Forces can be grouped by how they transfer energy as an object moves. Conservative forces, such as gravity and ideal spring forces, store energy in a way that can be recovered later. Non-conservative forces, such as friction and air resistance, transform mechanical energy into other forms like thermal energy and sound.
This distinction helps students predict motion, calculate work, and understand why real systems lose useful mechanical energy.
Key Facts
- Work done by a conservative force is path independent: Wc depends only on initial and final positions.
- For a conservative force, Wc = -ΔU, where U is potential energy.
- For a closed path under a conservative force, Wc = 0.
- Mechanical energy is Emech = K + U, where K = 1/2 mv^2.
- If only conservative forces do work, K_i + U_i = K_f + U_f.
- Work done by friction is often Wf = -f_k d, where f_k = μ_k N and d is path length.
Vocabulary
- Conservative force
- A force whose work depends only on the starting and ending positions, not on the path taken.
- Non-conservative force
- A force whose work depends on the path taken and often converts mechanical energy into thermal energy or sound.
- Potential energy
- Stored energy associated with position or configuration, such as height in a gravitational field or stretch in a spring.
- Path independence
- The property that the work done between two points is the same for every route connecting those points.
- Energy dissipation
- The conversion of organized mechanical energy into less useful forms, usually thermal energy, due to non-conservative forces.
Common Mistakes to Avoid
- Assuming all forces have potential energy is wrong because only conservative forces can be described by a potential energy function.
- Using W = -ΔU for friction is wrong because friction is non-conservative and its work depends on the length and details of the path.
- Ignoring the sign of work is wrong because a force opposite the displacement does negative work and reduces kinetic energy.
- Treating mechanical energy as always conserved is wrong because mechanical energy is conserved only when non-conservative work is zero or accounted for.
Practice Questions
- 1 A 2.0 kg ball drops from rest from a height of 5.0 m with no air resistance. Find its speed just before hitting the ground using energy conservation.
- 2 A 4.0 kg box slides 6.0 m across a horizontal floor with μ_k = 0.25. Find the work done by friction. Use g = 9.8 m/s^2.
- 3 A cart moves from point A to point B by two different paths. Gravity does the same work on both paths, but friction does more work on the longer path. Explain which force is conservative, which is non-conservative, and why.