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

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.