A rider on a playground swing passes the low point quickly.
She rises, slows, and for an instant at the end of the swing she is not moving at all. Then she falls back.
On a frictionless path, where is an object fastest, and where does it momentarily stop?
Give the rider numbers: at the end of her swing, KE 0 J and GPE 90 J; passing the low point, KE 90 J and GPE 0 J, measured from the low point.
On the way down, GPE falls and KE rises by the same amount: she speeds up the whole way down.
At the lowest point of the path, GPE is at its smallest, so KE is at its largest. The lowest point is the fastest moment.
A skater rolls back and forth in a frictionless half-pipe. Where is she moving fastest?
On the way up, the trade runs in reverse: KE falls as GPE grows, so she slows.
Where ALL the kinetic energy has become gravitational potential energy, the speed is zero: she is momentarily at rest. That is the highest point she reaches.
A pendulum swings with negligible air resistance. Where is the bob momentarily at rest?
A marble is released on a frictionless curved track with one low section. State where along the track it moves fastest, and why.
Mechanical energy is conserved on the frictionless track, so KE is largest where GPE is smallest.
GPE is smallest at the lowest point of the track.
The marble moves fastest at the lowest point of the track.
A cart is released from rest at the top of one slope of a frictionless valley track. State where on the far slope it momentarily comes to rest.
It started at rest, so its whole total began as GPE at the release height.
It momentarily stops where ALL its kinetic energy has become GPE again: at that same height.
It momentarily comes to rest at its release height on the far slope.
Cleo says: on a frictionless track, a cart moves fastest at the track's lowest point. Is Cleo right?
A marble rolls through a smooth, frictionless valley. Where is it moving fastest?
A skateboarder starts from rest at the top edge of a frictionless bowl and rolls down and across. Where does she momentarily come to rest on the far side?
A frictionless track runs through a shallow dip, over a low crest, then through a deeper dip. A cart rolls along the whole track. Where is the cart moving fastest?