An object with mass m1 = 4.00 kg, rests on a frictionless horizontal table and i

Question

An object with mass m1 = 4.00 kg, rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 = 10.0 kg. Find the acceleration of each object and the tension in the cable.
mass m1

mass m2

tension

Explanation / Answer

For mass m1 : T - m1 g = m 1 a For mass m2 m2 g - T = m2 a From above two equations we have m2 g - ( m1 g + m 1 a ) = m2 a ==> g ( m2 - m1) = a ( m1 + m2) ==> acceleration a = g (m2 - m1) / (m1 + m2) = 9.8 * (10 - 4) / (4 + 10) = 4.2 m/s^2 Tension T = m1 ( a + g) = 4 * (4.2 + 9.8) = 56 N acceleration of the each mass = 4.2 m/s^2 Tension T = 56 N

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