Do not round Intermediate calculations; however, for display purposes report int

Question

Do not round Intermediate calculations; however, for display purposes report intermediate steps rounded to five significant figures. Give your final answer(s) to five significant figures. Blocks A abd B are connected by a pulley system. The coefficient of kinetic friction between the blocks A and the incline is mu_K = -0.2 and static friction is insufficient to prevent slipping. The mass of A is m_A = 7 Kg, the mass is m_B = 20 Kg. and the angle between the incline and the horizontal is 0 = 24 degree. Determine the acceleration of A, the acceleration of B, and the tension in the rope after the system is realeased.

Explanation / Answer

Let the Tension in the string be T,

Now,
mB*g - 4*T = mB*aB
20*9.8 - 4*T = 20*aB
196 - 4*T = 20*aB -------1

2T - mA*g*sin(24) - uk*mA*g*cos(24) = mA*aA
2T - 7*9.8*sin(24) - 0.2*7*9.8*cos(24) = 7*aA
2T - 15.4 = 7*aA -------2

aA = 2*aB -----------3

Solving these 3 eq,
aA = 6.883 m/s^2
aB = 3.442 m/s^2
T = 31.79 N

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