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

Question

A four 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 18.8 kg, and his centre of mass is b = 60.8 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?

A four 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 18.8 kg, and his centre of mass is b = 60.8 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

Use the principle of moments. The fulcrum of the moments on the system can be considered to be the point where the boys feet touch the base of the TV stand. The point of equilibrium where the moment exerted by the boy offsets the combined moments of the TV and TV Stand about this point is the maximum angle at which the boy can position himself without the stand tipping over.

Assume the Boy is standing at an angle (x) to the vertical. Therefor the moment exerted by him about the fulcrum is :

18.8 X 60.8 sin(x)

The moment exerted by the TV = 20 X 15

The moment exerted by the TV Stand = 10 X 25

Equating the two, we have:

20X15 + 10X25 = 18.8 X 60.8 sin(x)

Therefore sin(x) = 0.4811

Hence x=28

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