Vector Addiction Homework: Solve Vector Sum of A + B + C

[aheimer89]

Homework Statement

In the drawing below, what is the vector sum of forces vector A + vector B + vector C if each grid square is 12 N on a side?

I have been working at this problem for awhile now and the webassign keeps saying i have the wrong answer. I have one more shot at getting the answer correct. I have two problems like this one and can't seem to figure it out. I know that vector B = 48N, vector C = 24N, and using the pythagorean theorem i found vector A = 60N. Adding all of them up the sum is 132N, that is not correct. I am not sure exactly what to do. I also found the vectors that make up A_x = 36 and A_y = 48. Do i need these to solve the question. Is vector B supposed to be subtracted since it goes in the -y direction, as well as vector C going in the -x direction.

 

[rock.freak667]

Consider the two directions separately. In the x-direction you have

A_x=36N and C= -24N (Remember, vectors have direction, I chose right as positive)


So what is the resultant of these two?


Then do the same for the y-direction.

Then the Pythagorean theorem will get you A+B+C

 

[aheimer89]

The resultant of Ax and C = 12N. That is my x direction. the y component ends up being 0, Ay = 48N and B = -48N. I am not sure where to go from here using the pythagorean theorem.

 

[rock.freak667]

The resultant of Ax and C = 12N. That is my x direction. the y component ends up being 0, Ay = 48N and B = -48N. I am not sure where to go from here using the pythagorean theorem.

Right well in that case, the resultant force = R

So you have R_x= +12 N and R_y=0 N. So your resultant is just R_x. Also remember, to put the direction in your final answer.

 

[aheimer89]

So i figured out the answer to my first two problems, now I am on the third and final one. Can anyone explain to me what the component method of adding vectors is. It differs from the vector sum in a certain way and i can't really distinguish that. My next problem i have solved for all x directions and y directions but the answer doesn't seem to be correct. Here is my 3rd question and the values i have calculated

Use the component method to find the vector sum D + E + F. Each grid square is 3 N on a side.

My x directions are:
Vector F = 6N
Vector Ex= 6N
Vector Dx = -9N

x = 5N

My Y directions are:
Vector F = 0
Vector Ey = -12N
Vector Dy= -12N

y = -24N

The picture i drew makes the shape into a trapezoid. I thought that adding up just the x vectors would find the resultant, obviously that did not work. I guess what i will try next is solving for vector D and vector E, using the pythagorean theorem.

vector d² = d_x² + d_y²
vector e² = e_x² + e_y²

That comes out to equal

vector d² = 81 + 144
vector d² = 225
vector d = 15

vector e² = 36 + 144
vector e² = 180
vector e = 13.4

Will my answer be vector d = 15, vector e = 13.4, and vector f = 6 all added together.

Which equals 34.4N, is this the correct answer?Thanks for all the help everyone

 

[rock.freak667]

My x directions are:
Vector F = 6N
Vector Ex= 6N
Vector Dx = -9N

x = 5N

My Y directions are:
Vector F = 0
Vector Ey = -12N
Vector Dy= -12N

y = -24N

Your directions of D_x and D_y should be positive.

But once you have that, the parts in red, are the resultant forces in the x and y directions. So the magnitude of the resultant is just resultant = √(x²+y²)

 

[aheimer89]

I'm not sure I follow why those two should be positive...drawing my arrows from head to tail those both would be negative as well as Ex would be negative while Ey would be positive...could u explain why those would be positive? if they are positive then my answer would be 21N, since y would equal 0

 

[rock.freak667]

I'm not sure I follow why those two should be positive...drawing my arrows from head to tail those both would be negative as well as Ex would be negative while Ey would be positive...could u explain why those would be positive? if they are positive then my answer would be 21N, since y would equal 0

Vectors pointing towards the east are positive in x and towards the north are positive for y.

So the components of E would be E_x pointing towards the east and E_y pointing towards the South (away from North).

Hence the directions of D should be changed, else how you have it, your picture would show D pointing in the opposite direction.

 

[aheimer89]

Awesome, thank you so much...21N is the correct answer. THANK YOU for the great explanation i understand how to do this now!

 

[Terocamo]

So i figured out the answer to my first two problems, now I am on the third and final one. Can anyone explain to me what the component method of adding vectors is. It differs from the vector sum in a certain way and i can't really distinguish that. My next problem i have solved for all x directions and y directions but the answer doesn't seem to be correct. Here is my 3rd question and the values i have calculated

Use the component method to find the vector sum D + E + F. Each grid square is 3 N on a side.

My x directions are:
Vector F = 6N
Vector Ex= 6N
Vector Dx = -9N

x = 5N

My Y directions are:
Vector F = 0
Vector Ey = -12N
Vector Dy= -12N

y = -24N

The picture i drew makes the shape into a trapezoid. I thought that adding up just the x vectors would find the resultant, obviously that did not work. I guess what i will try next is solving for vector D and vector E, using the pythagorean theorem.

vector d² = d_x² + d_y²
vector e² = e_x² + e_y²

That comes out to equal

vector d² = 81 + 144
vector d² = 225
vector d = 15

vector e² = 36 + 144
vector e² = 180
vector e = 13.4

Will my answer be vector d = 15, vector e = 13.4, and vector f = 6 all added together.

Which equals 34.4N, is this the correct answer?


Thanks for all the help everyone

Have you try graphical method? I am pretty sure the question is intentionally desighned for you to use graphical method.

 

[aheimer89]

it says to use the compenent method to find the vector sum. What is the graphical method?

 

[Terocamo]

it says to use the compenent method to find the vector sum. What is the graphical method?

It is to simply move the position of vectors on the so that they are connected head-to-tail.
The vector sum is the vector drawn by joinning the free ends. The magnitude can be found by
counting the square grids it occupies.
Sorry for my bad English btw... if you don't know what i am talking, i can try to draw you a solution.

 

[aheimer89]

Oh, that's actually what i did and it forms a trapezoid, that way is extremely simple...thanks for the explanation