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A weight supported by two ropes

by chudd88
Tags: ropes, supported, weight
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Feb21-10, 12:19 PM
P: 17
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 T1, and the right rope have tension T2. So, the horizontal component of T1 is cos(60)*T1, which must equal the horizontal component of T2, which is cos(40)*T2. So:

cos(60)*T1 = cos(40)*T2
T1 = (cos(40) / cos(60)) *T2
T1 = 1.532*T2

So T1 has the greater tension.

The problem states that the maximum tension for either T1 or T2 is 5000N. So, since T1 has the greatest tension, we give it a tension of 5000N. This means that T2 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)*T1 + sin(40)*T2

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.

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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