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3.2 Work

Learning objectives

3.2A—Describe the work done on an object or system by a given force or collection of forcesDescribe the work done on an object or system by a given force or collection of forces.• Work is the amount of energy transferred into or out of a system by a force exerted on that system over a distance.- i. The work done by a conservative force exerted on a system is path-independent and only depends on the initial and final configurations of that system.- ii. The work done by a conservative force on a system—or the change in the potential energy of the system—will be zero if the system returns to its initial configuration.- iii. Potential energies are associated only with conservative forces.- iv. The work done by a nonconservative force is path-dependent.- v. Examples of nonconservative forces are friction and air resistance.• Work is a scalar quantity that may be positive, negative, or zero.• The amount of work done on a system by a constant force is related to the components of that force and the displacement of the point at which that force is exerted.- i. Only the component of the force exerted on a system that is parallel to the displacement of the point of application of the force will change the system’s total energy. Relevant equation:- ii. The component of the force exerted on a system perpendicular to the direction of the displacement of the system’s center of mass can change the direction of the system’s motion without changing the system’s kinetic energy.• The work-energy theorem states that the change in an object’s kinetic energy is equal to the sum of the work (net work) being done by all forces exerted on the object. Relevant equation:- i. An external force may change the configuration of a system. The component of the external force parallel to the displacement times the displacement of the point of application of the force gives the change in kinetic energy of the system.- ii. If the system’s center of mass and the point of application of the force move the same distance when a force is exerted on a system, then the system may be modeled as an object, and only the system’s kinetic energy can change.- iii. The energy dissipated by friction is typically equated to the force of friction times the length of the path over which the force is exerted AP Physics 1: Algebra-Based Course and Exam Description Work, Energy, and Power UNIT 3• Work is equal to the area under the curve of a graph of F as a function of displacement. BOUNDARY STATEMENT AP Physics 1 only expects students to analyze the transfer of mechanical energy (as defined in Unit 3, Topic 4: Conservation of Energy), although students should be aware that mechanical energy may be dissipated in the form of thermal energy or sound. In AP Physics 2, students will also study how thermal energy can be transferred between systems through heating or cooling. AP Physics 1: Algebra-Based Course and Exam Description Work, Energy, and Power UNIT 3 TOPIC 3.3 Potential Energy | AP Physics 1: Algebra-Based Course and Exam Description

Identify the energy transfer

Work is energy transferred into or out of a system when a force acts through a displacement of its point of application. Work is a scalar: positive work transfers energy into the system, negative work transfers energy out, and zero work transfers no energy by that force.

$W=F_{\parallel}d=Fd\cos\theta$

Use the parallel force

Constant-force example: A $20\,\text{N}$ force acts $60^\circ$ to a cart's $3.0\,\text{m}$ displacement.

$W=(20\,\text{N})(3.0\,\text{m})\cos60^\circ=30\,\text{J}$ .

Only the parallel component, $F_{\parallel}=10\,\text{N}$ , transfers energy. A perpendicular component can turn the velocity but does zero work and does not change kinetic energy.

Connect net work to kinetic energy

For all forces acting on an object, add their work algebraically:

$\Delta K=K_f-K_i=\sum_i W_i=W_{\text{net}}.$

Thus positive net work increases kinetic energy, negative net work decreases it, and zero net work leaves it unchanged. When the system's center of mass and the force's point of application move the same distance, the system may be modeled as an object for this kinetic-energy change.

Read work from a graph

On a graph of the parallel force component $F_{\parallel}$ versus displacement $x$ , work equals the signed area between the curve and the $x$ -axis. Area above the axis is positive work; area below it is negative work. This rule also handles a force that changes with position.

Distinguish force types

Force type	Does work depend on the path?	Consequence
Conservative	No—only the initial and final configurations matter	Potential energy can be associated with the interaction; returning to the initial configuration gives zero total work by that force
Nonconservative, such as friction or air resistance	Yes	Mechanical energy may be dissipated as thermal energy or sound; for constant friction opposing motion, $W_f=-F_fd$ and the dissipated amount is $F_fd$

Control the system model

Always name the system and the displacement of the force's point of application. An external force can also change a system's internal configuration, so its work need not appear only as center-of-mass kinetic energy. AP Physics 1 analyzes mechanical-energy transfer here; it recognizes dissipation to thermal energy or sound but does not require the AP Physics 2 treatment of energy transfer by heating or cooling.

Next Topic

—3.3 Potential EnergyRead