Name: free-body diagrams on inclined planes
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 30 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 Diagrams: Problem Solving

Consider a block of mass 10 kg released on a rough slope, inclined to the horizontal at an angle of 30 degrees. Its acceleration needs to be determined where the coefficient of friction is 0.2.
A free-body diagram of the block is drawn. The forces acting on it are its weight, the normal force, and the frictional force.
Using trigonometry functions, the weight of the block can be resolved into parallel and perpendicular components.
The normal force is perpendicular to the inclined surface and counteracts the perpendicular component of the weight.
To determine the value of the frictional force between the block and the inclined surface, multiply the coefficient of friction by the normal force.
The net force is the difference between the gravitational force parallel to the inclined plane and the opposing friction force. It is obtained by substituting their values in the equation.
Finally, applying Newton&#39;s second law of motion, the acceleration of the block is derived.

free-body diagrams: problem solving

Free-body diagrams are essential tools for physicists and engineers studying the motion of objects. Free-body diagrams are graphical representations of the object or system under consideration, and they focus solely on the essential forces acting on the object. This tool helps break down complex problems into simpler models that are easier to understand and solve.
For example, consider a block with a mass of 10 kg released on an inclined plane at an angle of 30&#176; to the horizontal, where the coefficient of friction is 0.2. The free-body diagram of this scenario displays the forces acting on the block, which include the gravitational force due to the weight of the block, the normal force acting perpendicular to the plane, and the frictional force. We can determine the resultant force the block experiences by understanding these forces.
When an object is placed on an inclined plane, the weight of the object has two components: one parallel to the slope and another perpendicular to the slope. The perpendicular component acts opposite to the normal force, and the net force in this direction is zero, as these two forces balance each other out. On the other hand, parallel to the slope, the weight has a non-zero component that causes the block to slide downward. The parallel component is the force that causes acceleration and opposes the resistance provided by the frictional force between the block and the surface. The frictional force opposes the object&#39;s motion, even when it is not moving. To calculate the frictional force, the normal force is multiplied by a coefficient of friction.
The net force is obtained by taking the difference between the gravitational force parallel to the slope and the frictional force. The value of the net force is substituted into Newton&#39;s second law of motion to obtain the acceleration value.

Free-body diagrams are essential tools for physicists and engineers studying the motion of objects. Free-body diagrams are graphical representations of ...

Education

JoVE Core

Mechanical Engineering

Unit 1

Equilibrium of a Particle

KEY TERMS AND CONCEPTS

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 key forces used to find the block’s resultant force.

The weight of the block can be split into two components on the slope. One component acts parallel to the incline, and the other acts perpendicular to it. The perpendicular component is balanced by the normal force, so the net force in that direction is zero. The parallel component is not balanced and helps the block slide downward.

Friction opposes the motion of the block, even when the block is not moving. To find the frictional force, the normal force is multiplied by the coefficient of friction. The net force is the difference between the downhill component of gravity and the frictional force. That net force is then used in Newton’s second law of motion to calculate the acceleration.

Free-Body Diagrams on Inclined Planes

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 diagram

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...

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 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 help analyze forces on a block on an inclined plane, including gravity, normal force, friction, net force, and acceleration.

Free-Body Diagrams on Inclined Planes | JoVE K12

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Texas Essential Knowledge and Skills

Physics

PHYS.1

IPC.1.G

Chemistry and Physics

IPC.1

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HS-PS2-2

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HS-PS2-6

Free-Body Diagrams on Inclined Planes

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