A wooden rod of negligible mass and length 84.0 cm is pivoted about a horizontal

Question

A wooden rod of negligible mass and length 84.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.600 kg clings to one end of the stick, and a mouse with mass 0.200 kg clings to the other end. The system is released from rest with the rod horizontal. If the animals can manage to hold on, what are their speeds as the rod swings through a vertical position?

Explanation / Answer

Mass of rat Mr = 0.600 kg Mass of mouse Mm = 0.200 kg The length of the rod = L = 0.84 m According to conservation of energy we have Change in KE = - change in PE So that we can write 0.5 [ Mr + Mm] Vf^2 = - [Mr g dr + Mm g dm ] Where - dr = dm = L / 2 ==> 0.5 [ Mr + Mm] Vf^2 = -g [-Mr + Mm ] (L/2) => Vf = [ g L ( Mr - Mm) / (Mr + Mm) ] ^1/2 = [ 9.8 * 0.84 * (0.6 - 0.2) / (0.6 + 0.2) ]^1/2 = 2.028 m/s

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