How can I find the resultant force using only the law of cosines and sines?

In summary, Casey is trying to use the law of cosines and sones to find the resultant force F_r, but is struggling to find a usable angle. After some discussion and hints, it is suggested to draw a diagram and use head-to-tail addition to identify the angle between the vectors. The angle is found to be 60 degrees and Casey realizes that vectors can be moved around to generate more information.
  • #1
Saladsamurai
3,020
7

Homework Statement


Okay, I am only allowed to use law of cosines and sones to find the resultant force F_r

I am having a hell of a time finding a usable angle after drawing my parellelogram..so obviously I am in need of sleep.

What am I missing here? (pic is clickable)
th_Photo2.jpg



Casey
 
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  • #2
I know I need to isolate a triangle, but I really suck at similar triangles when they are not necessarily right triangles.
 
  • #3
Draw yourself a diagram where you add the vectors (head to tail addition). The two vectors are the two sides of a triangle. You should be able to identify the angle between them and apply the law of cosines to find the third side of the triangle, which will be the resultant.
 
  • #4
The 120 degree angle should be the angle corresponding to your resultant vector in the triangle. For the other angles:

HINT: What is the angle between the 80lb force and the -x axis? Does this help you find another angle in your parallelogram?
 
  • #5
Is the angle between them by any chance 60 degrees? In the parellepgram 2(120)=240 leaving 120/2 to give me four angles that add to 360
 
  • #6
Saladsamurai said:
Is the angle between them by any chance 60 degrees?
Yes. (Assuming you're talking about the triangle I referred to.)
 
  • #7
I'll be back in 20 minutes. All of the theological students just showed up at StarBucks and I can't take their banter...I'm going home.

Casey

Doc Al said:
Yes. (Assuming you're talking about the triangle I referred to.)

Angle between 60 and 80 with tail of 60 at tip of 80.
 
  • #8
Run for it, man! :wink:
 
  • #9
I made it home!

Thanks Doc and G01! I am taking this Statics course over X-mass break :points gun into mouth and fake blows brains out:

So is the general approach to these to use the fact that vectors can be moved around to redraw the scenario in a manner that helps to generate more information from the given info?

Casey
 
  • #10
Yes. When adding vectors, you can move them around at will as long as you keep the magnitude and direction the same.
 

What is the definition of resultant force?

The resultant force is the single force that has the same effect as all the individual forces acting on an object combined. It is the vector sum of all the forces acting on the object.

How do you find the resultant force?

To find the resultant force, you must first identify all the individual forces acting on the object. Then, use vector addition to add all the forces together. The resultant force will be the magnitude and direction of the final vector.

What is the difference between resultant force and net force?

The resultant force is the overall effect of all the forces acting on an object, while the net force is the sum of all the forces in a specific direction. The resultant force takes into account both the magnitude and direction of the forces, while the net force only considers the magnitude.

Can the resultant force be zero?

Yes, the resultant force can be zero if all the forces acting on an object are balanced and cancel each other out. This means that the object is in a state of equilibrium and will not accelerate in any direction.

How does the angle between forces affect the resultant force?

The angle between forces affects the magnitude and direction of the resultant force. If the forces are in the same direction, the resultant force will be equal to the sum of the individual forces. If the forces are in opposite directions, the resultant force will be the difference between the two forces. If the forces are at an angle, the resultant force can be found using trigonometry.

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