If the 20-kg block A is moving down at 0.6 m/s at the instant shown (t = 0), det

Question

If the 20-kg block A is moving down at 0.6 m/s at the instant shown (t = 0), determine the velocity of the 6-kg block B in t = 4 s.  Also, determine the tension in the cord during the motion.  The coefficient of kinetic friction between the block B and the surface is

If the 20-kg block A is moving down at 0.6 m/s at the instant shown (t = 0), determine the velocity of the 6-kg block B in t = 4 s. Also, determine the tension in the cord during the motion. The coefficient of kinetic friction between the block B and the surface is muk = 0.2. Neglect the mass of the pulleys and cord.

Explanation / Answer

Tension in rope = T

Acceleration of blocks = a

Normal force on B, N = m_b*g*Cos60

Friction force on B = 0.2*N = 0.2*m_b*g*Cos60

For block A, m_a*g - 3T = m_a*a

For block B, T - m_b*gSin60 - 0.2*m_b*g*Cos60 = m_b*a

Putting m_a = 20 kg, m_b = 6 kg, g = 9.81 m/s^2 and solving the above eqns gives,

T = 60.9 N

and a = 0.674 m/s^2

At t = 0, v_b/3 = v_a

v_b = 3*0.6 = 1.8 m/s

At t = 4 s, we get by using v = u + at

v_b = 1.8 + 0.674*4 = 4.5 m/s

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