Determine the components of P in the i, j, and k directions.

[anonymous812]

Homework Statement

As shown, a pole is subjected to three forces: F, P, and T. The force F expressed in Cartesian vector form is F=[5 i+7 j+6 k] N. Force P has magnitude 7.48 N and acts in the direction given by these direction angles: α=143∘, β=57.7∘, and γ=74.5∘ to the x, y, and z axes, respectively. Force T lies within the yz plane, its direction is given by the 3-4-5 triangle shown, and its magnitude is 14 N.
Determine the components of P in the i, j, and k directions.

Homework Equations

A_x=Acos(α)
cos^2(α)+cos^2(β)+cos^2(λ)=1

The Attempt at a Solution

Honestly, I'm very confused as to how to approach this problem. I was under the impression that the x component was 0, y component was 8.40 and the z component was 11.2. I solved these by making a 2D plane from the P vector into a 3-4-5 right triangle. 3 on y, 4 on z, and 5 as the hyp.
I would really appreciate a better explanation of how to approach this question..I think I'm making it more difficult than it is.
Thank you!

 

[rude man]

Why arer F and T given if P is the only force to be found? It's not as if P is somehow related to T and/or F.

 

[anonymous812]

There are multiple parts to the question.. I'm only asking about the P vector.

 

[rude man]

1. . I was under the impression that the x component was 0, y component was 8.40 and the z component was 11.2. I solved these by making a 2D plane from the P vector into a 3-4-5 right triangle. 3 on y, 4 on z, and 5 as the hyp.
I would really appreciate a better explanation of how to approach this question..I think I'm making it more difficult than it is.
Thank you!

Taking just the x component of P, the only way that component could be zero is if alpha = 90 (or 270) deg.

Look at P: what is the projection of P along the x axis?
Hint: cos(α) = P*i/|P|

(vectors in bold, * signifies dot product)

 

[Nickie]

To determine the components of P in the i, j, and k directions, we can use the given magnitude and direction angles to calculate the x, y, and z components of P.

First, we can use the formula A_x = A*cos(α) to find the x component of P. Plugging in the values, we get A_x = 7.48*cos(143°) = -2.69 N.

Next, we can use the formula A_y = A*cos(β) to find the y component of P. Plugging in the values, we get A_y = 7.48*cos(57.7°) = 4.77 N.

Lastly, we can use the formula A_z = A*cos(γ) to find the z component of P. Plugging in the values, we get A_z = 7.48*cos(74.5°) = 2.63 N.

Therefore, the components of P in the i, j, and k directions are -2.69 N, 4.77 N, and 2.63 N, respectively.

It is important to note that while your approach of using a 3-4-5 right triangle to solve for the components may work, it is not a generalizable method and may not be accurate for other vectors with different magnitudes and direction angles. Using the formulas for calculating the components is a more reliable and efficient method.