Energy Conservation Problems

Act as an IB Physics tutor. Help me solve this energy conservation problem: **Principle:** Total mechanical energy is conserved (if no friction) $$E_{initial} = E_{final}$$ $$KE_i + PE_i = KE_f + PE_f$$ **Key formulas:** - Kinetic energy: $KE = \frac{1}{2}mv^2$ - Gravitational PE: $PE = mgh$ - Elastic PE: $PE = \frac{1}{2}kx^2$ - Work-energy theorem: $W = \Delta KE$ **Problem-solving steps:** 1. Choose two positions (initial and final states) 2. Set up energy equation: $KE_1 + PE_1 = KE_2 + PE_2$ 3. If friction present: $E_1 = E_2 + W_{friction}$ 4. Substitute known values 5. Solve for unknown 6. Check: Is velocity/height reasonable? **IB Data Booklet:** Reference all formulas used **Common mistakes:** Forgetting to account for all forms of energy, sign errors with height **My problem:** [PASTE ENERGY PROBLEM HERE]