AP Physics C: Fundamentals of Work and Energy

Work

A measure of energy transfer that occurs when an object is moved over a distance by an external force.

Dot Product

A mathematical operation that multiplies two vectors to obtain a scalar, defined by W = F • r = F |r| cos(θ).

Scalar Quantity

A quantity that is fully described by a magnitude alone, without any direction.

Joule (J)

The unit of work, where 1 J = 1 N • m.

Positive Work

Occurs when 0° ≤ θ < 90°, indicating that force adds energy to the system.

Zero Work

Occurs when θ = 90°, meaning the force is perpendicular to the motion with no energy transfer.

Negative Work

Occurs when 90° < θ ≤ 180°, indicating that force removes energy from the system.

Variable Force

A force that changes in magnitude and direction over the displacement of an object.

Integral Definition of Work

Work done by a variable force is calculated using W = ∫{xi}^{x_f} F(x) dx.

Line Integral

An integral used to calculate work done along a path in three dimensions, represented as W = ∫_C F • dr.

Hooke's Law

The principle stating that the force exerted by a spring is proportional to its displacement, expressed as F_s = -kx.

Kinetic Energy (K)

The energy of motion, calculated as K = (1/2)mv².

Work-Energy Theorem

The theorem that states net work done on an object equals the change in its kinetic energy.

Net Work

The total work done by all forces acting on an object.

Translational Motion

Straight-line movement of a body from one location to another.

Frictional Force (f_k)

The force exerted by a surface to oppose the motion of an object in contact with it.

Normal Force (N)

The force exerted by a surface perpendicular to the object resting on it.

Elastic Potential Energy

The energy stored in a spring when it is stretched or compressed, calculated as U = (1/2)kx².

Angle of Application (θ)

The angle between the force vector and displacement vector when calculating work.

Equilibrium Condition

The state in which all forces on a particle balance out, resulting in no net force or acceleration.

Energy Transfer

The process during which energy moves from one system to another or changes form.

Work Done by Friction

Negative work performed due to the frictional force opposing the direction of motion.

Graphical Interpretation of Work

On a Force vs. Position graph, work is represented as the area under the curve.

Coefficient of Kinetic Friction (μ_k)

A dimensionless constant that represents the friction between moving surfaces.

Work Calculation

Involves summing the works done by each force acting on an object to find total work.

Critical Conditions for Theorem

Considerations such as the need for net work to calculate changes in kinetic energy.

Mistakes in Work Calculation

Common errors in calculating work, including incorrect angle selection or confusion between net and specific force work.