← Energy charts, diagrams and conservation solves

Read a potential energy diagram

A cart rolls along a hilly track: down into a dip, up the far rise, back again.

At every position, its GPE is set by the track's height there. Its speed keeps changing with it.

How can you tell, for every position at once, how fast the cart is moving?

Here is the cart's energy against its position along the track.

position along the trackenergy (J)10455560total energyPEleft risethe dipright shoulderKE 50 J
The PE line follows the track's height; the level line is the 60 J total; KE is the gap.

The rising-and-falling line is the cart's gravitational potential energy at each position: high where the track is high, lowest in the dip. A drawing like this is called a potential energy diagram.

The level line is the cart's total mechanical energy: 60 J at every position, because the track is frictionless.

The cart's kinetic energy at any position is the gap between the two lines: total minus PE.

In the dip the PE line sits at 10 J, so the gap is 60 - 10 = 50: the KE there is 50 J, the largest anywhere. KE is largest where the PE line dips lowest.

At the right shoulder the PE line reads 45 J, so the gap narrows to 15 J. The cart is slow wherever the PE line climbs close to the total line.

Reads off the diagrampositionPEgap = KEleft rise55 J5 Jthe dip10 J50 Jright shoulder45 J15 J
Each read is one subtraction: total minus PE.

On the diagram above, read the cart's kinetic energy at the right shoulder.

The total line sits at 60 J; the PE line at the right shoulder reads 45 J.

KE is the gap: 60 - 45 = 15.

The cart's kinetic energy at the right shoulder is 15 J.

The diagram shows a marble's PE line and its 70 J total-energy line. At which position is the marble's kinetic energy largest?

position along the trackenergy (J)12386070total energyPEthe left lipthe low pointthe right ledge

On the diagram, the total-energy line sits at 70 J and the PE line reads 30 J at the ramp ledge. Enter the skater's kinetic energy at the ramp ledge in J.

position along the trackenergy (J)3070total energyPEthe ramp ledge

A pendulum's potential energy diagram dips to its lowest at the mid-swing position. Where along the swing is the bob's KE largest?

position along the swingenergy (J)total energyPEmid-swing
The pendulum's PE line dips to its lowest at mid-swing.

KE is the gap between the total line and the PE line.

The gap is widest where the PE line is lowest: at the mid-swing position.

The bob's KE is largest at mid-swing, the bottom of the dip.

The diagram shows a cart's PE line and its 72 J total-energy line. At which position is the cart's kinetic energy smallest?

position along the trackenergy (J)15336572total energyPEthe starting crestthe hollowthe mid-rise

Your turn

The diagram shows a roller cart's PE line and its 60 J total-energy line. At which position is the cart moving fastest?

position along the trackenergy (J)520355560total energyPEthe boarding deckthe first hollowthe low point between the humpsthe far hump

On the diagram, the total-energy line sits at 90 J and the PE line reads 65 J at the gully wall. Enter the sled's kinetic energy at the gully wall in J.

position along the trackenergy (J)6590total energyPEthe gully wall

On a potential energy diagram with a constant total-energy line, what does the vertical gap between the total line and the PE line at a position show?