3.3
Steps for Free-Body Diagram
When it comes to studying the behavior of objects in mechanics, one of the most important tools available is the free-body diagram. Consider a simple…
Consider a system of two blocks coupled by a massless string over a pulley. Block 1 is sliding over a table pulled by block 2 as it falls under gravity.
The acceleration of the system can be derived by calculating the net force on the system.
A free-body diagram for this system can be drawn by representing the two blocks with their outline. Here, the blocks are considered to be isolated.
The external forces acting on them are identified and represented by vector arrows.
The forces on block 1 are its weight, normal force, tension force due to the rope, and friction force opposing the tension force causing the motion.
Similarly, the forces acting on block 2 are its weight and the tension force.
Applying Newton's second law of motion to the blocks, an equation for the net force can be derived.
Using the algebraic operation and rearranging the terms, the magnitude of the acceleration of the system can be obtained.
View the full transcript and gain access to JoVE Core videos
Q1: What forces should be included in a free-body diagram for a block on a table?
A free-body diagram for a block on a table includes its weight, the normal force perpendicular to the surface, tension force from any attached rope or string, and friction force opposing motion. Each force is represented as a vector arrow showing its direction and magnitude. These external forces are essential for applying Newton's second law to calculate the system's acceleration.
Q2: How do you isolate a system when drawing a free-body diagram?
To isolate a system, represent each object with its outline and consider it separated from the environment. Identify only the external forces acting on that isolated object, such as weight, normal force, tension, and friction. Internal forces between connected objects, like the string coupling two blocks, are shown separately on each block's diagram to maintain clarity.
Q3: Why is a free-body diagram important for calculating system acceleration?
A free-body diagram provides a clear visual representation of all forces acting on each object, making it easier to apply Newton's second law accurately. By identifying and representing forces as vectors, you can derive equations for net force and solve for acceleration using algebraic operations. Without this tool, analyzing complex systems with multiple forces becomes significantly more difficult.
Q4: What is the relationship between free-body diagrams and Newton's second law?
Free-body diagrams visually organize all external forces acting on an object, which is the foundation for applying Newton's second law. Once forces are identified and represented, you write equations using F = ma for each object. This systematic approach allows you to derive expressions for acceleration and solve coupled systems like two blocks connected by a string.
Q5: How do tension and friction forces differ in a block system?
Tension force pulls a block along the direction of the string, causing motion, while friction force opposes this motion by acting in the opposite direction. In a two-block system, tension pulls block 1 across the table as block 2 falls, but friction resists this motion. Both forces are critical to determining the net force and resulting acceleration of the system.
Q6: What forces act on a falling block in a pulley system?
A falling block experiences two forces: its weight acting downward due to gravity and tension force acting upward from the string. These are the only external forces on the falling block in an idealized pulley system. Applying Newton's second law to these forces allows you to derive the acceleration of the entire coupled system.
Q7: How do you solve for acceleration after drawing a free-body diagram?
After drawing the free-body diagram and identifying all forces, apply Newton's second law to write force equations for each object. Combine these equations to find the net force on the system. Use algebraic operations to rearrange and solve for acceleration, which yields a numerical value representing how the system behaves under the applied forces.