The resultant of two equal forces is double of either of the force the angle between them is

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The resultant of two equal forces is double of either of the force. The angle between them is :

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The resultant of two equal forces is double of either of the force. What is the angle between them?

Answer: Let the two equal force each are F and their resultant is 2F. Angle between the vectors is Theta. By vector addition law, F^2+F^2+2*F*F*Cos Theta= 4F^2 or, 2F^2+ 2F^2 Cos Theta= 4F^2 or, 2F^2(1+Cos Theta)= 4F^2 or, 1+Cos Theta= 2 or, Cos Theta = 1 or, Theta =0 degree Therefore, th...

The resultant of two equal forces is double of either of the force. What is the angle between them?

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Answered Dec 22, 2021 · Author has 155 answers and 23K answer views

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At what angle should two equal forces act so that the resultant is equal to either of the force?

Wouldn’t we be looking at an equilateral triangle? Whose interior angles would be 60°.

Having two of these triangles side by side: and sharing one side; the angle from one force vector to the other force vector would be 120°

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Sourav Mondal

, B.Sc Physics & Mathematics, University of Calcutta (2007)

Answered 9 months ago · Author has 170 answers and 33K answer views

Let the two equal force each are F and their resultant is 2F. Angle between the vectors is Theta.

By vector addition law,

F^2+F^2+2*F*F*Cos Theta= 4F^2

or, 2F^2+ 2F^2 Cos Theta= 4F^2

or, 2F^2(1+Cos Theta)= 4F^2

or, 1+Cos Theta= 2 or, Cos Theta = 1 or, Theta =0 degree

Therefore, the angle between the vector is 0 degree i.e. these vectors are acting along the same line or parallel.

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Answered 2 years ago · Author has 916 answers and 535.5K answer views

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One of the two forces is double the other and resultant is equal to the greater force, what is the angle between?

Thank you Aamna Shoukat for A2A.

I found some errors in the text of the question. So made minor corrections.

Solution:

Given: Force one = F

Force two = 2F Resultant = 2F

Using Law of parallelogram of forces

|R| = sqrt (|P|^2 + |Q|^2 +2|P||Q| cos θ) …………(1)

where θ is angle between the two forces.

Inserting given values in (1) we get

2F = sqrt (F^2 + (2F)^2 + 2 F (2F) cos θ)

squaring both sides we get

4F^2 = 5F^2 + 4F^2 cos θ

or 4 cos θ = -1

or θ = arc cos (-1/4)

or θ = 104.5 deg Hope this helps

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Aamna Shoukat Kim Aaron

, Has PhD in fluid dynamics from Caltech

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The resultant of two equal forces may have the magnitude equal to one of the forces. At what angle between the two equal forces is this possible?

The resultant of two equal forces may have the magnitude equal to one of the forces. At what angle between the two equal forces is this possible?

Two of them drawn tip to tail:

The same two drawn tail to tail and “the angle between them.”

So 120° is the answer to your question.

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Sejal Bhatt Waqas Saeed

, studied at Massachusetts Institute of Technology (2005)

Answered 1 year ago Related

The resultant of two forces of equal magnitudes is equal to the magnitude of force. What is the angle between them?

The angle is 120°. Let F be the magnitude of each of the vectors as well as its resultant.

Using parallelogram law,

F^2=F^2+F^2+2F^2cosθ​

∴cosθ=−1​/2 ∴θ=120∘

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Gopal Menon

, B Sc (Hons) Mathematics, Indira Gandhi National Open University (2010)

Answered 3 years ago · Author has 9.7K answers and 7.8M answer views

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Two equal forces have their resultant equal to either. What is the angle between them?

Let the two forces by

F ⃗ 1 F→1 and F ⃗ 2 F→2

and let the angle between them be

θ. θ.

Then, the magnitude of the resultant force,

F ⃗ F→ is given by, | F ⃗ |= | F ⃗ 1 | 2 +2| F ⃗ 1 || F ⃗ 2 |cosθ+| F ⃗ 2 | 2 − − − − − − − − − − − − − − − − − − − − − − − − √ .

|F→|=|F→1|2+2|F→1||F→2|cos⁡θ+|F→2|2.

It is given that the two forces as well the resultant force are equal in magnitude.

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The resultant of two equal forces is equal to either of these forces. The angle between them is

The resultant of two equal forces is equal to either of these forces. The angle between them is

JEE QuestionsThe Resultant Of Two Equal Forces Is Equal To Either Of These Forces The Angle Between Them Is

The resultant of two equal forces is equal to either of these forces. The angle between them is

Let each of 2 equal forces be of magnitude P and let them be inclined at angle ɑ. Then their resultant R is given by R = 2P cos (ɑ / 2), but R = P.

P = 2P cos (ɑ / 2) cos (ɑ / 2) = 1 / 2 (ɑ / 2) = π / 3 ɑ = 2π / 3

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Text Solution

Solution : Two two forces are equal (i.e.,) <br> P = Q <br> Here R `= sqrt(3P)` <br> `R = sqrt(P^(2) +Q^(2) + 2P Q cos theta)` <br> Substituting the values <br> `sqrt(3P) = sqrt(P^(2) + P^(2) + 2P^(2) cos theta)` <br> Squaring both sides <br> `3P^(2) + P^(2) + P^(2) + 2P^(2) cos theta` <br> `3P^(2) = P^(2) (1 + 1+ 2cos theta)` <br> `= 2P^(2) + 2P^(2) cos theta` <br> `:. P^(2) = 2P^(2) cos theta` <br> `2 cos theta = 1` <br> `cos theta = (1)/(2) (or) theta = 60^(@)` .