Answer "Homework: P & Q Forces Resultant & Angle

In summary, to find the values of P, use the trigonometric identity cos^2Θ + sin^2Θ = 1 and substitute for sinΘ in equation (2). This will give you an equation with P as the only unknown variable, which you can then solve for to find the possible values of P.
  • #1
kalupahana
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Homework Statement


The resultant of two forces P & Q is √3Q. It make angle of 30o with the direction of force P. Show that P is either equal to Q or equal to 2Q.


Homework Equations


R2 = P2 + Q2 + 2PQcosΘ
tanα = QsinΘ/[P+QcosΘ]

The Attempt at a Solution


From R2 = P2 + Q2 + 2PQcosΘ

3Q2 = P2 + Q2 + 2PQcosΘ
2Q2 = P2 + 2PQcosΘ
4Q2 = P[P+QcosΘ]---------------(1)

From tanα = QsinΘ/[P+QcosΘ]
tan 30 = QsinΘ/[P+QcosΘ]
1/√3 = QsinΘ/[P+QcosΘ]
P+QcosΘ = √3QsinΘ-------------------(2)

replacing 1 with 2
4Q2 =√3 PQsinΘ
PsinΘ = 4/√3

from here what should I do to find the values of P.
 
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  • #2


To find the values of P, you can use the trigonometric identity cos^2Θ + sin^2Θ = 1 and substitute for sinΘ in equation (2). This will give you an equation with P as the only unknown variable, which you can then solve for to find the possible values of P.
 

1. What are P and Q forces?

P and Q forces are two different types of forces that act upon an object. P force, also known as the applied force, is the force that is directly applied to the object. Q force, also known as the resisting force, is the force that opposes the applied force.

2. What is a resultant force?

The resultant force is the single force that has the same effect as all the original forces acting upon an object. It is the combination of all the forces acting on an object, taking into account their magnitude and direction.

3. How do you calculate the resultant force?

To calculate the resultant force, you need to first find the horizontal and vertical components of each force. Then, add all the horizontal components together and all the vertical components together. Finally, use the Pythagorean theorem to find the magnitude of the resultant force, and use trigonometry to find its direction.

4. What is the angle between two forces?

The angle between two forces is the angle formed between the two forces when they are acting on the same object. It is measured in degrees and can be found using trigonometric functions such as sine, cosine, and tangent.

5. How do P and Q forces affect the resultant force?

If P and Q forces are acting in the same direction, they will add up to a larger resultant force. However, if P and Q forces are acting in opposite directions, they will cancel each other out, resulting in a smaller resultant force or no resultant force at all.

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