What Forces Balance a Knot Pulled by Three Different Ropes?

In summary, the conversation discusses the forces and angles involved in pulling on three ropes tied together in a knot. The question is how much force and in what direction must be applied to the third rope to prevent the knot from moving. The expert summarizer assumes that the vectors formed a right triangle and that the third rope would require 4.0 units of force. However, it is pointed out that since the angle between the ropes is 120 degrees, the vectors do not form a right triangle. The relevant equation to find the magnitude and direction of the resultant vector is mentioned to help solve the problem.
  • #1
mjunderhill
1
0
The figure shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. These two ropes are being pulled 120 degrees apart.


How hard must you pull on the third rope to keep the knot from moving?

In what direction must you pull on the third rope to keep the knot from moving?


I assumed the vectors formed a right triangle and the 5.0 force was the hypotenuse, so the third rope would require 4.0 units of force.
 
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  • #2
Why did you assume the vectors formed a right triangle? They're 90 degrees apart.
Break up the vectors into X & Y components first.
 
  • #3
mjunderhill said:
The figure shows three ropes tied together in a knot. One of your friends pulls on a rope with 3.0 units of force and another pulls on a second rope with 5.0 units of force. These two ropes are being pulled 120 degrees apart.How hard must you pull on the third rope to keep the knot from moving?

In what direction must you pull on the third rope to keep the knot from moving?I assumed the vectors formed a right triangle and the 5.0 force was the hypotenuse, so the third rope would require 4.0 units of force.
welcome to PF.
Since angle between the ropes is 120o, vectors do not form a right triangle.
If two vectors and angle between them are given, what is the relevant equation to find the magnitude and direction of the resultant vector?
 

FAQ: What Forces Balance a Knot Pulled by Three Different Ropes?

What is a vector of rope problem?

A vector of rope problem is a physics problem that involves calculating the tension and direction of multiple ropes that are connected to an object or system.

How do you solve a vector of rope problem?

To solve a vector of rope problem, you need to first draw a free body diagram to identify all the forces acting on the object or system. Then, you can use trigonometry and vector addition to calculate the tension and direction of each rope.

What are some common mistakes when solving a vector of rope problem?

Some common mistakes when solving a vector of rope problem include forgetting to consider the weight of the object or system, using the wrong angles or trigonometric functions, and not properly labeling the forces on the free body diagram.

What is the difference between a static and dynamic vector of rope problem?

A static vector of rope problem involves a system or object that is not moving, while a dynamic vector of rope problem involves a system or object that is in motion. In a static problem, the sum of all forces must equal zero, while in a dynamic problem, the sum of all forces must equal the mass times acceleration.

What real-life applications use vector of rope problems?

Vector of rope problems are commonly used in engineering and construction to determine the forces acting on structures such as bridges and buildings. They are also used in physics to understand the forces involved in objects that are suspended or connected by ropes, such as a pendulum or a pulley system.

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