All Flashcards
What are the steps to calculate the work done by a conservative force?
- Identify the conservative force. 2. Determine the initial and final positions. 3. Use the formula (W = -Delta U) or (W = int_{a}^{b} F cdot dr).
What are the steps to determine the potential energy stored in a spring?
- Determine the spring constant, k. 2. Measure the displacement from equilibrium, Δx. 3. Use the formula (U_s = frac{1}{2}k(Delta x)^2).
What are the steps to find force from a potential energy graph?
- Determine the potential energy function, U(x). 2. Find the slope of the graph at the point of interest. 3. Take the negative of the slope to find the force: (F = -frac{dU}{dr}).
What are the steps to derive the general formula for gravitational potential energy?
- Start with the definition of work: (W = int_{r_i}^{r_f} F(r) dr). 2. Substitute Newton's Law of Universal Gravitation: (F(r) = frac{Gm_1m_2}{r^2}). 3. Integrate to find the change in potential energy. 4. Set initial potential energy to 0 at infinity.
What are the differences between conservative and dissipative forces?
Conservative Forces: Path independent, total work in a closed path is zero. Dissipative Forces: Path dependent, energy is lost from the system (usually as heat).
What are the differences between gravitational potential energy near Earth and at large distances?
Near Earth: Uniform field, (Delta U = mgDelta h). Large Distances: Non-uniform field, (U = -frac{Gm_1m_2}{r}).
What happens when a spring is compressed or stretched?
Elastic potential energy is stored in the spring.
What happens when work is done by a conservative force?
There is a negative change in potential energy: (W = -Delta U).
What happens when the slope of a potential energy graph is zero?
The system is in equilibrium (no net force).
What happens when an object moves higher in a gravitational field (near Earth)?
Its gravitational potential energy increases: (Delta U = mgDelta h).
What happens when the distance between two masses increases?
The gravitational potential energy becomes less negative (increases).