Free Body Diagrams

Objectives What is a Free Body Diagram

Our Concern We are concerned with applications that involve constant forces Constant forces result in constant accelerations and allow the use of the kinematic equations to analyze motion.

Variable Forces When there is a variable force, Newton’s second law holds for the instantaneous force and aceleration, but the acceleration will vary with time, requiring more advance mathematics.

Free Body Diagrams Free Body diagrams are illustrations of a physical situation. They depict the forces acting on an object. The arrows that are used to represent the force all originate from the same point. Usually the origin of the x-y axes. Sometimes we have to resolve force vectors into their components using trigonometry.

Free Body Diagrams In a FBD, the vector arrows do not have to be drawn exactly to scale. The diagram should clearly show whether there is a net force and whether forces balance each other in a particular direction. When the forces aren’t balanced, by Newton’s second law, there must be an acceleration.

Steps to Constructing a FBD Make a sketch of the situation (typically a box or a point to represent the object) and identify the forces acting on each part of the system.

Steps to Constructing a FBD Isolate the part of the system for which the FBD is to be constructed. Label the Cartesian axes.

Steps to Constructing a FBD Draw properly oriented force vectors (including angles) on the diagram, emanating from the middle of the box or point. If there is an unbalanced force, assume a direction of acceleration and indicate it with an acceleration vector. Be sure to include only those forces that act on the isolated body of interest.

Steps to Constructing a FBD Resolve any forces that are not directed along the x or y axis into x or y components.

Steps to Constructing a FBD Use the FBD and force components to analyze the situation in terms of Newton’s second law of motion

From Here on Out You must always draw a FBD for all Force Problems!

Example Two masses are connected by a light string running over a light pulley of negligible friction. One mass (m1 = 5.0 kg) is on a frictionless 20 degree inclined plane, and the other (m2 = 1.5 kg) is freely suspended. What is the acceleration of the masses? What is the tension in the string?

Example A force of 10.0 N is applied at an angle of 30 degrees to the horizontal on a 1.25 kg block initially at rest on a frictionless surface. A) What is the magnitude of the blocks acceleration? B) What is the magnitude of the Normal Force?