Question

For a equilibrium shown. the strings are strong enough to withstand a maximum tension of 100 n. what is the largest value of w they can support

Answer 1

Hope this helps!!!The answer is 35 N.

Answer 2

First let us draw the free body diagram for showing the forces acting along the strings for withstanding a maximum tension of 100 N

                                        A.sin37 = B.sin53 ---(1)

To get the value of sin37 and sin 53, we need to remember one fact

In a right angle whose sides are of lengths 3, 4, 5 or are of lengths 6, 8, 10, the angles other than 90 degrees are $37^o$ and $53^o$

So,

                 $sin37^{o} = 3/5 = cos53^{o}\\sin53^{o} = 4/5 = cos37^{o}\\tan37^{o} = 3/4 = cot53^{o}\\tan53^{o} = 4/3 = cot37^{o}$

Thus, Substituting the values in (1), we get

                  $A\times 3/5 = B\times 4/5$

                        3A = 4B

From this equation, we can clearly conclude that A > B

And as it is given that the maximum tension is 100 N  

                        A = 100N

So, $B = 3/4\times 100 = 75 N$

Substituting the values  

         A cos37 = W + B cos53

         $100\times \frac {4} {5} = W + 75 \frac {3} {5}$

We get  

80 = W + 45

W = 35 N

The largest W that the strings can support is 35N .