Translational Equilibrium (College Board AP® Physics 1: Algebra-Based)

Translational equilibrium

• Translational equilibrium is defined as

A configuration of forces such that the net force exerted on a system is zero

Stationary object

• We know that if there is no net force acting on an object then there is no change in the object's motion

  • Therefore a stationary object remains stationary

• Vectors can be added together using a vector sum

• The force vectors acting on a picture modeled as a hanging object are:

  • Tension is the macroscopic net result of forces that segments of the string exert on each other in response to an external force

  • The weight exerted on the object by the gravitational field strength,

Translational equilibrium of a stationary hanging object

• When an object is stationary, the force vectors acting on the object are arranged using the tip-to-tail method so that the vector sum is equal to zero

Force diagram of a stationary hanging object

Moving objects

• If there is no net force acting on an object, then there is no change in the object's motion

  • Therefore, a moving object remains moving at a constant velocity in the same direction

• This means the force vectors acting on the object are also arranged using the tip-to-tail method so they combine to equal zero

• The force vectors acting on the object are:

  • The weight exerted on the object by the acceleration due to gravity,

  • The friction exerted on the object due to the interaction between the object and the surface of the slope

  • The normal force is the perpendicular component of the force exerted on an object by the surface with which it is in contact; it is directed away from the surface.

Translational equilibrium of a moving object at a constant velocity

• When an object is moving at a constant speed, the force vectors acting on the object are arranged using the tip-to-tail method so that the vector sum is equal to zero

Force diagram of a moving object at a constant velocity

Derived equation

• A configuration of forces such that the net force exerted on a system is zero

Derivation:

Step 1: Identify the fundamental principle

• Newton's second law is given by:

• Where:

  • = net force exerted on the system, in

  • = mass of the system, in

  • = acceleration of the system, in

Step 2: Apply the specific conditions

• When an object is in transitional equilibrium, it is either at rest or moving with a constant velocity

• As there is no change in velocity, acceleration is zero, = 0

• The equation for net force becomes:

• To maintain transitional equilibrium, the sum of the forces exerted on the system must equal zero: