Equilibrium of Tensions A 100-lb weight hangs from a string as shown in the figure. Find the tensions T1 and T2 in the string.
To find: To find the tensions
Answer to Problem 73E
The tension
Explanation of Solution
Given:
Tension
Calculation:
Consider a coordinate system with origin
Figure (1)
As the system is in equilibrium, the resultant of forces acting in horizontal and vertical direction should be zero.
Sum of vertical components of tensions
Figure (2)
Angle made by
The horizontal component of the vector v, which makes angle
of
Therefore, horizontal component of
Vertical component of vector v, which makes angle
Therefore, vertical component of
Angle made by
So, horizontal component of
Vertical component of
Sum of horizontal components of tensions
Sum of vertical components of tensions
Put values of cosine and sine terms in equation (1)
Use values of cosine and sine terms in equation (2).
Solve equation (3).
Substitute
Solve further,
Substitute
A vector v is represented as,
Therefore, Tension
Substitute
Tension
Substitute
Thus, the tension
Chapter 9 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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