cartesian position vector from A to B like so:

r_{AB}=((400\,+\,125\text{sin}(25^0))i\,-\,125\text{cos}(25^0)j)

(Here, we wrote the components of the x-axis and y-axis separately)

 

Simplifying the terms inside the brackets gives us:

r_{AB}=\left\{452.83i\,-\,113.3j\right\} mm

 

Now, we can find the length by finding out the magnitude of r_{AB} like so:

r_{AB}=\sqrt{(452.83)^2\,+\,(-113.3)^2}

r_{AB}=467 mm

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-86.

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