Question

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.

Answer 1

Answer:

— 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

Answer 2

Answer:

The equilibrium points include

x₁ = - 1.177

x₂ = 0

x₃ = 1.177

Explanation:

At equilibrium, the sum of forces acting on a body is equal to zero.

F(x) = ax (b − cx²) [a = 8.97, b = 7.83, c = 5.65]

F(x) = (abx - acx³)

= (8.97×7.83)x - (8.97×5.65)x³

F(x) = 70.2351x - 50.6805x³

At equilibrium, F(x) = 0

70.2351x - 50.6805x³ = 0

x(70.2351 - 50.6805x²) = 0

x = 0 or (70.2351 - 50.6805x²) = 0

70.2351 - 50.6805x² = 0

50.6805x² = 70.2351

x² = (70.2351/50.6805)

x² = 1.385840708

x = ± 1.177

So, x = -1.177, 0 and 1.177

x₁ = - 1.177

x₂ = 0

x₃ = 1.177

Hope this Helps!!!