A beam weighing 800 kg has a length of 4 m and is supported at a distance of 1.9 m from its left end.

| February 16, 2021 | education

A beam weighing 800 kg has a length of 4 m and is supported at a distance of 1.9 m from its left end. At what distance from this end must a person weighing 80 kg be in order for the beam to remain in balance?

Data: mb (beam weight) = 800 kg; L (beam length) = 4 m; Ll (distance between the support and the left end) = 1.9 m; mh (human weight) = 80 kg.

1) Mass of the left end of the beam: ml = mb * Ll / L = 800 * 1.9 / 4 = 380 kg.

2) The mass of the right end of the beam: mpr = mb – ml = 800 – 380 = 420 kg.

3) Length of the right end of the beam: Lpr = L – Ll = 4 – 1.9 = 2.1.

4) The sum of the moments of forces: Fch * l + Fl * Ll / 2 – Fpr * Lpr / 2 = 0.

mh * g * l + ml * g * Ll / 2 – mp * g * Lpr / 2 = 0.

l = (mp * Lpr 2 – ml * Ll / 2) / mh = (420 * 2.1 / 2 – 380 * 1.9 / 2) / 80 = 1 m.

Answer: The person should stand at a distance of 1 m from the support (0.9 m from the left end).



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