EK 1001 Physics #281 pretty please help me

[generator]

If m = 100kg, theta1 = 30deg and theta2 = 30deg, the tension T1 is:
A. 500 N
B. 866 N
C. 1000 N
D. 1732 N

The correct answer is C, 1000 N. I chose answer A because I used mgsin(theta), so I did (100kg)(10m/s^2)(1/2) = 500N.

What did I do wrong? I'm sure it is really simple and I'm just being an idiot :]

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[MT Headed]

First, solve for the vertical component of T1. It's just mg/2, or 500N, because both ropes contribute equally to pulling up the block.

Next, solve for the total tension T1. It's a 30-60-90 triangle, so the ratios are 1:2:sqrt(3). You know the "1" side is 500N, therefore the hypotenuse "2" side is 1000N.

 

[Arctangent]

Looking at your use of m * g * sin(theta), it looks like you did not take into account the second rope that also contributed to holding up the mass. Thus, your calculation would be correct if there was just one rope at an angle of 30 degrees holding up the weight, but since there are two, your calculated tension is double what it should be.

 

[generator]

Alright, but why do I have to account for both ropes? The question asks for only for T1... the tension of Rope 1.

Am I reading this wrong?

and btw, thank you so much for responding MT Headed and Arctangent! <3

 

[exquisitemelody]

You can basically ignore the T3 and think about this vertically. Both tensions have to support the weight, so

mg=T1*sin(theta) + T2*sin(theta)

(T1*sin (theta) is the vertical component of that T)

Because the angles are the same, the tensions are going to be equal, so

mg=2Tsintheta

Solve for T, you get 1000.

 

[Arctangent]

Alright, but why do I have to account for both ropes? The question asks for only for T1... the tension of Rope 1.

Am I reading this wrong?

and btw, thank you so much for responding MT Headed and Arctangent! <3

The two ropes in this question are identical. Even though the question asks about one of the ropes, you still have to know that the weight is distributed between the two.

A relevant analogy would be say that $100 will buy you two cows. How much is a cow? You must take into account that two cows are equivalent to $100. Even though the question asks for the price of one, the answer is not $100, but $50, as the value of $100 is split between the two.

Similarly, in this question, the quantity of downward weight is split between two ropes. Though the question asks for the tension in only one of the ropes, the other rope still accounts for a portion (half in this case) of the upward force.