A box is suspended by two ropes, each making an angle of 30° with the vertical. If the box weighs 100 N, what is the tension in each rope?
Options
A
50 N
B
57.74 N
C
100 N
D
43.3 N
Answer & Analysis
Answer
B
Analysis
To find the tension in each rope when a box
is suspended, we can use the equilibrium condition for the vertical components
of the tension.
1. The weight of the box is given as 100 N.
2. Let be the tension in each rope.
Since each rope makes an angle of 30° with the vertical, the vertical component
of the tension can be expressed as:
Using , the equation for the vertical forces becomes:
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