Which of these forces are conservative? Explain how you decide.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Which of these forces are conservative? Explain how you decide.
Gravity; the force of a spring; friction; air resistance; the tension of a string holding a pendulum bob.
Need a reminder? The key ideaShow
Gravitational potential energy near the Earth is , with measured from any level we choose; only changes in matter. A spring stores . The force is .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Test each force with a round trip.
Step 1. Gravity. Up and back down: the work out cancels the work back. Conservative.
Step 2. Spring. Stretch and release: the spring gives back what it took. Conservative.
Step 3. Friction and air resistance. They act against the motion on every part of any path, so the work round a closed path is negative. Not conservative.
Step 4. The string's tension. It is always at right angles to the bob's motion, so it does no work at all. It neither stores nor wastes energy, and it does not spoil the conservation of energy.
Answer: Gravity and the spring force are conservative. Friction and air resistance are not. The string does no work.
Watch out. A force that does no work is not the same as a conservative force with potential energy; it just drops out of the energy account.
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