Mechanical Engineering - Engineering Mechanics - Discussion
Discussion Forum : Engineering Mechanics - Section 1 (Q.No. 10)
10.
If the resultant of two equal forces has the same magnitude as either of the forces, then the angle between the two forces is
Discussion:
35 comments Page 1 of 4.
Kesav said:
4 years ago
According to Lamis theorem, sine α = sine β = sine γ.
i.e. α + β + γ =360 so 360 /3 =120 =α = β= γ.
i.e. α + β + γ =360 so 360 /3 =120 =α = β= γ.
(29)
Panneerselvam N said:
4 years ago
To find the resultant
R= √(A2)+(B2)+2ABcosx
As given in the query, the magnitude of the force is the same and let it be f whose resultant be f too.
Substituting the variables in the above equation we get
f= √(f2)+(f2)+2(f2)cosx
Squaring on both sides we get
f2=2(f2)+2(f2)cosx
f2/f2 = 2 + 2 cos x
1 - 2 = 2 cosx
-1/2 = cos x
Therefore x=120°.
R= √(A2)+(B2)+2ABcosx
As given in the query, the magnitude of the force is the same and let it be f whose resultant be f too.
Substituting the variables in the above equation we get
f= √(f2)+(f2)+2(f2)cosx
Squaring on both sides we get
f2=2(f2)+2(f2)cosx
f2/f2 = 2 + 2 cos x
1 - 2 = 2 cosx
-1/2 = cos x
Therefore x=120°.
(12)
Vaibhav said:
5 years ago
The resultant force is the same value of one of this either forces, so we can assume R=P, P1=P, P2=P.
Let using parallelogram therom,
R^2 = P1^2+P2^2+2P1P2COSθ
P^2 = P^2+P^2+2P^2COSθ
P^2 = 2P^2+2P^2COSθ
2P^2COSθ = -P^2
And θ=120°.
Let using parallelogram therom,
R^2 = P1^2+P2^2+2P1P2COSθ
P^2 = P^2+P^2+2P^2COSθ
P^2 = 2P^2+2P^2COSθ
2P^2COSθ = -P^2
And θ=120°.
(3)
S V Manikandan. said:
5 years ago
The two forces acting with the same magnitude and resultant too same magnitude. So the angle between each two forces is equal. So we can divide the circle into three equal segments. The angle of a circle is 360°. Then 360/3 = 120°each.
(2)
Sachin said:
7 years ago
Based on the Law of parallelogram.
(1)
P.Chilambarasan said:
9 years ago
R^2 = P^2 + q^2 + 2pq Cosθ.
R = P = Q = F.
Substitute F in the equation, you get Cosθ = -1.
So, θ = 180°.
R = P = Q = F.
Substitute F in the equation, you get Cosθ = -1.
So, θ = 180°.
Ankit ughade said:
9 years ago
For getting the equilibrium condition all these forces must have the same angle to each other.
Hence 360/3 = 120.
Hence 360/3 = 120.
Dhanendra said:
9 years ago
Correct answer will be 60θ as in fcosθ plus fcosθ equal to f which gives θ equal to 60θ.
Srinu said:
9 years ago
It is based triangle law of forces.
Komal said:
9 years ago
It is based on the law of parallelogram.
Two adjacent sides having forces say 'P' & 'Q' then resultant 'R' is given by,
R^2 = P^2 + Q^2 + 2PQ Cosθ.
Solving this equation taking P = Q will get answer as 120.
Two adjacent sides having forces say 'P' & 'Q' then resultant 'R' is given by,
R^2 = P^2 + Q^2 + 2PQ Cosθ.
Solving this equation taking P = Q will get answer as 120.
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