The cart from the last lesson rolls up the track's far wall, slows, hangs for an instant, and rolls back the way it came.
Run after run, it turns around at the same spot.
What marks that exact spot, before the cart ever rolls?
Here is the cart's energy against position again, with the track's walls now in view and the same level 60 J total line.
Follow the cart up a wall. As the PE line climbs toward the total line, the gap shrinks, so the kinetic energy falls toward zero.
At the position where the PE line meets the total line, the gap is 0 J: the kinetic energy is zero, and the cart is momentarily at rest.
It cannot go past that position. Beyond it the PE line sits above the total line, and the stored energy would have to exceed the whole total. So the cart reverses direction.
A motion trapped in a dip has two turning points, one on each wall: the object runs back and forth between them.
The diagram shows a cart's PE line and its 60 J total-energy line. At which marked position does the cart turn around?
On a track's diagram, the total-energy line sits at 50 J and the PE line at the hump's peak reads 65 J. Can a cart with that total cross the hump?
The PE line passes 50 J partway up the hump's near slope, below the peak.
Where it meets the total line, the kinetic energy falls to zero: a turning point.
No: the cart stops and reverses on the slope, before the top.
The diagram shows a cart's PE line, reaching 70 J at the hump's top, and its 60 J total-energy line. Does the cart reach the top of the hump?
On a pendulum's potential energy diagram, the PE curve meets the total-energy line at two positions. What happens at each?
At a meeting position the gap is 0 J, so the kinetic energy is zero there.
The bob is momentarily at rest and reverses direction.
Two meeting positions means two turning points: the two extremes of the swing.
At each meeting position the bob momentarily stops and reverses: they are the swing's two extremes.
Zeke says: at a turning point, the object's kinetic energy is zero for an instant. Is Zeke right?
The diagram shows a marble's PE line and its 80 J total-energy line. Which marked position is a turning point?
The diagram shows a skater's PE line for a bowl, with her 55 J total-energy line. How many turning points does her motion have?
A marble rolls along a track whose potential energy diagram shows the PE curve meeting the total-energy line at one position ahead of the marble. What happens when the marble arrives there?