Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and also Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

You are watching: Determine the coordinate direction angle α of the resultant force.

Solution:

August 23, 2016 in Mechanics: Statics tagged engineering Mechanics: Statics / rectangular components

Solution:### We will begin off by illustration a vector diagram to aid us visualize the steps far better like so:

Note that us only emphasis on force F_1 since the question just asks us to recognize the coordinate direction angle of pressure F_1. Thus, we only attracted the vector materials of pressure F1. No need to draw unnecessary components because that will just make that more an overwhelming for us to visualize the steps.### Let us currently look in ~ the materials of force F_1.

### We can write every component prefer so:

### (F_1)_x=600(\frac45)\,\textcos\,30^0 N

### (F_1)_y=600(\frac45)\,\textsin\,30^0 N

### (F_1)_x=600(\frac35) N

### We can now write pressure F_1 in Cartesian vector type like so:

### F_1=600\left\\frac45\,\textcos\,30^0(+i)\,+\,\frac45\,\textsin\,30^0(-j)\,+\,\frac35(+k)\right\

### F_1=600\left<0.6928i-0.4j+0.6k\right> N

(the indications for i,j, and k deserve to be checked out looking at the diagram. We have the right to see the the j ingredient is in the an adverse direction, thus, we have the right to write it as -j)### Now, we require to uncover the unit vector. To perform so, remember the we merely divide the Cartesian vector type by the value of F_1 which in this case is 600 N.

### (u_F)_1=\frac600(0.6928i-0.4j+0.6k)\,\textN600\,\textN

### (u_F)_1=0.6928i-0.4j+0.6k

### The last action is to find the coordinate direction angles.

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### \alpha=\textcos^-1((u_F)_1)_x

### \alpha=\textcos^-1(0.6928) =46.1^0

### \beta=\textcos^-1((u_F)_1)_y

### \beta=\textcos^-1(-0.4) =114^0

### \gamma=\textcos^-1((u_F)_1)_z

### \gamma=\textcos^-1(0.6) =53.1^0

This question deserve to be uncovered in engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-75.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and also Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

You are watching: Determine the coordinate direction angle α of the resultant force.

Solution:

See more: Pandemic Legacy Military Base, Pandemic Legacy: Season 1 Review (W/ Spoilers)