Question

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.

Answer 1

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