Vector question, concerning direction

In summary: Apparently, this angle stuff is important because if you use vectors that make an angle with the downward direction, the resultant force will be weaker.
  • #1
Spydermonkey
11
0

Homework Statement


2 vectors of equal magnitude act in a vertical plane perpendicular to each other. If their resultant is 81.0 N directly downward then
Part A use components to find thew magnitude of each of the two vectors
and Part B use components to find the angle each vector makes with the resultant force, use counterclockwise angles vectors make with downward direction.


Homework Equations


No equations given. I am not quite sure how to start, since no magnitudes are even given, and only one angle which I do not understand.


The Attempt at a Solution


I am stumped by the language, what does 81 N directly down even mean? Does that mean that the resultant faces at an angle 81 degrees off the x-axis to the east, west, or am I way off? Sorry, this is my first week of my first Physics course ever, I know nothing!
 
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  • #2
"81 N" : That's the "magnitude." Magnitude is a word that means "size" or "quantity." 81 N directly down means 81 Newtons of force, pointing directly down. Directly down is the direction. OK so far?
 
  • #3
Spydermonkey said:

Homework Statement


2 vectors of equal magnitude act in a vertical plane perpendicular to each other. If their resultant is 81.0 N directly downward then
Part A use components to find thew magnitude of each of the two vectors
and Part B use components to find the angle each vector makes with the resultant force, use counterclockwise angles vectors make with downward direction.


Homework Equations


No equations given. I am not quite sure how to start, since no magnitudes are even given, and only one angle which I do not understand.


The Attempt at a Solution


I am stumped by the language, what does 81 N directly down even mean? Does that mean that the resultant faces at an angle 81 degrees off the x-axis to the east, west, or am I way off? Sorry, this is my first week of my first Physics course ever, I know nothing!
I believe that the "N" stands for Newtons, the magnitude of the force vector. So that means that an 81 Newton force acts vertically down. The sum of the vertical components of each of the unknown (but equal in magnitude, and perpendicular to each other) vectors must add to 81, because that is the resultant force in the downward vertical direction. The sum of their horizontal components must add to 0, because there is no horizontal resultant force, since the resultant force acts directly vertically down. Does this help at all?
 
  • #4
Okay, so when I draw this bad boy up, my resultant points directly down, but the other two vectors form a right angle and everything connects tail to head or whatnot. Now, if 81 N is the only number I am given, how can I find the magnitude of the two vectors? Will they be equal? Essentially, I don't know the set-up for the problem, once I know how to set it up, I am sure I can get it. Thanks for the help so far, love that their is a forum out there for this.
 
  • #5
You have two vectors at a right angle to each other, and one connecting them, pointing straight down. Just draw it and solve for the right triangle.
 
  • #6
Spydermonkey said:
Okay, so when I draw this bad boy up, my resultant points directly down, but the other two vectors form a right angle and everything connects tail to head or whatnot. Now, if 81 N is the only number I am given, how can I find the magnitude of the two vectors? Will they be equal? Essentially, I don't know the set-up for the problem, once I know how to set it up, I am sure I can get it. Thanks for the help so far, love that their is a forum out there for this.

Your life would be extremely easy if you'd set your problem up in a coordinate system and if you'd choose the standard basis {i, j} and express your vectors in that basis. If you do not know what I'm talking about, then all you need to do is recall what a component of a vector is and use basic geometry/trigonometry.
 
  • #7
Okay, so essentially I have a 90, 45, and 45 degree angle, then does this talk of "use clockwise angles vectors make with downward direction" even matter?
 
  • #8
Sorry guys, I am hopeless, I am going to try a few things then I will get back to you if I am still lost.
 

1. What is a vector and how is it different from a scalar?

A vector is a mathematical quantity that has both magnitude (size) and direction. This is different from a scalar, which only has magnitude. For example, velocity is a vector because it has both speed and direction, while temperature is a scalar because it only has magnitude (no specific direction).

2. How can vectors be represented visually?

Vectors can be represented visually using arrows, where the length of the arrow represents the magnitude and the direction of the arrow represents the direction of the vector.

3. What is the difference between a displacement vector and a position vector?

A displacement vector measures the change in position from one point to another, while a position vector represents the location of a point in relation to an origin. Displacement vectors are typically written as Δx or Δr, while position vectors are written as r.

4. How do you calculate the magnitude of a vector?

The magnitude of a vector is calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the vector's components. For example, if a vector has components x and y, its magnitude would be √(x² + y²).

5. Can vectors be added or subtracted?

Yes, vectors can be added or subtracted using the parallelogram rule or the head-to-tail method. This involves placing the tail of one vector at the head of another and drawing a new vector from the tail of the first vector to the head of the second. The resulting vector is the sum or difference of the original vectors, respectively.

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