Describing Systems (College Board AP® Physics 1: Algebra-Based)

Describing systems

• In physics, a system is defined as:

A specific object or a collection of objects

• Connecting objects in this way enables us to understand, model, or predict the behaviors of those objects

• Any objects that are not part of the system are considered as the surroundings

Single object systems

• Many problems in physics can be simplified by modeling systems as single objects

• This applies to systems where the properties or interactions of the individual objects in the system are not important in modeling the behavior of the macroscopic system

• When a system is treated as a single object:

  • its internal structure can be ignored

  • its properties can be determined by the properties of the individual objects in that system, e.g. the mass of the system

  • the forces on the system can be considered to act at the system's center of mass

  • every point on the system can be assumed to move in the same direction

• For example, when determining the acceleration of a car using Newton's second law :

  • The net force exerted on the system (the car) causes the entire system to accelerate as if it were a single object of total mass

  • The internal structure of the car (its engine, wheels, etc) is not relevant to the situation, so it can be ignored

  • The net force, mass, and acceleration can be assumed to act at the car's center of mass

Example of a single object system

Open and closed systems

• A system can be classified as either:

  • an open system

  • or, a closed or isolated system

• Defining a system as open or closed depends on whether:

  • a net external force acts on the system

  • there is an exchange of energy or mass between the system and the surroundings

Open systems

• In an open system, interactions between the system and the surroundings may result in the transfer of energy or mass

• Open systems are characterized by

  • a net external force acting on the system, meaning total mechanical energy and total momentum are not conserved

  • an exchange of energy, such as work or heating, between the system and the surroundings

• An example of an open system is a mass moving on a rough surface

  • If the surface is rough, then friction acts as an external force on the single object system (i.e. the surface is not included in the system)

  • When work is done by friction, energy is dissipated to the surroundings as heat

  • Both the total mechanical energy and momentum of the mass decrease, therefore, these quantities are not conserved

Example of an open system

Closed system

• In a closed system, no energy or mass is transferred between the system and the surroundings

• Closed systems are characterized by

  • no net external force acting on the system, meaning total mechanical energy and total momentum are conserved

  • no exchange of energy, such as work or heating, between the system and the surroundings

• An example of a closed system is a mass being projected up a smooth incline by a compressed spring

  • If the surface is smooth, then no external forces act on the mass-spring-Earth system

  • When work is done to compress the spring, energy is transferred to kinetic energy and gravitational potential energy within the system, and no energy is dissipated to the surroundings

  • Both the total mechanical energy and momentum of the mass remain constant, therefore, these quantities are conserved

Example of a closed system

Internal structure of a system

• When the internal structure of a system is significant, the system cannot be modeled as a single object

• This applies to systems containing individual objects which may behave differently from each other as well as from the system as a whole

• Some examples of this are:

  • object-Earth systems

  • multiple object systems

  • object-string systems

  • object-spring systems

• The selection of individual objects in a system can significantly affect the analysis of that system

Object-Earth systems

• If the system consists of an object and the Earth, then any force other than the gravitational force acting on it is considered an external force

• For example, consider a ball falling toward the Earth's surface

  • In the ball-only system: the gravitational force from the Earth exerts a net external force on the ball, causing it to accelerate

  • In the ball-Earth system: the forces exerted by the Earth on the ball, and by the ball on the Earth, are equal in magnitude and opposite in direction, so their effects cancel. These forces are internal to the system, so no net external force acts on the system, hence it does not accelerate

Example of an object-Earth system

Multiple object systems

• If the system consists of multiple objects, then any force other than the internal forces between the objects is considered an external force

• For example, consider a collision between two objects

  • In the two-object system: when the two objects collide, the force they exert on one another is internal to the system, so the total momentum of the system remains constant

  • In the single object system: the force exerted by one ball on the other acts as a net external force, causing its momentum to change

Example of a multiple object system

Systems involving strings and springs

• If the system consists of an object attached to a string (or rope), then any force other than tension in the string is considered an external force

• For example, consider a tug-of-war between two people on a cart

  • In the person-rope-person-cart system: the tension in the rope due to the people pulling on it is internal to the system. There is no net external force exerted on the cart, so it does not accelerate

  • In the person-cart system: if one person moves off the cart and becomes part of the surroundings, the tension becomes a net external force on the system, which causes it to accelerate

Example of a multi-object-string system

• If the system consists of an object attached to a spring, then any force other than the spring force is considered an external force

• For example, consider a mass-spring system (see the following worked example)