Work & Energy
A bookkeeping system so reliable that you can answer questions without ever solving the motion.
Introduction
A skater drops into a curved ramp, and there is a way to find their speed at the bottom that ignores the shape of the ramp entirely.
Two skaters start from rest at the same height, one on a gentle ramp and one on a steep one. Both reach the bottom. Who is moving faster there?
Same drop, same speed
Work and energy
Gravity does work on the falling skater, and work changes kinetic energy: , with . The track pushes at right angles to the motion, so it does no work. Gravity's work depends only on the drop, so it can be banked as potential energy, . With no friction,
A kg skater starts from rest m above the bottom of a frictionless valley. How fast is the skater moving at the bottom? Use m/s².
Where the energy goes
With friction on, the skater never gets back up to the release height. Where did that energy go?
What comes next
You found a speed from a height alone, whatever the track, and followed the energy friction takes into heat. Energy says nothing about directions, because it is a scalar; next comes a conserved quantity that is a vector, and it is what you need for collisions.
Ideas this lesson took on
Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.
- “Energy gets used up”
- “The speed at the bottom depends on the path”
- “Kinetic energy is a force pushing the object along”
Finished with this lesson?
Progress is stored on this device only. There is no account and nothing is sent anywhere.
Research behind this lesson
- Lawson & McDermott 1987: Students who could state both theorems often could not apply them, and frequently treated energy as a substance that gets used up rather than a quantity that is transferred.
- Wieman et al. 2008: Well-designed simulations can teach concepts more effectively than the corresponding real equipment, because they make the invisible visible and remove incidental difficulty.
- Meltzer 2005: The same physics question produces markedly different success rates depending on whether it is posed verbally, graphically, diagrammatically or symbolically.