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natka813 [3]
2 years ago
13

Three small spheres, having masses m1 = 1 kg, m2 = 3 kg, and m3 = 4 kg, are held fixed on the x axis in deep space where the eff

ects of earth's gravity can be neglected. They are positioned at x = 0, x = 3 m, and x = 6 m, respectively. What is the magnitude of net gravitational force on m2?

Physics
2 answers:
Vlad [161]2 years ago
6 0

Answer: F_{net} = 0.7411 N towards the mass m_{3}

Explanation: We know that the gravitational force is a long range force which is always attractive in nature.

Given that:

  • mass m_{1} = 1 kg
  • mass m_{2} = 3kg
  • mass m_{3} = 4kg

The masses are positioned on X-axis at the following points:

  • Position of mass m_{1}  x_{1} = 0
  • Position of mass m_{2}  x_{2} = 3
  • Position of mass m_{3}  x_{3} = 6

Mathematically:

<em>Gravitational force on mass </em>m_{2}<em> due to mass </em>m_{1}<em> is given by </em>

F_{21} = G \frac{m_{1}.m_{2}}{(r_{21})^2}...................(1)

  • where: (r_{21})^2= the radial distance between masses m_{2} & m_{1}=3

Similarly, g<em>ravitational force on mass </em>m_{2}<em> due to mass </em>m_{3}<em> is given by </em>

F_{23} = G \frac{m_{3}.m_{2}}{(r_{23})^2}............................(2)

  • where: (r_{23})^2= the radial distance between masses m_{2} & m_{3}=3

Now, put the respective values in the above equations.

F_{21} = 6.67 \times 10^{-11 }\times \frac{1\times 3}{3^2}

F_{21} = 2.2233\times 10^{-11} N

Again,

F_{23} = 6.67 \times 10^{-11 }\times \frac{1\times 4}{3^2}

F_{23} = 2.9644\times 10^{-11} N

∵Mass m_{2} is in the middle of the masses m_{3} & m_{1} therefore the forces  F_{23} & F_{21} will attract them in radially opposite direction.

∴F_{net} = F_{23} -F_{21} \\\\F_{net} = 2.9644-2.2233\\\\F_{net} = 0.7411 N towards the mass m_{3}

san4es73 [151]2 years ago
4 0

Answer:

The magnitude of the net force on m_{2} is 7.411\times 10^{- 11}\ N

Solution:

As per the question:

m_{1} = 1\ kg

m_{2} = 3\ kg

m_{3} = 4\ kg

Respective positions of the above mentioned masses are:

x = 0 m

x = 3 m

x = 6 m

Now,

We know that the gravitational force between two masses separated by some distance is given by:

F_{G} = \frac{GMm}{x^{2}}

Therefore. the net gravitational force on m_{2} is given by:

F_{G, net} = F_{G,2-3} - F_{G, 1-2}

F_{G, net} = \frac{Gm_{2}m_{3}}{x^{2}} - \frac{Gm_{1}m_{2}}{x^{2}}

F_{G, net} = \frac{G}{x^{2}}(m_{2}m_{3} - m_{1}m_{2})

where

G = Gravitational constant

F_{G, net} = \frac{6.67\times 10^{- 11}}{3^{2}}(4\times 3 - 1\times 2)

F_{G, net} = 7.411\times 10^{- 11}\ N

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