[STRIKE](adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Two ropes are connected to a steel cable that supports a hanging weight as shown.

If the maximum tension either rope can sustain without breaking is 5000 N, determine the maximum mass m that the ropes can support.

2. Relevant equations

Newton's equations #1, #3.

3. The attempt at a solution

Let the left rope have tension T_{1}, and the right rope have tension T_{2}. So, the horizontal component of T_{1}is cos(60)*T_{1}, which must equal the horizontal component of T_{2}, which is cos(40)*T_{2}. So:

cos(60)*T_{1}= cos(40)*T_{2}

T_{1}= (cos(40) / cos(60)) *T_{2}

T_{1}= 1.532*T_{2}

So T_{1}has the greater tension.

The problem states that the maximum tension for either T_{1}or T_{2}is 5000N. So, since T_{1}has the greatest tension, we give it a tension of 5000N. This means that T_{2}has a tension of 3266N.

The weight of the block is equal to the sum of the vertical components of the two tensions. So:

w = sin(60)*T_{1}+ sin(40)*T_{2}

So we have:

w = sin(60)*5000N + sin(40)*3266N

w = 5035N

That's the answer I get. My book tells me the answer is 6400N. I'm not sure where I've gone wrong here.[/STRIKE]

Nevermind all of this. As it turns out, I was just screwing up the final calculation. sin(60)*5000N + sin(40)*3266N doesn't equal 5035N, as I indicated.

So, nothing to see here...

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# A weight supported by two ropes

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