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Grade: 12th pass

                        

The resultant of two forces p and q is of magnitude p show that if p is doubled the new resultant is at rightangles to q and its magnitude Will be (4p^2-q^2)^2 answer from statics

2 years ago

Answers : (1)

Arun
24742 Points
							

use the following resultant formula

R = [A 2 + B 2 + 2ABCosθ] 1/2

where 'A 'and 'B' are two forces inclined at an angle 'θ' to each other giving a resultant force 'R'.

in the first case case

R1 = p

A = p

and B = q

so,

p2 = p2 + q2 + 2pqCosθ

or

q2 + 2pqCosθ = q + 2pCosθ = 0 (1)

or in other terms

-q2 = 2pqCosθ (2)

 

and in the second case

A = 2p

B = q

 

thus,

R22 = 4p2 + q2 + 4pqCosθ = 4p2 + q2 +2(2pqCosθ)

or

by using equation (1)

R22 = 4p2 + q2 - 2q2

or the new resultant is

R2 = [4p 2 - q 2 ] 1/2 (3)

 

the angle between R2 and q would be

α = tan-1[qSinθ / (2p + qCosθ)]

or

according to (1),

2p + qCosθ = 0

thus

tanα = qSinθ / 0 = undefined

thus,

α = 90 o

 

so, the forces q and R2 are perpendicular to each other.

2 years ago
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