The figure below shows a metal slab. Half of the slab consists of aluminum of de
ID: 2262686 • Letter: T
Question
The figure below shows a metal slab. Half of the slab consists of aluminum of density 2.70 g/cm3 and half of the slab consists of iron of density 7.85 g/cm3. If the dimensions of the slab are d1 = 11.0 cm, d2 = 2.80 cm, and d3 = 13.0 cm, where is the centre of mass? Express your final answer as an (x, y, z) position coordinate.
Explanation / Answer
first af all we find the centre of mass of iron in all three axes it can be found out just by considering symmetry
centre of mass of iron x axis d3/2 = 13/2 = 6.5cm
centre of mass in y = d1 / 2 = 11/2 = 5.5
centre of mass in z axes = 2.8/2 = 1.4
similarly for aluminium they are
for x axis = 13 +6.5 = 19.5
for y = 5.5
for z = 1.4
mass of aluminium (m1)= density * volume = 13*11*2.8 *density = 1081.08 g
mass of iron (m2) = 13*11*2.8*7.85 = 3143.14 g
centre of mass of combined slab
for x axis = (m1*6.5+m2*19.5)/(m1 +m2 ) = 9.82 cm
similarly for yaxis it is 5.5
for z axis = 1.4
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