A ball drops from a gym storage shelf to the floor. You know its energy story at the start.
Drawing the story's ending has one rule: nothing goes missing.
How do you build the after snapshot so the energy adds up?
Take the drop: at release the ball is already moving a little, carrying KE 5 J and GPE 40 J.
Its total is 5 + 40 = 45: there are 45 J of mechanical energy to account for.
Run the gatekeeper scan: a short drop through air, no friction, no collision before landing. Conserved. So the after snapshot's bars must total 45 J too.
Just before landing, the height is 0, so the GPE bar is drawn at 0 J. The KE bar must carry everything: 45 J.
A ball leaves a shelf with KE 5 J and GPE 40 J. Construct the just-before-landing snapshot (height 0, conserved run).
Write down the values:
before: KE 5 J, GPE 40 J, a total of 45 J.
The height at landing is 0, so draw GPE at 0 J.
The run is conserved, so the after bars must also total 45 J.
Substitute in the values, and calculate:
after KE = 45 - 0 = 45
The after snapshot: KE 45 J, GPE 0 J.
The before snapshot shows a toy car at the top of a frictionless ramp. Construct the after snapshot at the floor, where its GPE is 0 J: enter the KE bar's value in J.
The same ball is instead caught at a point where its GPE is 20 J. Construct that snapshot.
The total to account for is still 45 J.
Draw the known bar: GPE 20 J.
Size the remaining bar so the totals match: KE = 45 - 20 = 25.
The snapshot at the catch: KE 25 J, GPE 20 J.
The before snapshot shows a cart high on a frictionless track. At the lower ledge its GPE bar is drawn at 15 J. Construct the rest of that snapshot: enter the KE bar's value in J.
If a run converts mechanical energy to thermal energy, a thermal bar joins the after snapshot, and all the bars together still match the before total.
The before snapshot shows a skateboard rolling off a low platform on a conserved run. Which bar set completes the after snapshot at ground level?
The before snapshot shows a sled at the top of an icy, frictionless slope. Partway down, its GPE bar is drawn at 13 J. Construct the rest of the partway snapshot: enter the KE bar's value in J.
The before snapshot shows a ball rolling off a porch on a conserved run. Which bar set completes the after snapshot at the ground?
The before snapshot shows a dart pressed against a launcher spring on a frictionless bench rig. Partway up the launch ramp, the spring has released and the dart's GPE bar is drawn at 6 J. Construct the rest of that snapshot: enter the KE bar's value in J.