Component vector method for resultant force

In summary, the problem involves finding the resultant force and angle of an object with two ropes attached using the component vector method of addition. The given information includes a 60 lb force on the positive x-axis and a 30 lb force at a 120 degree angle from the first rope. The equations used are Fa + Fb = R and the components are multiplied by the cosine of the angle in that direction. The solution involves finding the components Ax, Bx, Ay, and By.
  • #1
argentnox
2
0

Homework Statement



An object has two ropes attached. One is on the x-axis (positive) with a 60 lb force. One is 120* (Quadrant II) from the first rope with a 30 lb force. I have to find the resultant force and angle using the component vector method of addition NOT the parallelogram method.

Homework Equations



Fa + Fb = R

The Attempt at a Solution



I set up a table of components, but I am not sure if they are correct. I am just really confused as to how to approach this problem. I know how to do it using the parallelogram method, but it seems like some important piece of information is missing for doing it using the component vector method.

A=30 lb
B= 60 lb

Angle A=120*
Angle B=0*

Ax = ??
Bx = 60 lb

Ay = ??
By = 0
 
Last edited:
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  • #2
welcome to pf!

hi argentnox! welcome to pf!

(try using the X2 icon just above the Reply box :wink:)

to find the component in a direction, always multiply by cos of the angle to that direction :smile:
 
  • #3
Thank you, I will try that and see how I do. If it is okay, I will probably come back to make sure I got the correct answer. I figure if I got the answer correct, I must have done the work correctly. ;)
 

1. What is the component vector method for resultant force?

The component vector method for resultant force is a mathematical approach used to determine the magnitude and direction of a resultant force acting on an object. It involves breaking down the force into its horizontal and vertical components and using trigonometric functions to find the resultant force.

2. How is the component vector method different from other methods?

The component vector method is different from other methods, such as the parallelogram method, because it breaks down the force into its components rather than using the force as a whole. This allows for a more precise calculation of the resultant force.

3. When is the component vector method used?

The component vector method is commonly used in physics and engineering to calculate the resultant force on an object when multiple forces are acting on it at different angles. It can also be used to calculate the direction and magnitude of a single force acting on an object at an angle.

4. What are the steps involved in using the component vector method?

The first step is to draw a diagram of the forces acting on the object. Then, break down each force into its horizontal and vertical components. Next, use trigonometric functions to find the magnitude and direction of each component. Finally, use the Pythagorean theorem and inverse trigonometric functions to find the resultant force.

5. Are there any limitations to the component vector method?

One limitation of the component vector method is that it can only be used for forces acting in two dimensions. It also assumes that all forces are acting at a single point on the object, which may not always be the case in real-world scenarios. Additionally, the method may become more complex and time-consuming when dealing with multiple forces at different angles.

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