The force F acting on a particle constrained to move along the x - axis is given by the fucntion F ( x ) = a x ( b − c x 2 ) [ a = 8.97 , b = 7.83 , c = 5.65 ] Find the three equilibrium points x 1 , x 2 , and x 3 , and enter them in order of ascending x ‑coordinate.

— 1.177

0

1.177

Explanation:

Given that,

F(x) = ax(b — cx²)

Given that,

a = 8.97

b = 7.83

c = 5.65

F(x) = ax(b—cx²)

F(x) = abx — acx³

F(x) = 8.97 × 7.83x — 8.97 × 5.65x³

F(x) = 70.2351x —50.6805x³

Then, For a body to be in equilibrium the sum of forces acting on the body is zero. i.e. F(x) = 0

0 = 70.2351x —50.6805x³

70.2351x —50.6805x³ = 0

x(70.2351 —50.6805x²) = 0

For the multiplication of two number to be zero, it is either one of the number is zero or both of the number is zero

Therefore,

x = 0 OR 70.2351 —50.6805x² = 0

x=0

70.2351 — 50.6805x² = 0

50.6805x² = 70.2351

x² = 70.2351/50.6805

x² = 1.38584

x = √1.38584

x = ± 1.177

Then, the equilibrium position is

- 1.177, 1.177 and 0

So, the ascending order of the equilibrium position is -1.177, 0, 1.177

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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