The two angled ropes are used to support the crate

Asked by maham237 @ in Physics viewed by 261 People

The two angled ropes are used to support the crate in the picture. The sum of the tension in the ropes can have any value up to 1500 N. When the tension in the ropes exceeds 1500 N the rope will break. What is the largest mass the ropes can support?

Answered by maham237 @


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

T_{1}\cos\theta=T_{2}\cos\theta

Put the value into the formula

T_{1}\cos30=T_{2}\cos45

T_{1}\dfrac{\sqrt{3}}{2}=\dfrac{T_{2}}{\sqrt{2}}

T_{1}=\dfrac{\sqrt{2}}{\sqrt{3}}\times T_{2}

If T_{2}=1500\ N

T_{1}=\dfrac{\sqrt{2}}{\sqrt{3}}\times1500

T_{1}=1224.74\ N

We need to calculate the largest mass

Using balance equation

mg=T_{1}\sin30+T_{2}\sin45

mg=1224.74\times\dfrac{1}{2}+1500\times\dfrac{1}{\sqrt{2}}

mg=1673.03\ N

m=\dfrac{1673.03}{9.8}

m=170.7\ Kg

Hence, The largest mass is 170.7 Kg.


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