The figure shows four penguins that are being playfully pulled along very slippe

Question

The figure shows four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are m1 = 10.0 kg, m3 = 14 kg, m4 = 21 kg, T2 = 117 N, and T4 = 214 N. What is the mass of the second penguin (the mass m2 not given)?

Explanation / Answer

There is no friction, thus all force is used to accelerate the penguins. All are tied together, so they each undergo the same acceleration. So apply F=ma twice, solve these equations for m2. Apply F = ma ==> a = F/m a = T2 / (m1 + m2) a = T4 / (m1 + m2 + m3 + m4) Set equal, T2 / (m1 + m2) = T4 / (m1 + m2 + m3 + m4) Invert, divide both sides by T2, regroup: (T4/T2 - 1) m2 = (1 - T4/T2)m1 + m3 + m4 Now just plug in values in right side, divide by (T4/T2 -1) to get m2

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