The figure to the left shows block A (5.70 kg) resting on a smooth (no friction)

Question

The figure to the left shows block A (5.70 kg) resting on a smooth (no friction) horizontal surface. Block A is connected by a mass-less string over a mass-less, frictionless pulley to block B (3.20 kg). Find the acceleration of block A (magnitude and direction). The figure to the right shows block A (10.70 kg) resting on an inclined surface (mu _s = 0.35, mu _k = 0.25). Block A is connected by a mass-less string over a mass-less, frictionless pulley to block B (3.20 kg). Determine if the blocks moving. If they are moving, determine the acceleration of the blocks (magnitude and direction).

Explanation / Answer

5) on block B, 3.20g - T = 3.20a

on block A, T = 5.70a

3.20g = (3.20 + 5.70)a

a = 3.53 m/s^2

6) when bloacks are at rest,

T = mBg = 3.20 x 9.81 =31.39 N
Weight force along incline on A = 10.70 x 9.81 x sin37 = 63.17 N

force difference = 31.78

normal force on A = 10.70gcos37

Max friction = uN = 0.35 x 10.70 x cos37 = 29.34 N

max. forces is less than force diff so blocks will start tomove and kinetic friction will work.

on A,

63.17 - T - (0.25 x 10.70 x 9.81 x cos37) = 10.70 a

onB,

T - 3.20g = 3.20a

adding them,

a = 0.78 m/s^2

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