Vector resolution and vector addition

In summary, it is important to double-check calculations and use the correct values and equations when solving problems in physics. If needed, reach out to your professor or classmates for clarification.
  • #1
pooker
16
0

Homework Statement



We were given six homework assignments for lab. We were required to find the force and angle through three given experiments.

1. Experimental using a force table
2. Graphically using head to tail, etc
3. Analytical using basic means to find the answers

Homework Equations



I have two problems

1st problem
Vector resolution
F1 = (.1)gN theta = 30
F2 (.2)gN theta = 90
F3 (.3)gN theta = 225

2nd Problem
Vector resolution
F = (.3)gN theta = 60

Find fx and Fy

Find graphical answer, analytical answer and Experimental answer for each

The Attempt at a Solution



1st Problem attempt at solution

Using the force table I got F = (.130)gN Theta = 150
Using Graphical I got F = (.131)gN theta = 162

Now my problem is with analytical

I used these equations

Rx = Rcostheta
Ry = Rsintheta
r = sqrt(rx^2 + ry^2)
theta = arctan rx/ry

rx = .1cos30 + .2cos90 + .3cos225 = -.1255
ry = .1sin30 + .2sin90 + .3sin225 = .038

R = sqrt( -.1255^2 + .038^2) = .131

Theta = arctan .038/-.1255
Theta = 343.2 ? It seems grossly off. I feel like I am forgetting something, but our book does not even really cover three vectors. I had to look online for how to do it.


2nd problem attempt

Using force table
Fx = .140gN
Fy = .245 gN

Using graphical (I plotted this like a 90 degree triangle
Fx = .16gN
Fy = .25gN

Using analytical


I know c^2 = a^2 + b^2 so .9 = a^2 + b^2

b / sintheta = R / sin Y


sin theta is the angle R casts onto A which equals 60
Sin Y is the angle sides B and A make

b / sin60 = .3/sin90

b / .866 = .3

b = .866(.3) = .2598

so Fy = .2598

.9 = .2598^2 + a^2
.9 = .0675 + a^2
.8325 = a^2 = .91

so Fx = .91 ? Why is it so low as compared to the graphical and experimental? I feel something is off. All of my other calculations were pretty dead on .
 
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  • #2


Hello! Thank you for sharing your attempts at solving these problems. I would suggest that you review your calculations and make sure you are using the correct equations and units. It is also important to double-check your work and make sure you are using the correct values for the given angles and forces.

For the first problem, it seems like your analytical solution is off because you are using the wrong values for the angles. The given angles for F1, F2, and F3 are 30, 90, and 225 degrees respectively, but in your calculation for theta, you are using 150 degrees. This may be why your analytical solution is off.

For the second problem, I would suggest reviewing your calculation for Fx. It seems like you are using the wrong values for the angles and forces. The given angle for F is 60 degrees, but in your calculation, you are using 90 degrees. Also, the given force for F is 0.3gN, but in your calculation, you are using 0.9gN.

In general, as a scientist, it is important to double-check your work and make sure you are using the correct values and equations. If you are still having trouble with these problems, I would suggest reaching out to your professor or a classmate for help. Good luck!
 
  • #3


I would advise you to carefully check your calculations and make sure you are using the correct equations and values. It is possible that you made a mistake in your analytical calculations, which is why your results do not match the graphical and experimental ones. I would also suggest double checking the values and angles given in the problem, as even a small error can lead to significant differences in the final result.

Furthermore, it is important to understand the concept of vector resolution and vector addition in order to properly solve problems like these. Vector resolution involves breaking down a vector into its components in order to find the individual forces in different directions. Vector addition, on the other hand, involves combining multiple vectors to find the overall resultant vector. Make sure you are using the correct equations and methods for each step of your solution.

Additionally, I would recommend practicing more problems and seeking help from your teacher or classmates if you are still having difficulty. With enough practice and understanding of the concepts, you will be able to solve these types of problems accurately and confidently.
 

1. What is vector resolution and why is it important?

Vector resolution is the process of breaking down a single vector into its horizontal and vertical components. This is important because it allows us to analyze and solve problems involving multiple vectors in different directions.

2. How do you calculate the horizontal and vertical components of a vector?

To calculate the horizontal component, you can use the formula H = V*cos(theta), where V is the magnitude of the vector and theta is the angle between the vector and the horizontal axis. To calculate the vertical component, you can use the formula V = V*sin(theta).

3. How do you add two or more vectors together?

To add vectors, you must first resolve them into their horizontal and vertical components. Then, you can simply add the horizontal components together and the vertical components together to get the resultant vector.

4. What is the difference between vector addition and scalar addition?

Vector addition involves adding vectors in different directions, taking into account their magnitudes and directions. Scalar addition, on the other hand, involves adding quantities that have only magnitude and no direction.

5. Can you use vector addition to find the resultant displacement of an object?

Yes, vector addition can be used to find the resultant displacement of an object by adding together the individual displacements in different directions. This is often used in physics and engineering to solve problems involving motion and forces.

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