Unit 8: Potential Energy and Conservation of Energy
Energy stored in height and springs, read off a potential energy curve like a ball rolling through valleys and over hills.
6 topics · 21 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Gravitational Potential Energy
- How it worksHow does lifting an object against gravity convert work directly into stored potential energy?
- Worked exampleFind the gravitational potential energy of a 2 kg book raised 1.5 m above a table, taking the table as zero.
- Common mistakeWhy doesn't gravitational potential energy have one single correct value that every observer must agree on?
Your turn1 of 2
A book of mass m is raised a height h above a table, taken as zero potential energy, with gravitational acceleration g. Write an expression, in terms of m, g, and h, for its gravitational potential energy.Elastic Potential Energy
- How it worksHow does compressing or stretching a spring store energy according to one-half k x squared?
- Worked exampleFind the elastic potential energy stored in a spring with k = 150 N/m compressed 0.2 m.
- Going furtherWhat happens to the elastic potential energy stored in a spring if you double how far you stretch it?
Your turn1 of 2
A spring with spring constant 233 N/m is compressed 0.18 m from its natural length. How much elastic potential energy is stored in it, in joules?Conservative and Nonconservative Forces
- How it worksHow do you tell a conservative force from a nonconservative one by checking whether its work depends on the path?
- Common mistakeWhy isn't friction a conservative force even though it's a perfectly real, well-defined force?
- Going furtherWhat happens to the total mechanical energy of a system once a nonconservative force starts acting on it?
Your turn1 of 2
A roller coaster car of mass 718 kg descends a total height of 29 m along a long, winding track. How much work does gravity do on the car over this descent, in joules (g = 9.8 m/s2)?Energy Diagrams and the Ball-in-a-Valley Picture
- How it worksHow does reading a potential energy curve like landscape hills and valleys tell you where a particle turns around?
- How it worksHow does the local minimum of a potential energy curve mark a point of stable equilibrium?
- Worked exampleFind the turning points of a particle with total energy 10 J moving in the potential well U(x) = 2x2.
- Common mistakeWhy doesn't a particle balanced at the top of a potential energy hill stay there under the slightest disturbance?
Your turn1 of 2
A particle moves in a potential well U(x) = 4 x2 (joules, x in meters) with total energy 28 J. What is the magnitude of its turning point, the value of x where it momentarily stops?Conservation of Mechanical Energy
- How it worksHow does kinetic energy trade for potential energy while their sum stays fixed throughout the swing?
- Worked exampleFind the speed of a 0.5 kg pendulum bob at the bottom of its swing after falling 0.8 m from rest.
- Common mistakeWhy doesn't a roller coaster car need any engine partway through a frictionless track?
- Going furtherWhat happens to the height a pendulum reaches on the far side of its swing once air resistance is added back in?
- Ties togetherHow does energy conservation in a swinging pendulum connect to the same bookkeeping used for a roller coaster loop?
Your turn1 of 2
A 1.45 kg pendulum bob falls 1.37 m from rest to the bottom of its swing. Ignoring air resistance, what is its speed at the bottom, in meters per second?Energy Accounting With Nonconservative Forces
- How it worksHow does the work done by friction show up as a loss from a system's total mechanical energy?
- Worked exampleFind the heat generated by friction as a 10 kg sled slides 20 m and stops, starting at 4 m/s.
- Ties togetherHow does the energy this friction destroys as mechanical energy reappear as heat in the first law of thermodynamics?
Your turn1 of 2
A 15 kg sled slides 29 m across the snow and comes to a complete stop, starting at 8 m/s. How much heat is generated by friction, in joules?