Statics Problem: Understanding the Dimensions of Force P in 3D | Homework Help

[adam.lee]

This is a problem in my homework. My friend and I have been working on it for the past week and cannot match the answer to the back of the book. I think my main problem is I don't understand what it is trying to say about the dimensions of the force P. The 5 degrees and the 70 degrees doesn't really make much sense. I know that if I could get the vector from point A to C and the components of the force then it would be easy. The hard part is I don't know how to find either of these. I tried using the method in Calculus 3 of converting spherical coordinates to cartesian and that didn't get me anywhere. Please help me interpret this graph. There was another problem after this one that I had to use this picture for and I was able to get it. It took me probably about a full day to get it, but I finally got it. Basically in that one I just had to find the perpendicular distance to point C which came out to be 8.07 in.

 

[Valkarie]

It looks like the problem is asking you to find the magnitude of the force, P, that is being applied at point A. To do this, you need to first determine the vector from point A to point C. This can be done using the coordinates given in the problem. Point A has coordinates (5, 70), and point C has coordinates (-15, 0). The vector from point A to point C can then be calculated by subtracting the two coordinate points, which gives the vector (20, 70). Next, you need to use trigonometry to calculate the components of the vector. The x-component of the vector is 20 cos 70 = -7.45 and the y-component is 20 sin 70 = 16.92.The magnitude of the force, P, is then given by the vector equation P = sqrt(x^2 + y^2). In this case, the magnitude of the force, P, is 18.66.

 

[piercas]

Hello there,

I understand that you are having trouble understanding a statics problem involving the dimensions of force P in 3D. It seems like you are having difficulty interpreting the angles and dimensions given in the problem.

Firstly, it is important to understand that in 3D problems, we often use spherical coordinates to represent points and vectors. This means that instead of using the traditional x, y, z coordinates, we use r, θ, and φ. In this case, the 5 degrees and 70 degrees are most likely referring to the angles θ and φ, which represent the direction of the force P.

To find the vector from point A to C, you can use the distance formula in 3D, which is:

d = √[(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2]

In this case, point A and point C would be the two points you are trying to find the distance between. Once you have the distance, you can use trigonometry to find the components of the force P.

As for converting spherical coordinates to cartesian, it is a useful method, but it may not be necessary for this problem. It would depend on how the problem is presented and if it specifically requires you to use that method.

I would also recommend reviewing the concepts of vector addition and resolving forces in 3D space, as these are important skills for solving statics problems.

I hope this helps you understand the problem better and gives you some guidance on how to approach it. Don't hesitate to reach out for further clarification or assistance. Good luck with your homework!