Calculating Resultants of Parallel/Anti-Parallel Vectors

[EK03]

Hey I am in 11th grade 1st year of Physics. I am doing this lab and my head is blanking out. Problem is how to calculate the resultants of 2 parallel vectos of 12N and 5N and the next is what would it be if its anti parallel. I think it might be 17N for the 1st 1 and 7 for the antiparallel vector question but I am not positivve. also i don't understnad what it means by asking what the maximum resultant of the 2 vectors would be and also the minimum. Thank you, and equations to help me out would be greatly appriciated

 

[chroot]

There aren't any equations really. To find the "resultant" or sum of vectors, stack them head to tail. In the first example, you have two vectors:

-----> 5 N
------------> 12 N

I made the 5 N vector boldface just to distinguish it. Stack them head to tail:

----->------------>

This is equivalent to one single vector:

-------------------> 17 N

In the second example, you have two vectors:

<----- 5 N
------------> 12 N

Stack them head to tail:

------<----->

You can see that the 5 N vector is basically "backtracking," going the opposite direction of the 12 N vector. The sum of these two vectors is

-------> 7 N

The last part of the question is asking "how should two vectors be oriented with respect to each other for the length of their sum to be the largest? or smallest?" You should be able to look at these pictures and explain this.

- Warren

 

[EK03]

thank you for validating my work. There are no pictures or diagrams on my assignment unfortunatley. Also I am not sure how to do the resultnat if they were mutually perpendicular, any suggestions?

 

[NateTG]

Use the pythagorean theorem.

 

[EK03]

thanks nate, for the lab we recorded 4 trials of aligning the 3 forces on a piece of paper. Do i choose the lowest vector resultant as the minimum and biggest as the max like in Algebra?

 

[chroot]

Originally posted by EK03
thank you for validating my work. There are no pictures or diagrams on my assignment unfortunatley. Also I am not sure how to do the resultnat if they were mutually perpendicular, any suggestions?

Of course you know how -- they're just triangles! Trig to the rescue. For example, you could solve for the length L and angle a of this triangle:

       5
---------------->
   . a       100 \
         .        \  4
      L        .   \
                    v

where the resultant vector is represented by the dotted line.

In components, vectors on a plane can be represented by ordered pairs, like $(a,b)$, where a is the horizontal component and b is the vertical component. To find the sum of two vectors $(a,b)$ and $(c,d)$, consider that the total horizontal distance must be $a+c$, and the total vertical distance must be $b+d$.

In other words, the sum is

$$(a,b) + (c,d) = (a + c, b + d)$$

To find the length and direction of this resultant vector, just imagine the right triangle it makes with the positive x-axis, and solve using the normal rules you'd use to solve any right triangle.

Does this make sense?

- Warren

 

[EK03]

yeah it did thanks a lot guys

 

[EK03]

is there some kind of physics dictionary? For instance i have to find the definition of the resultant (my teacher has his own book published we don't use normal school textbooks)

 

[chroot]

Originally posted by EK03
is there some kind of physics dictionary? For instance i have to find the definition of the resultant (my teacher has his own book published we don't use normal school textbooks)

Resultant = vector sum.

- Warren

 

[NateTG]

Originally posted by EK03
is there some kind of physics dictionary? For instance i have to find the definition of the resultant (my teacher has his own book published we don't use normal school textbooks)

Try google or Eric Weisstein's world of mathematics/physics for a start.