I have two doubts in this equilibrant problem (resultant force)

In summary, when two forces of 10 N [W] and 8.0 N are pushing an object along the ground, the equilibrant can be calculated to be 13 N [N51°E]. This can be determined by drawing a diagram and using the formula c^2 = a^2 + b^2 to find the magnitude of the equilibrant. The 51° angle represents the direction of the equilibrant in relation to the two forces. It is important to note that the equilibrant is the opposite of the resultant force, and its direction can be determined using trigonometric calculations.
  • #1
Benjamin_harsh
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Homework Statement
How to guess directions like "North East" in equilibrant problems and where does "51" angle fits in the triangle?
Relevant Equations
How to guess directions like "North East" in equilibrant problems and where does "51" angle fits in the triangle?
Two forces are pushing an object along the ground. One force is 10 N [W] and the other is 8.0 N. Sketch a diagram showing the equilibrant of these two forces, and determine the equilibrant.

Ans) Calculate the equilibrant...
C2 = a2 + b2 = 102 + 82
c = 13 NDiagram:
243237


tanΘ = opp/adj = 10 / 8
Θ = 51°

The equilibrant is 13 N [N51°E]. How to guess directions like "North East" in equilibrant problems and where does "51" angle fits in the triangle?
 
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  • #2
By "equilibrant" I think you mean "resultant force" (just different terms for the same thing, I think). :smile:

You shouldn't have to guess anything. If you are given the magnitude and direction of the two vectors (in either polar or rectangular coordinates), you should be able to draw them nose-to-tail to see the resultant (or add them using algebra in rectangular coordinates).
Benjamin_harsh said:
One force is 10 N [W] and the other is 8.0 N.
Is the "W" in your problem statement supposed to mean "West"? If so that is usually drawn as a horizontal vector pointing to the left (just like on a map with "North" at the top of the map). And why is there no direction given for the 2nd vector?
 
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  • #3
berkeman said:
By "equilibrant" I think you mean "resultant force" (just different terms for the same thing, I think).
As I read the drawing, the "equilibriant" is that force which when added to the existing forces results in a total of zero. So it is the opposite of the "resultant". [Google agrees]
 
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  • #4
where does "51" angle fits in the triangle?

You did this calculation...

Tan(angle)= Opposite/Adjacent = 10/8

So 51 degrees is the angle opposite the side of length 10.
 

1. What is an equilibrant in a force problem?

An equilibrant is a force that is equal in magnitude but opposite in direction to the resultant force of a system. It is used to balance out the forces acting on an object so that it remains in a state of equilibrium.

2. How do you determine the magnitude and direction of an equilibrant?

The magnitude of an equilibrant can be determined by using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The direction of the equilibrant can be found by taking the inverse tangent of the opposite and adjacent sides of the triangle.

3. Can there be multiple equilibrants in a force problem?

Yes, there can be multiple equilibrants in a force problem if there are multiple resultant forces acting on an object. Each equilibrant will be equal in magnitude but opposite in direction to its corresponding resultant force.

4. What happens if the equilibrant is not equal in magnitude to the resultant force?

If the equilibrant is not equal in magnitude to the resultant force, the object will not be in a state of equilibrium. This means that the object will either be moving or accelerating in the direction of the net force acting on it.

5. How is the concept of an equilibrant used in real-life situations?

The concept of an equilibrant is used in a variety of real-life situations, such as in structural engineering to ensure that buildings and bridges remain stable, and in physics and mechanics to calculate the forces acting on objects in motion. It is also used in sports, such as balancing on a skateboard or snowboard, to maintain equilibrium and prevent falling.

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