Parallelogram Law of Vector Addition

In summary, the conversation involves a student seeking help with a word problem using the parallelogram law of vector addition. They are asked to draw a diagram and calculate the magnitude of the resultant force. The student is unsure of how to do the calculation and is advised to use trigonometry to find the x and y components of the 11N force.
  • #1
Morphayne
13
0

Homework Statement



I'm having trouble with a word problem involving the parallelogram law of vector addition. The problem reads as follows:

Two forces with magnitudes 8N and 11N act on a large object. The angle between the forces is 30 degrees.

a) Draw a diagram to represent the combined effort of the forces.b) Calculate the magnitude of the resultant force.

Homework Equations



Not sure.

The Attempt at a Solution



a) I drew the 8N vector horizontal and the 11N 30 degrees from the horizontal. Both vectors are tail-to-tail.

b) I know that I'm supposed to use the parallelogram law of vector addition, complete the parallelogram and the resultant vector will share the same tail with my original two vectors and the head of the resultant vector will be at the opposite vertex of the parallelogram.

I just don't know how to do the actual calculation, which is where I need the help.
 
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  • #2
if I call the horizontal the "x-axis" then the x-component of the 8N force is 8N and the y-component of the 8N force is zero.

what are the x and y components of the 11N force? you will need to use trig.
 
  • #3
P.S. this should probably be posted in the introductory physics forum not the "calculus and beyond" forum... but whatever.
 

What is the Parallelogram Law of Vector Addition?

The Parallelogram Law of Vector Addition is a mathematical principle used to add two or more vectors geometrically. It states that if two vectors are represented by two adjacent sides of a parallelogram, then the resultant vector is represented by the diagonal of the parallelogram that passes through the point of intersection of the two vectors.

What is the formula for the Parallelogram Law of Vector Addition?

The formula for the Parallelogram Law of Vector Addition is R = √(A²+B²+2ABcosθ), where R is the magnitude of the resultant vector, A and B are the magnitudes of the two vectors being added, and θ is the angle between the two vectors.

How is the Parallelogram Law of Vector Addition applied in real life?

The Parallelogram Law of Vector Addition is often used in physics and engineering to calculate the resultant force of multiple forces acting on an object. It is also used in navigation and map-making to determine the direction and magnitude of movement.

What is the difference between vector addition and scalar addition?

Vector addition involves adding two or more vectors to determine the resultant vector, while scalar addition involves adding two or more scalar quantities to determine the total value. Vector addition takes into account both magnitude and direction, whereas scalar addition only considers magnitude.

Can the Parallelogram Law of Vector Addition be applied to more than two vectors?

Yes, the Parallelogram Law of Vector Addition can be applied to any number of vectors. Each vector can be added to the resultant vector one at a time, using the Parallelogram Law, to determine the final resultant vector.

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