Solving for Tensions with Different Angles

In summary, the problem involves a climber suspended between two cliffs with a weight of 535N. The left part of the rope makes an angle of 65 degrees to the cliff and the right part makes an angle of 80 degrees. To solve for the tensions (T1 and T2) in the ropes, trigonometry must be used to resolve the forces into their x and y components. The equations for the vertical and horizontal components are T1 Cos 65 + T2 Cos 80 = 535 and T1 Sin 65 + T2 Sin 80 = 0, respectively. It is important to note that the force due to the mass of the climber must also be taken into account in the vertical
  • #1
Paul_Bunyan
9
0

Homework Statement



A climber is suspended between two cliffs and is closer to the left cliff. The left part of the rope makes an angle of 65 to the cliff and the right part an angle of 80 to the cliff. The climber weighs 535N.

Prob.58.jpg


Homework Equations



Trigonometry...

The Attempt at a Solution



What I did at first was assume that the verticle force on the two sides is equal, then use Trig. to calculate the two tensions, but the answers I got seemed way off...And as I think of it more I think the two Y tensions of the ropes may not be 535/2 as I first thought...So I'm stuck here...

I keep re-reading my book for clarification, but I can't seem to grasp what I must do.
 
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  • #2
The tensions will not be the same. You must resolve the forces into their x and y components using trig, then sum them up in each direction to get your two equations with two unknowns.
 
  • #3
Ahhh, of course! I can't believe I overlooked that...I was thinking too much, thanks.

So, after doing all the algebra and trig, I came up with this...

From the equations for the components:

T1=Left, T2=Right

T1 Sin 65 + T2 Sin 80 = 0
T1 Cos 65 + T2 Cos 80 = 535

Left string's tension = T1 = 2032.654N
Right string's tension = T2 = 1870.629N

Does that look right?

Thanks again.
 
  • #4
Don't forget about the force due to the mass of the climber! You must use ALL the forces. That acts in the vertical direction.

Also, in the horizontal direction, the tension in the first rope acts in the opposite direction of the second rope. So you must subtract instead of add.
 
  • #5
So, in the vertical part:

T1 Cos 65 + T2 Cos 80 = 535

Doesn't the 535 take into account the weight of the climber? Since the two verticle upward forces of each rope must add together to equal the single downward force due to the mass of the climber?
 
  • #6
Paul_Bunyan said:
So, in the vertical part:

T1 Cos 65 + T2 Cos 80 = 535

Doesn't the 535 take into account the weight of the climber? Since the two verticle upward forces of each rope must add together to equal the single downward force due to the mass of the climber?

Yes, you are right about that. Sorry, I think I misread your earlier post.

As for the horizontal components of the tension, T1 acts to the left, while T2 acts to the right. So when summing up the forces it will be the difference between the two. Does that make sense?
 
  • #7
Yeah, I think I get it now, thanks a bunch!
 
  • #8
Hmmm, when I work through your equations, I get a different answer. One way to check if your that you didn't make a mistake in your algebra is to put your values back into your original equations, and see if they make sense.
 
  • #9
You're right, I went through it kind of fast and had a wayward "-" sign.

After fixing that I got:

T1 = 917.456
T2 = 844.18

Which makes a lot more sense, is that close to what you got?
 
  • #10
Yes, within rounding, those are the values I got.
 
  • #11
hi how would you soolve for t1 and t2?
 

What is tension with different angles?

Tension with different angles refers to the force that is exerted on an object when it is pulled or stretched in different directions. This force is measured in newtons and is dependent on the angle at which the object is being pulled.

How is tension affected by different angles?

Tension is affected by different angles because the angle at which an object is being pulled changes the direction of the force being exerted. This means that the magnitude of the tension will also change, as it is dependent on the angle of the force.

What is the relationship between tension and angle?

The relationship between tension and angle is that as the angle increases, the tension also increases. This is because a greater angle results in a larger component of the force being applied in the direction of the tension, leading to a greater magnitude of tension.

How do we calculate tension with different angles?

To calculate tension with different angles, we can use trigonometric functions such as sine, cosine, and tangent. These functions allow us to find the components of the force in the direction of the tension, which can then be added together to find the total tension.

Why is understanding tension with different angles important?

Understanding tension with different angles is important because it allows us to accurately predict and control the forces exerted on objects. This is crucial in many scientific fields, such as engineering and physics, where precise knowledge of tension is necessary for designing structures and predicting how they will behave under different conditions.

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