Module of Vector Sum: 3V2in, 3cm, 6cm & 5cm

In summary: Use the equations sin α = y/R and cos α = x/R to find the angle and magnitude of the vector sum. The magnitude can be found using the Pythagorean theorem, where a and b are the x and y components respectively. Therefore, the module of the vector sum is 4. In summary, the problem asks for the module (or magnitude) of the vector sum of four vectors given by their components. The given components are a = 3V2 cm, b = 3 cm, c = 6 cm, and d = 5 cm, and the given angles are sin α = 0.60, cos α = 0.80, and sin 45 degrees = cos 45 degrees =
  • #1
luiseduardo
30
0
Determine, using the vector components, the module of the vector sum of the four vector data in the figure.
Consider = 3V2 inches, b = 3 cm, c = 6 cm and d = 5 cm.
Adopt: sin α (alpha) = 0.60; cos α (alpha) = 0.80 and
sin 45 degrees = cos 45 degrees = V2/2

http://img233.imageshack.us/img233/5909/sssfv.jpg
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
If you are looking for help, please show an attempt at the solution. Don't just post the question and expect it to be answered.

Thanks
Matt
 
  • #3
Do you mean that the length of vector a is [itex]3\sqrt{2}[/itex] inches? And why in the world would one length be given in "inches" and the other in "cm"? Are you sure a is not [itex]3\sqrt{2}[/itex] cm as well?

Since the problem says "using the vector components", what are the vector components of the four vectors?
 
  • #4
I'm sorry, google translate :(
a = 3V2 cm , b = 3 cm, c = 6 cm e d = 5 cm.

sen α (alpha) = 0,60; cos α (alpha) = 0,80; e sen 45 graus = cos 45 graus = V2/2

And CFDFEAGURU, I don't know how to do this question, please if anyone knows how to do please tell me. I have the answer, but I don't know how to do.

The answer is 4.
 
  • #5
Add up all the x-components of the vectors and then add up all the y-components of the vectors.
 

Related to Module of Vector Sum: 3V2in, 3cm, 6cm & 5cm

1. What is the formula for calculating the magnitude of a vector sum?

The magnitude of a vector sum is calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of each component of the vector.

2. How do you represent vector components in the calculation of magnitude?

Vector components are typically represented using the standard notation of x and y, with x representing the horizontal component and y representing the vertical component.

3. Can you provide an example of calculating the magnitude of a vector sum?

For the given vector components 3V2in, 3cm, 6cm, and 5cm, the magnitude would be calculated as follows:
Magnitude = √(3² + 3² + 6² + 5²) = √(9 + 9 + 36 + 25) = √(79) = 8.888 inches (rounded to the nearest thousandth)

4. How does the direction of vector components affect the magnitude of the vector sum?

The direction of vector components does not affect the magnitude of the vector sum, as the magnitude is solely based on the length of the vector components.

5. What are some real-world applications of calculating vector sums?

Calculating vector sums is commonly used in physics, engineering, and navigation. For example, it can be used to calculate the resultant force on an object or the net displacement of an object. It can also be useful in calculating the trajectory of a projectile or the velocity of an object moving in multiple directions.

Similar threads

  • Classical Physics
Replies
4
Views
909
  • Introductory Physics Homework Help
Replies
4
Views
4K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
5K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
9K
  • Precalculus Mathematics Homework Help
Replies
3
Views
4K
  • Introductory Physics Homework Help
Replies
19
Views
7K
  • Special and General Relativity
Replies
19
Views
7K
Back
Top