12.2 Examples of Static Equilibrium
3 min read•june 24, 2024
is a crucial concept in physics, especially when it comes to real-world applications. From bridges to buildings, understanding how forces balance out is key to creating stable structures that can withstand various loads and stresses.
Free-body diagrams are essential tools for analyzing static equilibrium in extended objects. By identifying all forces acting on an object and applying equilibrium conditions, we can solve complex problems and ensure structures remain stable under different conditions.
Static Equilibrium in Real-World Scenarios
Real-world static equilibrium scenarios
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Examples of Static Equilibrium – University Physics Volume 1 View original
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Conditions for Static Equilibrium – University Physics Volume 1 View original
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- Bridges maintain equilibrium through careful design and distribution of forces
- use main cables, suspender cables, and anchorages to support the roadway and balance the forces (Golden Gate Bridge)
- employ triangular structures to distribute loads through and in the bridge's framework (Ikitsuki Bridge)
- Buildings achieve static equilibrium by properly distributing weight and forces
- Foundations provide a stable base and evenly distribute the structure's weight (Burj Khalifa)
- and columns support the weight of the roof and upper floors (Parthenon)
- Beams and girders distribute loads horizontally and transfer them to walls and columns (Sydney Opera House)
- Balanced objects maintain equilibrium when the aligns with the base of support and torques from opposing forces cancel out
- A person standing upright with feet shoulder-width apart maintains balance
- A see-saw with equal weights on both sides, equidistant from the pivot point, remains balanced
Free-body diagrams for extended objects
- Identify all forces acting on the object, including , , tension, compression, and
- Determine the direction and magnitude of each force using appropriate symbols ( for gravitational force, for normal force)
- Draw force vectors with arrows indicating the direction
- Label force vectors with their magnitudes
- Include the and relevant distances for calculations
- Ensure the net force and net torque on the object are zero for static equilibrium
- Consider the when analyzing objects on inclined surfaces or with potential sliding
Equilibrium conditions in force problems
- condition: , the sum of all forces acting on the object must be zero
- : Sum of forces in the x-direction equals zero
- : Sum of forces in the y-direction equals zero
- : Sum of forces in the z-direction equals zero
- condition: , the sum of all torques acting on the object about any axis must be zero
- Torque formula: , where is the perpendicular distance from the axis of rotation to the line of action of the force
- Solve for unknown forces or distances using equilibrium conditions
- Apply the equilibrium conditions to the
- Use trigonometry and vector components when necessary
- Consider the equilibrium conditions for each axis independently (x, y, and z)
Analyzing Static Equilibrium in Rigid Bodies
- A is an idealized solid object that maintains its shape under applied forces
- The describes the body's resistance to rotational acceleration
- The is the perpendicular distance from the axis of rotation to the line of action of a force
- in static equilibrium systems can be achieved by manipulating the lengths
Key Terms to Review (36)
Axis of Rotation: The axis of rotation is the imaginary line around which an object or system rotates. It is the fixed point or line that an object pivots or spins around as it undergoes rotational motion.
Center of gravity: The center of gravity is the point at which the entire weight of a body or system can be considered to act. It is crucial for analyzing static equilibrium and stability in physical systems.
Center of Gravity: The center of gravity is the point at which an object's weight appears to be concentrated. It is the average location of the weight of an object, where the object would balance if it were suspended from that point.
Center of mass: The center of mass is the point in an object or system where all its mass can be considered to be concentrated for the purpose of analyzing translational motion. It is the weighted average position of all the mass in the system.
Center of Mass: The center of mass is the point at which an object's entire mass can be considered to be concentrated. It is the average position of the mass of an object, and it is the point around which the object's rotation and motion can be analyzed.
Compression: Compression is the process of reducing the volume or size of an object or material by applying force or pressure. It involves the act of compressing, squeezing, or pressing something together, resulting in a decrease in its overall dimensions or density.
Compressions: Compressions are regions in a longitudinal wave where the particles of the medium are closest together. They represent areas of high pressure and density.
Free-body diagram: A free-body diagram is a graphical representation used to visualize the forces acting on an object. Each force is represented by an arrow pointing in the direction of the force with its length proportional to the magnitude.
Free-Body Diagram: A free-body diagram is a visual representation of an object or system that shows all the external forces acting on it. It is a fundamental tool used in physics to analyze the forces acting on an object and to solve problems involving Newton's laws of motion.
Friction: Friction is a force that opposes the relative motion between two surfaces in contact. It arises due to the microscopic irregularities on the surfaces, which create resistance to sliding or rolling. Friction is a fundamental concept in physics that plays a crucial role in various topics, including solving problems, understanding forces, and analyzing energy transformations.
Gravitational Force: Gravitational force is the attractive force that exists between any two objects with mass. It is the force that causes objects to be pulled towards each other, and is the fundamental force responsible for the motion of celestial bodies and the behavior of objects on Earth.
Hydrostatic equilibrium: Hydrostatic equilibrium is a state in which the pressure gradient force within a fluid balances the gravitational force acting on that fluid. This balance prevents the fluid from collapsing under its own weight or expanding uncontrollably.
Lever arm: The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. It is a crucial factor in determining the torque produced by a force.
Lever Arm: The lever arm is the perpendicular distance from the axis of rotation or pivot point to the line of action of a force. It is a fundamental concept in understanding the effects of forces on objects in rotational equilibrium or when analyzing torque.
Load-Bearing Walls: Load-bearing walls are structural elements in a building that support the weight of the structure above them, including floors, roofs, and any additional loads. These walls are designed to carry and transfer the vertical loads from the upper levels down to the foundation, ensuring the stability and integrity of the overall construction.
Mechanical Advantage: Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device, or machine system. It describes the relationship between the input force and the output force, allowing a smaller input force to generate a larger output force.
Moment Arm: The moment arm is the perpendicular distance between the line of action of a force and the axis of rotation or pivot point. It is a crucial concept in understanding the rotational effects of forces and the conditions for static equilibrium.
Moment of inertia: Moment of inertia is a measure of an object's resistance to changes in its rotational motion about a fixed axis. It depends on the mass distribution relative to the axis of rotation.
Moment of Inertia: The moment of inertia is a measure of an object's resistance to rotational acceleration. It is a scalar quantity that depends on the mass and distribution of an object's mass about a given axis of rotation. The moment of inertia is a crucial concept in the study of rotational dynamics, as it determines how an object will respond to applied torques.
Normal Force: Normal force is the support force exerted by a surface perpendicular to the object resting on it, preventing the object from falling through the surface. It plays a crucial role in balancing other forces acting on an object, particularly in scenarios involving gravity and acceleration.
Rigid Body: A rigid body is an idealized object that maintains its shape and size regardless of the forces acting upon it. It is a fundamental concept in classical mechanics that simplifies the analysis of the motion and behavior of objects.
Rotational Equilibrium: Rotational equilibrium is a state where the net torque acting on an object is zero, resulting in the object's rotational motion remaining constant or the object remaining at rest. This concept is fundamental in understanding the behavior of rigid bodies under the influence of external forces.
Stable Equilibrium: Stable equilibrium is a state of balance in a system where any small disturbance or displacement from the equilibrium position will result in a restoring force that pushes the system back towards its original state. This concept is crucial in understanding the behavior of physical systems and their tendency to maintain a state of stability.
Stable equilibrium point: A stable equilibrium point is a position where an object, when slightly displaced, experiences a net force or torque directed towards that position, causing it to return to equilibrium. In simple harmonic motion, this corresponds to the lowest potential energy configuration.
Static Equilibrium: Static equilibrium is a state in which the net force and net torque acting on an object are both zero, resulting in the object remaining at rest or in a constant position. This concept is crucial in understanding the behavior of objects under various physical conditions.
Static Friction Coefficient: The static friction coefficient is a dimensionless quantity that describes the ratio of the maximum force of static friction between two surfaces to the normal force pressing those surfaces together. It is a measure of the roughness or adhesion between the surfaces and determines the maximum force required to initiate sliding motion.
Suspension Bridges: Suspension bridges are a type of bridge design where the deck is suspended from cables that are anchored at both ends, allowing the structure to span long distances over obstacles such as rivers, valleys, or straits. These bridges are characterized by their ability to support heavy loads while maintaining a lightweight and elegant appearance.
Tension: Tension is a force that acts to pull or stretch an object, often along the length of a string, rope, or cable. It is a vector quantity, meaning it has both magnitude and direction, and it plays a crucial role in various physics concepts related to forces, motion, and equilibrium.
Torque: Torque is a measure of the rotational force applied to an object, which causes it to rotate about an axis. It is influenced by the magnitude of the force applied, the distance from the axis of rotation, and the angle at which the force is applied, making it crucial for understanding rotational motion and equilibrium.
Translational Equilibrium: Translational equilibrium is a state of balance where the net force acting on an object is zero, resulting in the object remaining at rest or moving at a constant velocity. This concept is particularly relevant in the context of examples of static equilibrium, where objects are in a state of equilibrium and do not experience any acceleration.
Truss Bridges: A truss bridge is a type of bridge structure that uses a series of interconnected triangular units, called trusses, to support the weight of the bridge deck and any loads placed upon it. These bridges are designed to efficiently transfer loads from the deck to the supporting piers or abutments, making them a popular choice for spanning longer distances.
Unstable Equilibrium: Unstable equilibrium refers to a state of balance where the slightest disturbance or perturbation can cause the system to move away from its initial position, leading to a significant change in the system's behavior. This term is particularly relevant in the context of potential energy diagrams, static equilibrium, and simple harmonic motion.
Weight Distribution: Weight distribution refers to the way in which the weight or force of an object or system is distributed across its supporting surfaces or structures. It is a critical concept in the study of static equilibrium, as the distribution of weight plays a key role in determining the stability and balance of a system.
ΣF = 0: The term ΣF = 0 represents the condition of static equilibrium, where the sum of all the forces acting on an object is equal to zero. This means that the net force on the object is zero, and the object remains at rest or maintains a constant velocity.
Στ = 0: The term Στ = 0 refers to the condition of static equilibrium, where the net torque or moment acting on an object is zero. This means that the object is not experiencing any rotational motion or acceleration around a specific axis or point.
τ = r × F: The equation τ = r × F represents the relationship between the torque (τ) exerted on an object, the distance (r) from the axis of rotation to the point of application of the force, and the magnitude of the applied force (F). This equation is fundamental in understanding the concept of static equilibrium, which describes a state where an object is at rest and the net force and net torque acting on it are both zero.