Name: free-body diagrams for force analysis
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Next Generation Science Standards

High School

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

HS-PS2-3

Free-body Diagram

The visual representation of all the forces acting on the particle is called a free-body diagram or force diagram. It transforms complex problems into simple representations.
In a free-body diagram, the direction of the arrows indicates the direction of forces, while the arrows&#39; length represents the magnitude of the forces.
Consider a stationary trolley on which two cardboard boxes are stacked.
Here, the two systems of interest, box one and box two, can be assumed to be isolated systems and can be represented using a free-body diagram in the form of a simple outline or a dot.
The forces acting on box one are the gravitational force, which defines its weight, and the counter-balancing normal force due to box two.
Similarly, the forces on box two are its own weight, the normal force due to the trolley, and the weight of box one.
Free-body diagrams play an integral part in the problem-solving process as a transition from a specific physical situation to an abstract mathematical equation in mechanics.

free-body diagram

In mechanics, understanding the motion of objects is essential, and one tool that helps solve this problem is the free-body diagram. It is a simple but powerful graphical representation that succinctly represents all the forces acting on an object. A free-body diagram can represent a stationary or moving object, and is used in mechanics to explain the cause of an object&#39;s motion.
A free-body diagram transforms a complex problem into a simple representation, making it easy to understand the essential forces acting on an object, leading to a mathematical equation. In many cases, the equation would be extremely complex to derive without using free-body diagrams. To make a free-body diagram, start by selecting the object or system under inspection, isolating it from its surroundings, and drawing it as a dot or a simple outline. Next, represent all the essential external forces acting on the object or system of interest with arrows. The direction of the arrows represents the direction of the force, while the length of the arrows depicts the magnitude of the force. It is important to note that in a free-body diagram, velocity and acceleration are not represented, but can be inferred from the forces applied on the object.
Some common types of forces that can be represented in a free-body diagram include weight, normal force, tension, friction, and applied force. Weight refers to the force of gravity acting on the object, typically represented by an arrow pointing downward. Normal force is the force between two objects when they come in contact with each other; this force acts in the opposite direction to the weight of the object. Tension is generally represented by an arrow pointing away from the object in the direction of the force, and friction is the force that resists sliding between surfaces. Finally, applied force refers to the force applied to the object by an external agent, such as a push or a pull. Applied forces are represented by an arrow pointing in the direction of the force.
Consider a stationary trolley, on which two cardboard boxes are stacked. The two systems of interest, box one and box two, can be assumed to be isolated systems and can be represented using a free-body diagram. The forces acting on box one are gravitational force, which defines its weight, and the counter-balancing normal force due to box two. Similarly, the forces on box two are its weight, the normal force due to the trolley, and the weight of box one.

In mechanics, understanding the motion of objects is essential, and one tool that helps solve this problem is the free-body diagram. It is a simple but ...

Education

JoVE Core

Mechanical Engineering

Unit 1

Equilibrium of a Particle

KEY TERMS AND CONCEPTS

free-body diagrams for force analysis

Free-body diagrams help analyze the forces acting on an object in mechanics. They give a simple picture of a stationary or moving object and show why it moves the way it does. By turning a complex situation into a clear sketch, they make it easier to write the equation needed to solve the problem.

To draw a free-body diagram, first choose the object or system you want to study. Then isolate it from its surroundings and draw it as a dot or a simple outline. Add arrows for every important external force. The direction of each arrow shows the direction of the force, and the length shows its size.

A free-body diagram does not show velocity or acceleration. Those quantities are not drawn on the diagram, but they can be inferred from the forces acting on the object. Common forces include weight, normal force, tension, friction, and applied force. Weight is the force of gravity and is usually shown with an arrow pointing downward.

Normal force is the contact force between two objects touching each other. It acts in the direction opposite to the object's weight in many situations. Tension is usually drawn as an arrow away from the object and along the direction of the pull. Friction resists sliding between surfaces. Applied force is an outside push or pull, and it is shown with an arrow in the direction of that force.

A stationary trolley with two cardboard boxes stacked on it gives a clear example. Box one and box two can each be treated as separate isolated systems and shown with their own free-body diagrams. For box one, the forces are gravitational force and the balancing normal force from box two. For box two, the forces are its weight, the normal force from the trolley, and the weight of box one.

Free-Body Diagrams for Force Analysis

equilibrium conditions for a particle

Balanced Forces and Torque in Equilibrium

Equilibrium depends on balanced forces and balanced torque. An object in equilibrium is either at rest or moving with a constant velocity. These two cases are called static equilibrium and dynamic equilibrium. Static equilibrium means the object is not moving. Dynamic equilibrium means the object is moving, but its velocity stays constant. In both cases, the forces acting on the object must balance each other. Different forces can add, subtract, or cancel each other out. When the vector sum...

Free-body diagrams help analyze the forces acting on an object in mechanics. They give a simple picture of a stationary or moving object and show why it moves the way it does. By turning a complex situation into a clear sketch, they make it easier to write the equation needed to solve the problem. To draw a free-body diagram, first choose the object or system you want to study. Then isolate it from its surroundings and draw it as a dot or a simple outline. Add arrows for every important...

steps for free-body diagram

Free-Body Diagram for Two-Block Motion

A free-body diagram helps analyze two-block motion in mechanics. It shows the forces acting on a system so the net force can be found and the acceleration can be calculated. The example in this lesson uses two blocks linked by a massless string over a frictionless pulley. Block 1 moves across a table while block 2 falls under gravity. The two blocks are treated as one isolated system. External forces are then identified and drawn as vector arrows on the diagram. For block 1, the forces...

free-body diagrams: problem solving

Free-Body Diagrams on Inclined Planes

Free-body diagrams help show the forces acting on an object on an inclined plane. A free-body diagram is a simple drawing that focuses only on the object or system being studied. It leaves out extra details so the force problem is easier to analyze and solve. For an example, a 10 kg block is released on a ramp that is 30° to the horizontal. The coefficient of friction is 0.2. The diagram for this block includes the weight from gravity, the normal force, and the frictional force. These are the...

coplanar forces

Resolving Coplanar Force Components

Coplanar forces act on an object in the same plane. To analyze this kind of system, each force is resolved into x and y components using Cartesian vector form and vector algebra. This makes it possible to test whether the object is in equilibrium. A coplanar system is in equilibrium when the resultant force is zero. That means the sum of the forces in each direction must also be zero. If the forces do not balance, the object is not in equilibrium and will accelerate in the direction of the net...

categories of equilibrium

Types of Equilibrium in Forces

Equilibrium in physics describes how forces act on a body so it stays still or moves at a constant speed. In two-dimensional force systems, equilibrium can be grouped into several categories based on how the forces are arranged. Collinear equilibrium is the simplest case. The forces act along one straight line, so only one force equation is needed in the direction of those forces. The other equations are already satisfied. Coplanar concurrent equilibrium is another category. In this case, all...

key terms and concepts

Learn how free-body diagrams show weight, normal force, tension, friction, and applied force. See how isolating an object simplifies force analysis in mechanics.

Free-Body Diagrams for Force Analysis | JoVE K12

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Free-Body Diagrams for Force Analysis

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