Question

In: Physics

Four identical masses of 2.6 kg each are located at the corners of a square with...

Four identical masses of 2.6 kg each are located at the corners of a square with 1.2 m sides. What is the net force on any one of the masses?
? ?? N toward ...............opposite corner

Solutions

Expert Solution

Let us consider the mass is m = 2.6 kg
Now the force on the mass on corner 1 due to mass on corner 2
F12 = Gm*m / r2
where r is the distance between the two mass
F12 = 6.754*10-11*(2.6*2.6) /(1.2)2 = 31.706*10-11 N
Now force on mass 1 due to mass 4 will also be same because the mass and distance is same , therefore
F14 = 31.706*10-11 N  
Now the force on mass 1 due to mass 3
Here the distance between the two mass r = (1.22 + 1.22)1/2 = 1.697 m
F13 = Gm*m /(r)2 = 6.754*10-11*(2.6*2.6) /(1.697)2 = 15.854*10-11 N
Now we will take the component of the F13 in horizontal and vertical direction as shown in the figure
Now the net force on mass toward opposite centre
Considering horizontal direction
Fnet = F12 + F13Cos45 = 31.706*10-11 + ( 15.854*10-11 )Cos45 = 42.917*10-11 N
Similarly in the y direction
Fnet = F14 + F13Sin45 = 31.706*10-11 + ( 15.854*10-11)Sin45 = 42.917*10-11 N
hence the net force on any mass toward opposite corner will be 42.917*10-11 N

genius_generous answered 1 year ago
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