Can an Object Be in Mechanical Equilibrium When Only a Single Force Acts on It?

First Condition

The first condition of equilibrium is that the cyberspace forcefulness in all directions must be zero.

Learning Objectives

Place the first status of equilibrium

Primal Takeaways

Cardinal Points

• In that location are two conditions that must be met for an object to be in equilibrium.
• The first condition is that the internet force on the object must be zero for the object to exist in equilibrium.
• If cyberspace forcefulness is zero, and so internet forcefulness along any management is zero.

Key Terms

• force: A physical quantity that denotes power to push button, pull, twist or accelerate a trunk which is measured in a unit of measurement dimensioned in mass × distance/time² (ML/T²): SI: newton (Northward); CGS: dyne (dyn)
• torque: A rotational or twisting effect of a strength; (SI unit of measurement newton-meter or Nm; imperial unit foot-pound or ft-lb)
• translation: Motion of a trunk on a linear path, without deformation or rotation, i.e. such that every part of the body moves at the same speed and in the same direction; also (in physics), the linear motion of a torso considered independently of its rotation.

Commencement Condition of Equilibrium

For an object to be in equilibrium, it must exist experiencing no acceleration. This ways that both the net force and the net torque on the object must be zero. Here we volition discuss the first condition, that of zip net forcefulness.

In the form of an equation, this get-go condition is:

[latex]\text{F}_\text{net} = 0[/latex].

In gild to attain this conditon, the forces acting along each centrality of motility must sum to zero. For example, the net external forces along the typical ten– and y-axes are zero. This is written equally

[latex]\text{net } \text{F}_{\text{10}} = 0[/latex] and [latex]\text{internet }\text{F}_{\text{y}} = 0[/latex].

The condition [latex]\text{F}_\text{net} = 0[/latex] must be truthful for both static equilibrium, where the object's velocity is nil, and dynamic equilibrium, where the object is moving at a constant velocity.

Below, the motionless person is in static equilibrium. The forces acting on him add up to zero. Both forces are vertical in this case.

Person in Static Equilibrium: This motionless person is in static equilibrium.

Below, the car is in dynamic equilibrium because it is moving at abiding velocity. There are horizontal and vertical forces, only the net external forcefulness in whatsoever direction is zero. The practical force between the tires and the route is balanced past air friction, and the weight of the car is supported by the normal forces, here shown to exist equal for all 4 tires.

A Car in Dynamic Equilibrium: This auto is in dynamic equilibrium considering it is moving at abiding velocity. The forces in all directions are balanced.

Second Condition

The second status of static equilibrium says that the net torque acting on the object must be zero.

Learning Objectives

Identify the 2nd condition of static equilibrium

Key Takeaways

Key Points

• The 2nd condition necessary to achieve equilibrium involves avoiding accelerated rotation.
• A rotating trunk or system can be in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it.
• The magnitude of torque about a centrality of rotation is defined to be τ=rFsinθ.

Key Terms

• torque: A rotational or twisting outcome of a strength; (SI unit newton-meter or Nm; purple unit foot-pound or ft-lb)
• equilibrium: The state of a body at rest or in uniform motion, the resultant of all forces on which is zero.

A child'due south seesaw, shown in, is an example of static equilibrium. An object in static equilibrium is one that has no acceleration in whatever direction. While in that location might be move, such motion is abiding.

Ii children on a seesaw: The system is in static equilibrium, showing no acceleration in whatever direction.

If a given object is in static equilibrium, both the net forcefulness and the net torque on the object must be zero. Let'southward interruption this downward:

Cyberspace Force Must Be Zero

The net force acting on the object must be nix. Therefore all forces remainder in each direction. For example, a auto moving along a highway at a constant speed is in equilibrium, equally it is not accelerating in any frontwards or vertical direction. Mathematically, this is stated as F_net = ma = 0.

Net Torque Must Be Zero

The second condition necessary to accomplish equilibrium involves fugitive accelerated rotation (maintaining a constant athwart velocity ). A rotating body or organisation can exist in equilibrium if its rate of rotation is constant and remains unchanged by the forces acting on it.

To empathize what factors touch on rotation, let us think near what happens when you open an ordinary door by rotating it on its hinges.The magnitude, direction, and point of application of the forcefulness are incorporated into the definition of the physical quantity called torque—the rotational equivalent of a force. It is a mensurate of the effectiveness of a strength in changing or accelerating a rotation (changing the angular velocity over a period of time).

In equation form, the magnitude of torque is defined to be τ=rFsinθ where τ (the Greek letter tau) is the symbol for torque, r is the altitude from the pivot bespeak to the indicate where the forcefulness is applied, F is the magnitude of the strength, and θ is the bending between the force and the vector directed from the point of application to the pivot point.

Two-Component Forces

In equilibrium, the net forcefulness and torque in whatsoever particular direction equal nil.

Learning Objectives

Summate the net strength and the net torque for an object in equilibrium

Primal Takeaways

Key Points

• In equilibrium, the cyberspace forcefulness in all directions is zero.
• If the net moment of inertia about an centrality is zero, the object will accept no rotational acceleration well-nigh the centrality.
• In each management, the net forcefulness takes the form: [latex]\sum \textbf{F}=\text{g}\textbf{a}=0[/latex] and the net torque take the form: [latex]\sum \boldsymbol{\tau}=\text{I}\boldsymbol{\alpha}=0[/latex] where the sum represents the vector sum of all forces and torques acting.

Key Terms

• equilibrium: The country of a trunk at rest or in compatible movement, the resultant of all forces on which is zero.

An object with constant velocity has zero acceleration. A motionless object even so has constant (zero) velocity, so motionless objects also have nothing dispatch. Newton's second law states that:

[latex]\sum \textbf{F}=\text{m}\textbf{a}[/latex]

so objects with constant velocity as well accept zero net external forcefulness. This means that all the forces interim on the object are balanced — that is to say, they are in equilibrium.

This rule also applies to motion in a specific direction. Consider an object moving forth the 10-axis. If no net force is practical to the object forth the x-axis, it volition continue to movement forth the x-axis at a constant velocity, with no dispatch.

Car Moving at Abiding Velocity: A moving car for which the net x and y force components are cipher

Nosotros can easily extend this rule to the y-axis. In any organization, unless the applied forces cancel each other out (i.east., the resultant strength is zero), in that location will be acceleration in the management of the resultant forcefulness. In static systems, in which motion does not occur, the sum of the forces in all directions ever equals nix. This concept tin can be represented mathematically with the following equations:

[latex]\sum \text{F}_{\text{10}}=\text{ma}_{\text{x}}=0[/latex]

[latex]\sum \text{F}_{\text{y}}=\text{ma}_{\text{y}}=0[/latex]

This rule also applies to rotational motion. If the resultant moment nearly a detail axis is null, the object volition have no rotational dispatch near the axis. If the object is not spinning, information technology will non kickoff to spin. If the object is spinning, information technology volition go on to spin at the same constant angular velocity. Again, nosotros can extend this to moments about the y-axis also. We tin can represent this rule mathematically with the following equations:

[latex]\sum \tau_{\text{10}}=\text{I}\alpha_{\text{ten}}=0[/latex]

[latex]\sum \tau_{\text{y}}=\text{I}\alpha_{\text{y}}=0[/latex]

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Source: https://courses.lumenlearning.com/boundless-physics/chapter/conditions-for-equilibrium/

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