A person with mass m 1 = 51 kg stands at the left end of a uniform beam with mas

Question

A person with mass m1 = 51 kg stands at the left end of a uniform beam with mass m2 = 105 kg and a length L = 3.3 m. Another person with mass m3 = 58 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 8 kg (assume that the medicine ball is at the far right end of the beam as well). Let the origin of our coordinate system be the left end of the original position of the beam as shown in the drawing. Assume there is no friction between the beam and floor.

I am confused about the position of m1, m3 and m4

Explanation / Answer

The objects are person 1 mass = 66 x =0 so mx= 0
beam mass = 104 x = 1.65m ( its centre is only half way along) mx= 172
person 2 mass = 62 x= 3.3 mx= 205
and ball mass = 12 x= 3.3m mx=40

Add up the total moments (416) and divide by the total mass (244 Kg)

Centre of mass is 416/244 = 1.7 m from the left end.

As there is no friction the centre of mass can't move no matter what. Momentum is always conserved. It remains at 1.7 m from the original position of the left end.

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