Resultants of Nonconcurrent Force Systems

In summary, to determine the magnitude, direction and sense of the resultant force of a nonconcurrent force system, one must first find the x and y components of the forces using trigonometric functions. Then, the Pythagorean theorem can be used to find the magnitude of the resultant force. The inverse tangent function can be used to find the direction. Lastly, the example in the book does not use all of the given numbers in the problem, so they can be assumed to not be relevant. The final answer is a magnitude of 16.76N, direction of -70.71 degrees, and a counterclockwise sense with respect to point O.
  • #1
JordanIV
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The question is to determine the magnitude, direction and sense of the resultant force of the nonconcurrent force system. Locate the resultant with respect to point O.

I've looked at example in the book and tried to follow this problem as close to it as possible.

(1)I first tried to find the x and y components of the forces. Since I'm finding the x component, it will be cosine. I set it up as 15cos75-25(12/13) but am not sure if that's correct. Also Correct me if I'm wrong with my signs. I then found the y value, but I'm still not sure if I have set it up correctly or have any of the signs right for the the 10, 15 and 25. Correct me if I'm wrong.

(2) I then used a^2+b^2=c^2. I did -5.73^2+15.75^2=square root of 280.89=16.76

(3) I don't know what its called but its a symbol of an 'x' with a line above it equals the inverse tangent of the y and x component. So i took the inverse tangent of the y component over the x component. As you can see i did the inverse tangent of 15.75/-5.73=-70.71.

(4)The example in the book did not use either of the 4 numbers pictured(8',6',5',4'). So I assumed that it was not used in this problem.
 

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  • #2
This is the answer I got. The magnitude is 16.76N, direction is -70.71 degrees, and the sense is counterclockwise with respect to point O.Is this answer correct? If not, can you show me how to do it correctly?
 

1. What are resultants of nonconcurrent force systems?

Resultants of nonconcurrent force systems refer to the single force that has the same effect on a body as the combined effect of all the individual forces acting on that body. In other words, it is the net force acting on a body in a nonconcurrent force system.

2. How are resultants of nonconcurrent force systems calculated?

To calculate the resultant of a nonconcurrent force system, you need to determine the magnitude, direction, and point of application of each individual force. Then, you can use vector addition or the parallelogram method to find the resultant force, taking into account the angle and direction of each force.

3. What is the difference between concurrent and nonconcurrent force systems?

Concurrent force systems are forces that act on a body at a common point, while nonconcurrent force systems are forces that do not intersect at a common point. In concurrent force systems, the resultant force can be easily calculated by adding the individual forces, while in nonconcurrent force systems, vector addition is needed to calculate the resultant force.

4. What are some real-life examples of nonconcurrent force systems?

Nonconcurrent force systems can be found in many everyday situations, such as a car being driven on a curved road, a person carrying a backpack while walking, or a building being supported by multiple beams and columns. In each of these examples, the forces acting on the object do not intersect at a common point.

5. Why is it important to understand resultants of nonconcurrent force systems?

Understanding resultants of nonconcurrent force systems is crucial for engineers and scientists in designing and analyzing structures and machines. It allows them to determine the overall effect of multiple forces acting on an object and ensure that it can withstand those forces without failing. It also helps in predicting the motion and stability of objects in various scenarios.

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