Calculating Resultant Force: Comparing Methods and Identifying Errors

In summary, the conversation discusses two methods for finding the resultant force of a given diagram. The first method, using the law of cosines, yields a result of 49N. However, the second method, breaking down the force vectors into x and y components and using the Pythagorean theorem, yields a result of 55N. The conversation concludes with the question of whether there is something wrong with the first method and a suggestion to use the second method instead.
  • #1
vipertongn
98
0
Ok so I have something like this...not drawn to scale

http://i53.tinypic.com/303l5k6.gif

I can see that with the law of cos I can get 49N

However...with this other method where you set Sum of F=0

With sqrt(Fx^2+Fy^2)=R

sqrt((40*cos(20)+20*cos(30))^2+(40*sin(20)-20*sin(30))^2)

I get 55N

Is there soemthing wrong? I'm pretty sure the first answer is correct...but I don't know why this one isnt...
 
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  • #2
The second one looks right, so I'm guessing the first is wrong... what do you mean using the law of cos?

I think the best way is to just break down each force vector into its x and y components; add those to find the resultant, then use the Pythagorean theorem to find the magnitude of the resultant (that's effectively what you did with your second method).
 

FAQ: Calculating Resultant Force: Comparing Methods and Identifying Errors

1. What is the definition of resultant force?

The resultant force is the single force that has the same effect on an object as all the individual forces acting on that object combined. It is the overall force acting on an object, taking into account both magnitude and direction.

2. How do you calculate the resultant force?

To calculate the resultant force, you must first find the vector sum of all the individual forces acting on an object. This means adding the magnitudes of the forces in the same direction and subtracting the magnitudes of forces in opposite directions. Then, use the Pythagorean theorem to find the magnitude of the resultant force and trigonometric functions to find its direction.

3. What is the importance of finding the resultant force?

Finding the resultant force is important because it allows us to determine the overall effect of multiple forces acting on an object. This is crucial in understanding the motion and behavior of objects, especially in complex systems where multiple forces are present.

4. Can the resultant force be zero?

Yes, the resultant force can be zero if the vector sum of all the individual forces acting on an object is equal to zero. This means that the forces are balanced and there is no overall effect on the object's motion.

5. How does the direction of the resultant force relate to the individual forces?

The direction of the resultant force will depend on the direction of the individual forces acting on an object. If the individual forces are all in the same direction, the resultant force will also be in that direction. If the forces are acting in different directions, the resultant force will be at an angle between them.

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