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

(x1x3) + (x4x3) = l2

(x1 -x4) + (x2x4) = 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 cos37o

fs = ms N

= 0.5 x 10 x 10 x 4/5

fs = 40 N

fk = mk N

= 0.3 x 10g cos37o

= 0.3 x 10x 10 x 4/5

10 g sin 37o

= 10 x 10 x 3/5

= 60 N

Now Pulling Force > therefore block will move

So,     10g sin37o fk = 10 a

10 x 10 x 3/5 – 24 = 10 a

Þ 10 a = 36

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