Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and also Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearchild, 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 drawing a vector diagram to assist us visualize the actions much better prefer so:

Note that we just emphasis on force F_1 because the question only asks us to identify the coordinate direction angles of pressure F_1. Hence, we just attracted the vector components of force F1. No must attract unnecessary components considering that that will certainly only make it even more hard for us to visualize the steps.### Let us now look at the components of force F_1.

### We have the right to create each component favor so:

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

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

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

### We have the right to currently compose force F_1 in Cartesian vector create favor so:

### F_1=600left\frac45, extcos,30^0(+i),+,frac45, extsin,30^0(-j),+,frac35(+k)
ight

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

(the indications for i,j, and k have the right to be seen looking at the diagram. We can watch that the j component is in the negative direction, therefore, we deserve to compose it as -j)### Now, we must uncover the unit vector. To carry out so, remember that we ssuggest divide the Cartesian vector form by the value of F_1 which in this case is 600 N.

### (u_F)_1=frac600(0.6928i-0.4j+0.6k), extN600, extN

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

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

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### alpha= extcos^-1((u_F)_1)_x

### alpha= extcos^-1(0.6928) =46.1^0

### eta= extcos^-1((u_F)_1)_y

### eta= extcos^-1(-0.4) =114^0

### gamma= extcos^-1((u_F)_1)_z

### gamma= extcos^-1(0.6) =53.1^0

This question have the right to be found 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: Pearchild, 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)