Potential Energy and Conservation of Energy

Name: Potential Energy and Conservation of Energy
Author: StemPy Lab

A stone held high, and a spring that is pressed, can both do work when we let them go. In this course we find which forces store energy and which do not, we write the potential energy of gravity and of a spring, and we use the conservation of energy to solve problems with slopes, pendulums, roller coasters and rough floors.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Conservative forces and potential energy
A force is conservative when its work depends only on where a body starts and ends, not on the path. Gravity and spring forces are conservative; friction and drag are not. For a conservative force we can define potential energy, so that $W = -\Delta U$ ; near the Earth $U = mgh$ . The force is the downhill slope of the potential energy: $F = -\dfrac{dU}{dx}$ .
1 simulation2 practice questions1 Python program4 problems1 question set
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Lesson 2about 25 min
The spring and the conservation of mechanical energy
When only conservative forces do work, mechanical energy is conserved: $K + U$ stays the same. A falling ball trades potential energy for kinetic energy; a mass on a spring trades back and forth between $\tfrac12 kx^2$ and $\tfrac12 mv^2$ . The turning points are where all the energy is potential. Energy methods give speeds without needing the path or the time.
1 simulation2 practice questions1 Python program4 problems2 Python labs
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Lesson 3about 25 min
Energy with friction and in curved paths
When friction or drag acts, mechanical energy is not conserved, but total energy is: $K_1 + U_1 = K_2 + U_2 + E_{\text{heat}}$ , where the heat equals the work against friction. On curved paths, energy gives the speed and Newton's second law gives the forces. A loop of radius $R$ needs a start at least $2.5R$ high. A string in a vertical circle needs $\sqrt{5gL}$ at the bottom.
1 simulation2 practice questions1 Python program4 problems1 note
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Conservation of Energy: Practice Paper

20 questions · 50 min

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Potential Energy and Conservation of Energy

Course outline (3 lessons)

Conservative forces and potential energy

The spring and the conservation of mechanical energy

Energy with friction and in curved paths

Test Your Learning

Your teacher

Discussion (0)