Forces In Static Equilibrium: 9 Facts You Should Know


In classical mechanics, equilibrium describes the balance of all the forces acting on a physical system. The static equilibrium is one of the types of physical equilibrium given in this post.

Static equilibrium refers to a physical system where all the forces are balanced, and there is no relative motion of the system so that the net force and torque acting on the system is zero. From the definition, we get to know all the forces are balanced in static equilibrium. So in this force, let us discuss involvement forces in static equilibrium.

The name of the static equilibrium itself suggests that the system must be under a stationary state to attain equilibrium. Then what forces evolved in the system to attain stationary conditions?

Well, we know that all the objects or systems on earth are largely influenced by one force called gravity, which does not care if the object is moving. This shows that one force is involved in static equilibrium. Some other forces in static equilibrium are discussed in the following sections.

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Forces in static equilibrium
Image credits: Wikimedia commons

What are the roles of forces in static equilibrium?

A static equilibrium means zero net force on the system. In order to make the net force to be zero, the individual forces acting on the system need to be balanced by compensating one another.

For better standing, let us illustrate a situation. Suppose an object is at rest and some force F is acting on the object. The static equilibrium is achieved by the object only when a force of –F compensates that object.

The above statement says that the force F is compensated by another force –F in static equilibrium. It shows that maintaining the balance in static equilibrium is the role of forces in static equilibrium.

How forces form static equilibrium?

The static equilibrium is formed by the two forces that have equal magnitude and are exerted opposite. To achieve static equilibrium, the sum of all the forces in each direction must be zero.

Let us brief the action of force to obtain static equilibrium. The downward pulling force of gravity also influences an object on rest. The upward force must balance the gravity to form a static equilibrium. The upwards resultant force nullifies the downward gravitational force.

The formation of static equilibrium strictly follows Newton’s second law of motion. In a static equilibrium condition, both linear and angular velocities are constant; thus, there is no possibility of producing acceleration. As the acceleration is zero, it gives the resulting total force zero.

What are the minimum number of forces involved in static equilibrium?

A minimum of two forces must be involved in static equilibrium. If one external force is involved in the system, then the system cannot be under equilibrium.

Since we know that equilibrium involves balancing the forces, it cannot be possible if only one force exists. So, there must be a minimum of two equal and opposite forces to balance each other.

If downward force is acting on the object, the upward force exerts on them to balance them in the opposite direction. If the forward force is acting, the backward force pulls the object to balance them.

To satisfy static equilibrium, an even number of forces must be involved rather than an odd number. But there are some exceptional cases in which three forces are involved to retain the static equilibrium. So static equilibrium does not depend on the number of forces, but at last, all the forces involved in the action must be balanced to give zero net force to satisfy the static equilibrium.

How to find the force of static equilibrium?

When the rigid body is in equilibrium, its linear and angular acceleration is zero; thus, to find forces of static equilibrium. First, we must find the acceleration because static equilibrium does follow Newton’s laws.

The formula gives the static equilibrium.

ΣFk=0; where Fk is the forces acting in every direction on the system.

This can be written using Newton’s laws as

ΣFk=Σmak=0

Where m is the mass, and ak is the acceleration of the physical system.

Suppose there are four forces, F1, F2, F3, and F4, acting on the system which are equal in magnitude and opposite in the direction of exertion, then

Fk=F1+F2+F3+F4

In vector form, this equation can be written as

ΣFkx=0; ΣFky=0; ΣFkz=0, where x,y and z represents the direction of forces.

The above equation means that the forces acting on the system under static equilibrium is zero in every direction.

Does static equilibrium have a net force?

The fundamental condition of static equilibrium is that a body must not involve in any type of motion, irrespective of translation and rotational motion. Since there is no motion possible for a body under static equilibrium, there is no net force.

An object under static equilibrium is either at rest or moving with constant velocity with zero acceleration. Since there is no acceleration, the force will be zero. Even though some forces are exerted on the object, they would have balanced by one another; thus, the net force will be zero.

An object under static equilibrium has zero net force no matter the reference point we choose. The object experiencing net torque is also similar. No net torque is possible in static equilibrium.

What is tension force in static equilibrium?

When an object is supposed to suspend freely with the help of a rope or string, the static equilibrium for the object-rope system is achieved by balancing the tension acting on the rope and the gravitational pull exerted on the object.

The object is supposed to hand on a non-moving string to balance the static equilibrium. Since gravity always pulls the weight downward, the tension on the string acts in the opposite direction, i.e., in an upward direction, to hold the object stationary to maintain static equilibrium.

The tension must equal the gravitational force exerted on the object to retain static equilibrium. If exertion of tension does not match the gravity, the object may accelerate, disturbing the static equilibrium condition.

When the tension on the string and gravity pulling the object is equal, all the forces are balanced, and thus net force becomes zero. Under such conditions, steady equilibrium is achieved and does not change. In this condition, the stress is directed away from the mass and toward the tension on the string, influencing the forces to balance the mass upward.

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Tension forces in static equilibrium
Image credits: Wikimedia commons

When three forces acting at a point are in equilibrium?

The equilibrium attained at a point involving three forces is given by Lami’s theorem, which states that “if three forces are acting at a point are in equilibrium, each individual forces are proportional to the sin of the angle between remaining two-point forces.” It also gives the values for each force numerically greater than the difference between the other two forces.

Let us consider three forces acting at point F1, F2, and F3, which makes an angle α, β, and γ, respectively; then, according to Lami’s theorem, these forces acting on the rigid pivot point is given as;

[latex]\frac{F_1}{sin\alpha}=\frac{F_2}{sin\beta}=\frac{F_3}{sin\gamma}[/latex]

forces in static equilibrium
Action of three forces in static equilibrium

The three forces acting at a point under equilibrium is observed in the glider of the flight in which lift(L), drag(D), and Weight(W or mg) is underbalanced condition. Since we know that weight always acts downward, the lift acts perpendicular to the flight path, and drag acts along the flight path, and these three will be in balance when their vector sum is zero.

The balancing of these three forces to get zero net force by increasing the lift and decreasing the drag at the top of the glider wing. However, weight is always the same. Such aircraft has the same forward, and backward velocity, and this action maintain the balance of all the three forces, or it is canceled out to maintain equilibrium.

What is the resultant of three forces on an object in equilibrium?

Since we are talking about equilibrium, the resultant of three forces will be zero as there is no net force acting on the system, and the three forces are balanced by one another.

We know that three forces acting on the object under equilibrium are a drag, lift, and weight. Weight always acts towards the center of the earth, and lift is a perpendicular force and drags exerted in a parallel direction.

If the angle of inclination of the flight path is θ, then the horizontal and vertical components of the vector equation can be written as

D*cos(θ)-L*sin(θ)=H=0

W-L*cos(θ)-D*sin(θ)=V=0

The above equation represents that all the forces are balanced in every flight path direction, i.e., horizontal and vertical directions. Thus the system is under equilibrium with three forces acting at a point.

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Resultant of three forces in static equilibrium
Image credits: Wikimedia commons

What is an example of forces in equilibrium?

If two equal and opposite forces are exerted on a single object, then we say that the forces acting on the object is in equilibrium. For example, if a ball is on a table, since the weight is acting downward, some horizontal force exerts on the ball to maintain the equilibrium on the ball.

In the same way, when you stand on the floor, gravity will act on you, pulling you downward. But have you ever thought you are not going through the floor; why?

The gravity acting on you pushes you downward is balanced by the normal reaction force exerted on you acting in the upward direction. This normal reaction is equal to the gravity exerted on you, which helps you stay on the floor, maintaining the equilibrium. If you calculate net force, it will be zero.

Does friction force involved in static equilibrium?

A stationary rigid body exerts friction to oppose the motion of the body to retain static equilibrium. The applied force and the friction force exerted on the object are equal, and the friction force is in the opposite direction of the applied force.

Friction means opposition force that opposes the relative motion. If you try to move an object at rest, it does not move, breaking the stationary condition, which means friction is involved in maintaining static equilibrium. The frictional force nullifies the applied force, and thus static equilibrium is maintained.

Frictional force in static equilibrium
Image credits: Flickr

Conclusion

Let us wrap up this post by stating forces in static equilibrium are equal in magnitude but exerted opposite on the system. The forces such as tension, friction, and gravity are also evolved on the object to satisfy the condition of static equilibrium.

Keerthi Murthi

I am Keerthi K Murthy, I have completed post graduation in Physics, with the specialization in the field of solid state physics. I have always consider physics as a fundamental subject which is connected to our daily life. Being a science student I enjoy exploring new things in physics. As a writer my goal is to reach the readers with the simplified manner through my articles. Reach me – keerthikmurthy24@gmail.com

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