# Determine the resulting motion of the body A, assuming the pulleys to be smooth and weightless as shown in fig.

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Determine the resulting motion of the body A, assuming the pulleys to be smooth and weightless as shown in fig. If the system starts from rest, determine the velocity of the body A after 10 seconds.

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Given data: Mass of Block A = 10Kg

Mass of Block B = 15Kg

Angle of inclination α = 300

Co-efficient of friction m = 0.2

Consider the motion of block B,

The acceleration of block B will be half the acceleration of the block A i.e. a/2,

M1g – 2T = m1(a/2)

15 X 9.81 – 2T = 15 (a/2)

147.15 – 2T = 7.5a ...(1)

Consider the motion of block B

T – W2sin α – µW1cos α = (W1/g)a

T - m2g sin α – 0.2m2 gcos α = m2a

T – 10 X 9.81sin 300 – 0.2 X 10 X 9.81cos300 = 10a

T – 66.04 = 10a ...(2)

Adding equation (1) with 2 X equation (2)

147.15 – 2T + 2T – 132.08 = 7.5a + 20a a = 0.54 m/sec2

Now velocity of the block after 10 sec,

Apply v = u + at

V = 0 + 0.54 X 10

V = 5.4m/sec