A crane in a marble quarry is mounted on the rock walls of the quarry and is sup

Question

A crane in a marble quarry is mounted on the rock walls of the quarry and is supporting a 2900 kg slab of marble as shown in the figure. The center of mass of the 900 kg boom is located one-third of the way from the pivot end of its 15-m length, as shown.

a) Find the tension in the horizontal cable that supports the boom.

b) What is the direction of the force on the boom at the pivot end? The angle measured from horizonal is which of the following

i) Same as 50 degree

ii) Less than 50 degree

iii) Greater than 50 degree

Explanation / Answer

The equilibrium condition for torques about the pivot does not contain the unknown pivot force, and thus allows the tension to be directly determined without use of the force equations.

Thus, T sin50 = M g cos50 + mg 1/3 cos50,

or

T = (M + 1/3 m)g cot 50

   = (2900 + 1/3 × 900)(9.8 N)× cot 50

   = 26.3 kN

Same as 50 degree

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.