The tower crane is used to hoist


The tower crane is used to hoist the 2-Mg load upward at constant velocity. The 1.5-Mg jib BD, 0.5-Mg jib BC, and 6-Mg counterweight C have centers of mass at G1, G2, and G3, respectively. Determine the resultant moment produced by the load and the weights of the tower crane jibs about point A and about point B.

The tower crane is used to hoist

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

Solution:

Show me the final answer↓

We can draw a simplified diagram showing the mass of each section, and the distances to calculate the moments at points A and B.

The tower crane is used to hoist

Notice how for both points A and B, the height does not factor into the moment equations because all forces are acting vertically, not horizontally. It also means that the moment at A is equal to the moment at B.

\circlearrowright M_A=(-6000)(9.81)(7.5)-(500)(9.81)(4)+(1500)(9.81)(9.5)+(2000)(9.81)(12.5)

M_A=-76027.5\,\text{N}\cdot\text{m}\circlearrowright

M_A=76027.5\,\text{N}\cdot\text{m}\circlearrowleft\,\text{(Counterclockwise)}

 

Again, note that the moment created at point A is equal to the moment created at point B. Thus,

M_B=76027.5\,\text{N}\cdot\text{m}\circlearrowleft\,\text{(Counterclockwise)}

 

Final Answer:

M_A=M_B=76027.5\,\text{N}\cdot\text{m}\circlearrowleft\,\text{(Counterclockwise)}

 

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 4, question 4-18.

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