Work and Energy Lecture Flashcards 06

This set of vocabulary flashcards covers concepts from Dr. Victor Castro's lecture on Work and Energy, including mechanical work, various forms of energy, conservation principles, and power.

Mechanical Work ($W$)

The product of an external constant force $F$ and the displacement $\triangle s$ through which it moves an object, defined as $W = F \triangle s \text{ cos}(\theta)$.

Joule ($J$)

The SI unit of work, where $1,J = 1,N \times m$.

Force vs. Distance Curve

A graph where the area under the curve represents the work done by a variable force.

Net Work ($W_{net}$)

The sum of the work done by all individual forces acting on an object, calculated either as $W_{net} = F_{net} \triangle x \text{ cos}(\theta_{net})$ or by summing the work of each individual force.

Kinetic Energy ($KE$)

The energy of moving objects, defined by the formula $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

Work-Energy Principle

A principle stating that the net work done on an object is equal to the change in its kinetic energy: $W_{net} = \triangle KE$.

Gravitational Potential Energy ($U$)

Energy due to an object's position in a gravitational field, defined as $U = mgh$, where $h$ is the height.

Path Independent

A characteristic of forces like gravity where the work done depends only on the initial and final points, not the specific path taken.

Hooke’s Law

The force a spring exerts when compressed or stretched, given by $F_s = -kx$.

Spring Constant ($k$)

A value representing the stiffness of a spring, measured in units of $N/m$.

Elastic Potential Energy

The potential energy stored in a deformed spring, defined as $U = \frac{1}{2}kx^2$.

Conservative Force

A force that is path independent and for which a potential energy can be defined ($W_c = -\triangle U$).

Non-conservative Force

A force that is path dependent, such as friction ($f_{air}$).

Total Mechanical Energy ($E$)

The sum of the kinetic energy and potential energy of a system: $E = KE + U$.

Conservation of Mechanical Energy

A principle stating that if there are no non-conservative forces ($W_{nc} = 0$), the total mechanical energy remains constant ($E_1 = E_2$).

Dissipative Processes

Processes involving non-conservative forces where the total mechanical energy is not conserved, described by $W_{nc} = E_2 - E_1$.

Power ($P$)

The rate at which work is done or energy is transformed, calculated as $P = \frac{W}{\triangle t}$.

Watt ($W$)

The SI unit of power, where $1,W = 1,J/s$.

Horsepower ($hp$)

A unit of power where $1,hp = 746,W$.

Average Power ($P_{avg}$)

Power expressed in terms of force and average velocity: $P_{avg} = Fv \text{ cos}(\theta)$.

Efficiency ($e$)

The ratio of the useful power output to the power input: $e = \frac{P_{out}}{P_{in}}$.