Child A (mA = 40 kg) and Child B(mB = 48 kg) are playing on a seesaw. The seesaw

Question

Child A (mA = 40 kg) and Child B(mB = 48 kg) are playing on a seesaw. The seesaw is made of a uniform wood plank (M = 25 kg) that is L = 4 m long, w = 20 cm wide, and d = 4 cm thick. The plank is supported in its middle by a frictionless fulcrum. Initially, the children are seated so that the seesaw is horizontal and at rest. If child A sits at the very end of the seesaw, how far from the fulcrum should Child B sit so that the seesaw is perfectly balanced? Suppose that Child B jumps off the seesaw very quickly. What is alpha the magnitude of the initial angular acceleration of Child A after Child B jumps off the seesaw?

Explanation / Answer

As it is connected from center, the moment about the centre point due to two sides of the plank would be zero. The only moment would be due to moment from child. 1) for balance , net moment should be zero. moment = force*distance So 40*2 = 48*x So x = 1.67 m So child B should sit at distance 1.67 m from center. 2) if child B jumps, then net moment = 40*2 = 80 Nm Also net moment of inertia = (Mass of Block)*L^2 / 12 + mass of child A* distance^2 So initial angular acceleration = 80 / Net moment of inertia found in above step. = 80/360 = 0.22 rad/sec^2

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