The answers are physically and mathematically reasonable, since both have the <em>same</em> order of magnitude of the <em>external</em> forces shown in the figure.
<h3 /><h3>Procedure - Determination of forces acting on a rigid body</h3>
Let be a system at equilibrium, which mathematically is represented by the following formulas:
(1)
(2)
<h3>a) Force acting on the crane at point A</h3>
We construct equations around points A and B by Newton's Laws and D'Alembert Principle:
<h3>Point A</h3>
(3)
<h3 /><h3>Point B</h3>
(4)
<h3 /><h3>Entire system</h3>
(5)
(6)
The solution of the <em>entire</em> system is:
,
and
.
The magnitude of the force acting on the crane at point A is determined by the Pythagorean theorem:


The force acting on the crane at point A has a magnitude of approximately 67268.128 kilograms-force. 
<h3>b) The force acting on the crane at point B</h3>
The force acting on the crane at point B has a magnitude of approximately 66000 kilograms-force.
<h3>c) Order of Magnitude sense-making</h3>
The answers of parts (a) and (b) have an order of magnitude of
, the same order of magnitude of the external forces shown in the figure. Hence, those answers are physically and mathematically reasonable.
<h3>Remark</h3>
Figure is missing. The statement is incomplete. Complete statement is presented below:
<em>A 3000 kilograms-force is supporting a 10000 kilograms-force crate. The crane pivots about point A and is at rest pressed against a support at B. </em>
<em>(a)</em><em> FInd the force acting on the crane at point A. </em>
<em>(b)</em><em> Find the force acting on the crane at point B. </em>
<em>(c)</em><em> Use order of magnitude sense-making to determine the reasonableness of your answers to parts (a) and (b). Hint: consider how the lever arm to the crate is much different than that to other points. </em>
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