Mechanical Energy, Non-Conservative Work, and Motion from Potential

All flashcards

Mechanical energy

The sum of kinetic and potential energy: $E=K+U$.

Conserved quantity

A quantity whose total for a defined system remains constant under relevant conditions, though it may be transferred or transformed.

Non-conservative work

Work that equals the change in mechanical energy: $W_{nc} = \Delta E$.

Mechanical energy dissipated

The positive magnitude of a decrease in mechanical energy due to non-conservative work.

Force from potential energy

In one dimension, the force associated with a potential $U(x)$ is $F=-dU/dx$.

Quiz questions

1. A pendulum of length $L$ is released from rest at angle $\theta$ from the downward vertical. With air resistance neglected, what is its speed at the lowest point?Answer: $\sqrt{2gL(1-\cos\theta)}$
2. A $15\,\text{kg}$ panel falls from rest through $1000\,\text{m}$ and reaches the ground at $45\,\text{m/s}$. Using $g=9.8\,\text{m/s}^2$, what is the approximate signed work by non-conservative forces?Answer: $-130\,\text{kJ}$
3. For one-dimensional motion with total energy $E$ and potential energy $U(x)$, which condition must hold at an accessible position?Answer: $E-U(x)\geq 0$
4. A particle moves in the potential $U(x)=E(x/x_0)$, where $E$ and $x_0$ are positive constants. What force acts on it?Answer: A constant force $-E/x_0$
5. When applying mechanical-energy accounting to a system of several particles, what must be included?Answer: The relevant particles' kinetic and potential energies, and non-conservative work