Introduction to statics The essential concept in engineering statics is that in
ID: 1492308 • Letter: I
Question
Introduction to statics
The essential concept in engineering statics is that in order for an object to be stationary, the sum of forces on it must be zero, which is quantified by the equation
?F=0
In dynamics, the sum of forces would instead equal the product of mass and acceleration which allows for moving objects. Note the force F is bolded to indicate a vector quantity with both magnitude and direction. Vectors, and vector equations, can be resolved into their x and y components to more easily handle them. The sum of forces then becomes
?Fx=0 and ?Fy=0
where Fx and Fy represent the x and y component of forces, respectively. These equations are then applied to an object in order to solve for desired unknown quantities. Consider, for example, solving for the tensions in ropes AB and AC that support the 50 kg crate in Figure 1. The connecting ring in the middle is subject to the force of the crate’s weight, as well as the tensions TAB and TAC in the supporting ropes. The force of the crate’s weight is
W=mg
and will be directed downward. Note that the weight paradoxically involves the product of a mass and acceleration despite the fact that nothing is moving in this problem. The tension forces in each rope will be point in the same direction as the ropes themselves.
Apply the sum of force equations by resolving the unknown tensions TAB and TAC into their x and y components using the given geometry in Figure 1. Notice that TAB and TAC will appear in both equations, requiring solving the equations simultaneously. Solve for the unknown tensions, being sure to express all equations with consistent units.
Explanation / Answer
on mass m,
total Fy = 0
Tad - mg = 0
Tad = mg .........Ans
on joint A,
total Fx = 0
Tab cos30 - Tac (4/5) = 0
Tab = 0.924 Tac
total Fy = Tabsin30 + Tac (3/5) - Tad = 0
putting Tad = mg and Tab = 0.924Tac
0.924 Tac sin30 + 0.6 Tac = mg
Tac = 0.942mg ..............Ans
and Tab = 0.924 x 0.942mg = 0.87mg .......Ans
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