Solids and Structures - Vector question

[J.Halliwell]

Homework Statement

The rope BC exerts an 800 N force F on the bar
AB at B. Determine the vector components of F
parallel to the bar.

Homework Equations

I already know how to complete dot product (e.g. a.b), cross product (e.g. axb) and understand the basic principles of these ideas but don't know how to use these within the question asked to get the answer.

The Attempt at a Solution

I have already been given the solution to the question but all my workings that I have done so far have not produced the correct answer. The answer is Ans: -396i –476j – 79k N

 

[nvn]

J.Halliwell: The given answer is correct. You must list relevant equations yourself, and show your attempt(s); and then someone might check your math.

 

[Mene]

it is important to understand the principles and equations involved in solving a problem, rather than just relying on the given solution. In this case, the principles of vector components and dot product can be applied to solve the problem.

First, we need to understand that the rope BC exerts a force on the bar AB at point B, which can be represented as a vector (800 N) in the direction of the rope. To find the vector components of this force parallel to the bar, we need to break down the force vector into its components along the x, y, and z axes.

Using the dot product formula, we can find the component of the force vector along the x-axis:

F_parallel = F · cosθ

Where θ is the angle between the force vector and the x-axis. In this case, θ = 0°, so cosθ = 1.

Therefore, F_parallel = 800 N · 1 = 800 N in the x-direction.

Similarly, we can find the component along the y-axis:

F_parallel = F · sinθ

Where θ is the angle between the force vector and the y-axis. In this case, θ = 90°, so sinθ = 0.

Therefore, F_parallel = 800 N · 0 = 0 N in the y-direction.

Lastly, we can find the component along the z-axis:

F_parallel = F · sinθ

Where θ is the angle between the force vector and the z-axis. In this case, θ = 90°, so sinθ = 0.

Therefore, F_parallel = 800 N · 0 = 0 N in the z-direction.

Therefore, the vector components of the force parallel to the bar are 800 N in the x-direction, 0 N in the y-direction, and 0 N in the z-direction. This can be represented as a vector as -800i + 0j + 0k N.

It is important to understand the principles and equations involved in solving a problem rather than just relying on the given solution. This will not only help in solving similar problems in the future but also in understanding the underlying concepts of the problem.