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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}).
In a Force vs Displacement Graph, what does the slope represent?
The slope of the graph represents the spring constant, k.
On a potential energy vs. position graph, what does the slope represent?
The slope of the potential energy graph gives you the negative of the force.
What are the steps to calculate the work done by a conservative force?
1. 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?
1. Determine the spring constant, k. 2. Measure the displacement from equilibrium, ฮx. 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?
1. 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?
1. 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.