Force and tension problems without using Newton's laws

In summary, the conversation discusses finding the tension in two wires supporting a weight of 200 kg at angles of 35 and 41 degrees. The individual used the law of sines to create equations for the tensions, but was unable to solve them. They also ask if there is another way to solve the problem without using Newton's laws.
  • #1
Shay10825
338
0
Hello. I was trying to find a way to solve the tension problems without using Newton’s laws. The problem says: A weight of 200 kg is supported by two wires. Find the magnitude of the tension in each wire. The angle in the top left is 35 and the angle in the top right is 41.

I used the law of sines and I said that the weight of 200 must be equal to the sum of the two tensions (u and v) which is (u*sin145 + v*sin41)

u/sin49 = (u*sin145 + v*sin41) / sin76

v/sin55 = (u*sin145 + v*sin41) / sin76

But I can’t solve these two equations and I don’t know why. The answer is u = 155.56 and v = 168.486. The answers work with the equation but for some reason I can’t solve these equations ( I keep getting zero).
How can I solve there to equations to get u = 155.56 and v = 168.486?

Also is there another way to solve these problems (without using Newton’s laws) using geometry or some other complicated way. I’m just playing around with the problems and I understand how to solve them using Newton’s laws. I am just curious.

http://img101.imageshack.us/img101/5670/tension2wf.jpg [Broken]

Thanks
 
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  • #2
You already had the answers when you wrote the law of sines for u and v right after the "so then:" line in your picture.

Also, you are, in fact, using Newton's laws when you wrote your equations. I don't see how you could avoid it.
 
  • #3
I wrote those two equations so you could see where I got the bottom two equations with just the u and v. I wanted to be able to solve the equations:

u/sin49 = (u*sin145 + v*sin41) / sin76

v/sin55 = (u*sin145 + v*sin41) / sin76

so i could solve these problens if they did not give wou the weight of 200.
 
  • #4
so is there any way i can solve the equations:

u/sin49 = (u*sin145 + v*sin41) / sin76

v/sin55 = (u*sin145 + v*sin41) / sin76

for u and v?
 
  • #5
You should have something like

[tex]v \sin 39 = u \sin 55[/tex]

and

[tex]u^2 + v^2 - 2 uv \cos 76 = 200^2[/tex]

and, once again, this is just another expression of Newton's Laws.
 

1. What is the difference between force and tension?

Force and tension are both types of forces that act on objects. Force is a push or pull that causes an object to accelerate, change direction, or change shape. Tension, on the other hand, is a specific type of force that occurs when an object is stretched or pulled. In other words, tension is the force that is transmitted through a string, rope, or other similar object when it is pulled on from both ends.

2. How do you calculate tension in a system without using Newton's laws?

To calculate tension in a system without using Newton's laws, you can use the following equation: T = m x a, where T is the tension, m is the mass of the object, and a is the acceleration. This equation is based on the concept of force = mass x acceleration, which is a fundamental principle of physics.

3. Can tension be negative?

No, tension cannot be negative. In physics, negative values usually indicate a force acting in the opposite direction. However, tension is always a positive value because it is a pulling force. If there is a force acting in the opposite direction, it would be called compression rather than tension.

4. How does the angle of a rope affect the tension in the system?

The angle of a rope can affect the tension in the system because it changes the direction and magnitude of the force. The tension in a rope is highest when it is pulled straight, and decreases as the angle increases. This is because the force is being divided between the horizontal and vertical components, resulting in a smaller tension force.

5. Is tension the same in every part of a rope or string?

No, tension is not the same in every part of a rope or string. In a simple system where a rope is being pulled from both ends, the tension is equal throughout the rope. However, in more complex systems with multiple ropes and angles, the tension can vary in different parts of the rope depending on the direction and magnitude of the forces acting on it.

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