Constraint Equation

CONSTRAINT EQUATION

Here in place of constraint we will apply a trick

or T. a = coust.

Note: T a 1/v

       

10g –T = 70 a

7T -10g = 10a

70g -7T = 490 a

60g -500a

       

Constraint Equations

Simple Case

Conclusion

V₁ = V₂

a₁ = -a₂

x₁ + x₂ = l = const.

 

V₁ + V₂ = 0

 

a₁ + a₂ = 0

COMPLEX CASE

x₁ + x₃ = l₁

(x₁ – x₃) + (x₄ – x₃) = l₂

(x₁ -x₄) + (_x2 –x₄) = l₃

 

V₁ + V₃ = 0

a₁ + a₃ = 0

a₁ + a₄ – 2a₃ = 0

a₁ + a₂ – 2a₄ = 0

Þ a₂ = -7a₁

SPECIAL CASE

 

 
 

 

V₂ = V₁ cos q

a₂ = a₁ cos q  

W + Y + Z = l

 

 

 

 

V₁ = V₂ (1 + sin q)

PSUDO FORCE

T sinq = ma

T cosq = mg

 

Example Elevator or lift

T + 20 - 4g = 4a

6g – T - 30 = 6a

2g -10 = 10a

10 = 10a

 

 T + 20 - 4g = 4 x1

T = 24N

Thrust on the pulley

F = 2T = 2 x 24 = 48 N

ROUGH INCLINED PLANE

  

 

N = 10g cos37^o

f_s = m_s N

    = 0.5 x 10 x 10 x 4/5

f_s = 40 N

f_k = m_k N

   = 0.3 x 10g cos37^o

   = 0.3 x 10x 10 x 4/5

 

10 g sin 37^o

= 10 x 10 x 3/5

= 60 N

Now Pulling Force > therefore block will move

So,     10g sin37^o –f_k = 10 a

   10 x 10 x 3/5 – 24 = 10 a

Þ 10 a = 36