Answer:
The largest mass is 170.7 Kg.
Explanation:
Given that,
Tension = 1500 N
We need to calculate the tension in the rope
Using balance equation
[tex]T_{1}\cos\theta=T_{2}\cos\theta[/tex]
Put the value into the formula
[tex]T_{1}\cos30=T_{2}\cos45[/tex]
[tex]T_{1}\dfrac{\sqrt{3}}{2}=\dfrac{T_{2}}{\sqrt{2}}[/tex]
[tex]T_{1}=\dfrac{\sqrt{2}}{\sqrt{3}}\times T_{2}[/tex]
If [tex]T_{2}=1500\ N[/tex]
[tex]T_{1}=\dfrac{\sqrt{2}}{\sqrt{3}}\times1500[/tex]
[tex]T_{1}=1224.74\ N[/tex]
We need to calculate the largest mass
Using balance equation
[tex]mg=T_{1}\sin30+T_{2}\sin45[/tex]
[tex]mg=1224.74\times\dfrac{1}{2}+1500\times\dfrac{1}{\sqrt{2}}[/tex]
[tex]mg=1673.03\ N[/tex]
[tex]m=\dfrac{1673.03}{9.8}[/tex]
[tex]m=170.7\ Kg[/tex]
Hence, The largest mass is 170.7 Kg.
