Free-body diagrams are powerful tools for visualizing forces acting on objects. They simplify complex systems, showing only external forces as vectors. This approach helps us apply ###'s_Laws_0### to analyze motion and predict outcomes.
Newton's laws form the foundation of classical mechanics. The first law describes , the second relates to , and the third explains action-reaction pairs. Understanding these laws is crucial for solving physics problems and grasping real-world applications.
Free-Body Diagrams and Newton's Laws
External forces in free-body diagrams
Simplified representation of an object or system showing only external forces acting on it
Object represented as a dot or simplified shape (often at its )
Forces represented as vectors with tail originating from object
Common forces include (W=mg) acting downward due to gravity, (N) acting perpendicular to surface opposing weight, (T) acting along length of rope or cable, (f) acting parallel to surface opposing motion, and applied forces (F) representing any additional external forces
Length of force vectors should be proportional to magnitude of forces (longer arrow for larger force, shorter arrow for smaller force)
Newton's laws for force interactions
First law (law of ) states an object at rest stays at rest and an object in motion stays in motion with constant unless acted upon by unbalanced force
In free-body diagram, if is zero, object is either at rest or moving with constant velocity (no acceleration)
Second law (F=ma) states acceleration of an object is directly proportional to net force acting on it and inversely proportional to its
In free-body diagram, net force is sum of all external forces acting on object
Direction of net force determines direction of object's acceleration (positive net force causes positive acceleration, negative net force causes negative acceleration)
Third law (action-reaction) states for every action there is an equal and opposite reaction
In free-body diagram, forces always occur in pairs (if object A exerts force on object B, then object B exerts equal and opposite force on object A)
Vector components of net force
Forces can be resolved into perpendicular components along x-axis (horizontal) and y-axis (vertical)
To resolve force into components, use :
Fx=Fcosθ where Fx is x- of force, F is magnitude of force, and θ is angle between force vector and positive x-axis
Fy=Fsinθ where Fy is y-component of force
Net force is vector sum of all forces acting on an object
To calculate net force in particular direction (x or y), add components of all forces in that direction:
Fnet,x=∑Fx
Fnet,y=∑Fy
Magnitude of net force can be calculated using : Fnet=Fnet,x2+Fnet,y2
Direction of net force can be determined using function: θnet=arctan(Fnet,xFnet,y)
Equilibrium and Torque
occurs when the net force and net on a are both zero
refers to a system where the net force is zero, but the object may be in motion with constant velocity
Torque is the rotational equivalent of force, causing an object to rotate around an axis
Torque is calculated as the product of the force and the (perpendicular distance from the axis of rotation to the line of action of the force)
involves separating a system into its individual components to analyze forces and torques acting on each part