Scale drawing with Cartesian solution and Polar representation

[mmd123]

PLEASE HELP ! THANK YOU (:

1. My teacher gave us a drawing with 4 vectors on it. Vector A = 130 N and is at a 20 degree angle. Vector B = 100 N and is at a 70 degree angle. Vector C = 70 N and is on the x-axis. Vector D = 50 N and is at a 10 degree angle. Given this picture we are told to draw an accurate scale drawing with appropriate scale and measurements, complete the Cartesian solution, complete the polar representation and provide a percent discrepancy.



2. How do I approach the Cartesian solution from this picture? What exactly is the Cartesian solution? I was absent from the class he explained this and just have notes that do not exactly explain well what I should be doing. Also what are "i hats" and "j hats"?



3. I was able to complete the first step by making a drawing using a scale of 1 cm = 15 N. Now I am unsure of what to do for the Cartesian solution and how to approach that from here.

 

[tiny-tim]

Welcome to PF!

How do I approach the Cartesian solution from this picture? What exactly is the Cartesian solution? I was absent from the class he explained this and just have notes that do not exactly explain well what I should be doing. Also what are "i hats" and "j hats"?

Hi mmd123! Welcome to PF!

Cartesian means use Cartesian coordinates, which is just a fancy way of saying use perpendicular (x and y or i and j) coordinates.

So just add all the x's and y's (separately).

ihat and jhat are the unit vectors (that is, the vectors of length 1) in the i and j directions (the x and y directions).

 

[thomate1]

1. I would approach this problem by first understanding the given information and then using mathematical methods to accurately represent it. I would start by creating a scale drawing using the given scale of 1 cm = 15 N. This will help visualize the vectors and their relative sizes and angles. Next, I would use trigonometry to find the x and y components of each vector, which will give me the Cartesian solution. For example, for Vector A, the x component would be 130 N * cos(20°) = 123.2 N and the y component would be 130 N * sin(20°) = 44.5 N. I would repeat this process for the other vectors and label them on the scale drawing. For the polar representation, I would use the magnitude and angle of each vector to plot them on a polar coordinate system. The percent discrepancy could then be calculated by comparing the lengths of the vectors on the scale drawing to their calculated lengths from the Cartesian solution. Any difference would be expressed as a percentage of the calculated length.

2. The Cartesian solution is a method of representing vectors using their x and y components. In this case, the vectors are given in terms of their magnitude and angle, so we can use trigonometry to find the x and y components. The "i hat" and "j hat" refer to unit vectors in the x and y directions, respectively. These are used to represent the x and y components of a vector in the Cartesian solution. For example, Vector A can be represented as 123.2 N * i hat + 44.5 N * j hat.

3. Now that you have a scale drawing, you can use trigonometry to find the x and y components of each vector, as mentioned in the first part of my response. Once you have these components, you can represent them in the Cartesian solution using the unit vectors i hat and j hat. For the polar representation, you can plot the magnitude and angle of each vector on a polar coordinate system. The percent discrepancy can be calculated by comparing the lengths of the vectors on the scale drawing to their calculated lengths from the Cartesian solution. Remember to convert your units to be consistent (e.g. if your scale is in cm, make sure your final calculations are also in cm).