A tour year old boy had to be admitted to hospital after tipping over a large te

Question

A tour year old boy had to be admitted to hospital after tipping over a large television set which landed on his head. He had been pulling himself up, holding on to a ledge at the front of the TV stand, when the accident happened. The boy spoke a few words, then lost consciousness. He had to spend three months in hospital and was still suffering from significant neurological deficits afterwards. Assume a TV stand that is h = 81.0 cm high and d = 50.0 cm deep, with a mass of 10.0 kg, and a centre of mass at its geometric centre. The TV set has mass 20.0 kg; it rests on top of the stand, with its centre of mass c = 15.0 cm back from the edge. The boy's mass is 15.3 kg, and his centre of mass is b = 59.0 cm away from his heels. If the boy was holding on to the top of the stand, with his toes pressed against the base, leaning straight back, what is the maximum angle of the boy's body (and legs) with respect to the vertical without the TV stand tipping over?

Explanation / Answer

Assume the Boy is standing at an angle (x) to the vertical.

Therefor the moment exerted by him about the fulcrum is : mg sin theta

Moment = 15.3 * 59 sin(x) = 902.7 sin x

The moment exerted by the TV = 20 * 15 = 300

The moment exerted by the TV Stand = 10 * 25 = 250

Equating the two, we have:

300 + 250 = 902.7 sin(x)

Therefore sin(x) = 550/902.7 = 0.609

x = 37.57 deg -------------------<<<<<<<<<<<<<<<<<Answer

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