Question

Derive an expression for the distance that the student indicated in part (b)(i) should

Answer 1

A system is in static equilibrium when the addition of the forces acting on it equals zero. The expression is L/X = (L/2 m₁ g) / (2.5 m₁ g).

What is static equilibrium?

The concept of static equilibrium is used to describe a stationary state in which the relative position of the components of a system does not change with time.

In the static equilibrium, the system is at rest or its mass center moves at a constant speed.

Static equilibrium refers to the forces that act on a certain resting object such that the resultant of these forces has a module equal to zero. The object expresses no motion.

We can simply think that the object or body in static equilibrium is being subjected to opposite forces acting on it, and that their addition equals zero.

......

In the exposed situation there are

• two girls sitting at opposite ends of a board.
• girl 1 has a mass m₁
• girl 2 has a mass m₂ = 2.5 m₁
• the board has a length L
• there is a support axis at the middle of the board

If we want the board to be in static equilibrium, girl 2 must sit closser to the support axis.

There is a relationship that can be used to determine the position at wich girl 2 must sit. Let us see,

There is a requisit for static equilibrium, that is that the moments of the forces acting on the system have the same magnitude and are opposite to each other.

→ The moment of a force -M- is the ratio -r- multiplied by the force -F- ⇒  

  M = rF

So, the moment of girl 1 -M₁- must be equal to the moment of girl 2 -M₂-.

M₁ = M₂

r₁F₁ = r₂F₂

→ r is the distance from the girl's position to the axis.

• If the board has a length of L meters, then the distance from each of the ends to the axis is L/2.

• r₁ = L/2

• r₂ = L/x = ?

→ Force -F- is mass -m- multiplied by gravity -g- ⇒ F = mg

  Gravity is the physical constant  

So,

• M₁ = r₁ m₁ g
• M₂ = r₂ m₂ g

In static equilibrium M₁ = M₂ ⇒ r₁ m₁ g = r₂ m₂ g

Since we need to get the position of girl 2, we will clear the equation as follows,

r₂ = (r₁ m₁ g) / (m₂ g)

Where,          

• r₂ = L/X ⇒ position of girl 2
• r₁ = L/2 ⇒ position of girl 2
• m₁ ⇒ girl 1's mass
• m₂ = 2.5 m₁ ⇒ girl 2's mass
• g is gravity

Now, replacing the terms, we have

L/X = (L/2 m₁g) / (m₂g)

L/X = (L/2 m₁) / (2.5 m₁)

L/X = L/2 / 2.5

Note: When aswering th question I suggest you check the terms used to express the relationship between forces and ratios.

You can learn more about static equilibrium at

brainly.com/question/12804448

brainly.com/question/3407536

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