Solving Cartesian Vectors in Mechanics: Expressing Force F(AB) in Cartesian Form

In summary, the site says to check my signs and I don't see anything wrong. I Express the force F(AB) as a cartesian vector and my results look correct.
  • #1
Robb
225
8

Homework Statement


Hibbeler14.ch2.p92.jpg


Express force F(AB) in cartesian vector form[/B]
Mastering engineering.com says to check my signs but I don't an see an issue. Please help!

2. Homework Equations 3. The Attempt at a Solution

A(0, -.75, 3) B(2cos40, 2sin40, 0) C(2,-1, 0)

r(
AB)= 1.53i +2.04j-3k
r(magnitude)= 3.94

u(ab)= .388i + .518j - 3k
F(AB)= 97i +130j - 190k
 
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  • #2
Your work looks correct to me. (You have a typo in the z-component of the unit vector u.)
 
  • #3
What is the question?
 
  • #4
andrewkirk said:
What is the question?
It's just below the figure.
 
  • #5
Masteringengineering.com says to check my signs. I do not see anything wrong with them. We are asked to express the force F(AB) as a cartesian vector.
 
  • #6
TSny said:
It's just below the figure.
Ah - I was fooled by the bold text. Because of the template format, I just automatically process anything in bold in these questions as a heading and it doesn't even register on my consciousness.
 
  • #7
So, what do you think?
 
  • #8
Your results look fine. I might have rounded the results a bit differently, but your signs are certainly correct.
 
  • #9
Thank you!
 
  • #10
How would you have rounded it. The site is now telling me I have a rounding error. I went through my numbers again and went out to 100 thousandths place. The only change I get is that i=97.1?
 
  • #11
Now that I've looked again at the problem statement I can see that there's a bit of a question about how many significant figures to use. Many of the distances are given as a single digit with no decimal indicated, but at least one has two decimal places (0.75 m). So do we round to one significant figure or assume that the single digit numbers were really measured to two decimals of accuracy but were shown as single digits for aesthetic reasons on the figure?

My own choice would be to round to two significant figures as you've done in your first post, but there's an argument to be made for rounding to one sig fig!
 
  • #12
The problem says to round to 3 sig-figs and I entered 97.1i +130j -190k
 
  • #13
Robb said:
The problem says to round to 3 sig-figs and I entered 97.1i +130j -190k
Okay then. What were your unrounded results to three decimals?
 
  • #14
97.1475I + 129.53j - 190.485k
 
  • #15
Robb said:
97.1475I + 129.53j - 190.485k
Did you round or truncate any of your intermediate results to five or fewer digits? I'm seeing slightly different values that could affect your rounding to three figures.

Generally I keep all intermediate values to full precision in calculator memory (or let a software package hold them in variables) and only round for presentation. This prevents rounding and truncation errors from creeping into the significant figure zone.

Before rounding and to three decimals I'm seeing values: 97.316; 129.297; -190.556
 
  • #16
ok. I got it. Guess I better play it safe and don't round till the end huh. Thanks so much!
 

Related to Solving Cartesian Vectors in Mechanics: Expressing Force F(AB) in Cartesian Form

1. What are Cartesian vectors?

Cartesian vectors are mathematical quantities used to represent physical quantities, such as position, velocity, and force, in a three-dimensional space. They consist of a magnitude and direction, and are typically represented by an arrow pointing from the origin to the point where the vector ends.

2. How are Cartesian vectors different from other types of vectors?

Cartesian vectors are unique in that they are specified using the coordinates of their endpoint in a three-dimensional space, rather than using polar coordinates or angles. This means that their components can be easily calculated and manipulated using basic algebraic operations.

3. What is the importance of Cartesian vectors in science?

Cartesian vectors are essential in many areas of science, including physics, engineering, and mathematics. They are used to describe the motion and forces of objects in three-dimensional space, making them crucial for understanding and analyzing physical phenomena.

4. How are Cartesian vectors represented mathematically?

Cartesian vectors are typically written as a column matrix with three components, representing the x, y, and z coordinates of the endpoint. They can also be represented using the unit vectors i, j, and k, which correspond to the x, y, and z axes, respectively.

5. Can Cartesian vectors be combined or separated?

Yes, Cartesian vectors can be added, subtracted, and multiplied by a scalar quantity, just like regular numbers. This allows for the combination and separation of multiple vectors to represent more complex physical quantities, such as acceleration or net force.

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