Potential Energy: Work, References, Gravity, Springs, and Conservation

All flashcards

Potential energy of an interaction

Energy associated with the interaction between objects in a chosen system, such as an object and Earth.

Additive constant in a potential energy function

A constant fixed by the chosen reference value; it shifts energy values without changing their differences.

Gravitational potential energy near Earth's surface

For vertical coordinate $y$ increasing upward, its change is $\Delta U_{\text{grav}}=mg\Delta y$.

Elastic potential energy of an ideal spring

With zero energy at the unstretched position, $U=\frac{1}{2}kx^2$, where $x$ is displacement from that position.

Turning point in a mass-spring motion

A position where the moving block momentarily has zero speed.

Quiz questions

1. For a one-dimensional conservative force $F(x)$, how is the work from $x_A$ to $x_B$ calculated?Answer: $W_{AB}=\int_{x_A}^{x_B}F(x)\,dx$.
2. What determines the additive constant in a potential energy function?Answer: The specified potential energy at the chosen reference position.
3. Which objects form the system for gravitational potential energy near Earth's surface?Answer: The object and Earth, because their gravitational interaction stores the energy.
4. For an ideal spring, what is the relationship between its elastic potential energies at displacements $+x$ and $-x$?Answer: They are equal because the energy depends on the squared displacement.
5. A block is released from rest at an unstretched vertical spring, with downward displacement negative. What is its nonzero turning-point position in the ideal model?Answer: $y_C=-\frac{2mg}{k}$.