5.13
Free Body Diagrams: Examples
Solving problems that involve forces is easy using free-body diagrams. A free-body diagram is a sketch showing all the external forces that are acting…
Free-body diagrams are graphical representations of various forces on an object. This can be understood with some examples.
The free-body diagram for a lamp hanging from a chain can be shown as a point with two forces: the gravitational force and the tension in the chain.
Taking another example, sketch a free-body diagram for a cart carrying a large box. Here, there are two systems of interest, the box and the cart; thus, there is a need to draw separate diagrams for each.
The forces acting on the box are the gravitational force due to its mass, the normal force, and the frictional force exerted by the cart on the box.
For the cart, the gravitational force, the net normal force due to the ground, a normal force due to the box on the cart, the net frictional force exerted by the ground and the box on the cart, and a push that is applied on the handle, all act together.
Q1: What is a free-body diagram and why is it useful?
A free-body diagram is a sketch showing all external forces acting on an isolated object or system, represented as a single point with force vectors extending outward. It simplifies force analysis by displaying only forces originating outside the object, making it easier to solve problems involving internal and external forces and apply Newton's laws to predict motion.
Q2: How do you represent forces in a free-body diagram?
Forces are represented as vectors extending outward from the free body point. Each vector's direction indicates the force direction, and its length represents the force magnitude. Directions are labeled with plus or minus signs, with conventions like rightward as positive. This visual representation helps identify which forces act on an object and their relative magnitudes.
Q3: Why do you need separate free-body diagrams for different objects in a system?
When analyzing a system with multiple objects like a cart carrying a box, separate diagrams isolate each object's external forces. The box experiences gravitational force, normal force, and friction from the cart, while the cart experiences its own weight, ground forces, and applied push. Separating them prevents confusion between internal forces between objects and external forces acting on each.
Q4: What forces act on an object hanging from a chain?
An object hanging from a chain experiences two forces: gravitational force pulling downward due to its mass and tension in the chain pulling upward. These opposing forces can be represented in a free-body diagram as vectors extending from a point, showing how the tension must equal the weight for the object to remain in equilibrium.
Q5: How do you handle force components on an inclined surface?
On an inclined surface like a slope, the normal force is drawn perpendicular to the slope surface and friction parallel to it. The weight vector has components along both axes: one perpendicular to the slope and one parallel to it. This decomposition allows you to analyze forces in directions relevant to the surface geometry and motion constraints.
Q6: When can vertical forces be ignored in a free-body diagram?
Vertical forces can be ignored when there is no vertical acceleration, meaning upward and downward forces cancel each other. For example, a rocket sled on a horizontal surface has normal force balancing weight, leaving only horizontal forces to analyze. This simplification reduces the problem to one dimension, making calculations more straightforward.
Q7: What forces must be included when drawing a free-body diagram?
Include only external forces acting on the object from outside sources: gravitational force, normal force, friction, tension, applied pushes, and thrust. Exclude internal forces between components within the system. For a person sitting on a chair, show only the chair's normal force upward and gravitational force downward, not internal muscle forces.