On a frictionless demonstration track, a cart sets off along a high section, already rolling.
It speeds up through the dip, slows on the climb, and crosses a crest at its starting height moving at exactly its starting speed.
Coincidence? Or is something being kept?
Track the cart's two stores with numbers. Setting off: KE 20 J, GPE 100 J. Partway down: KE 70 J, GPE 50 J. Through the lowest stretch: KE 120 J, GPE 0 J.
Add each pair: 20 + 100 = 120, then 70 + 50 = 120, then 120 + 0 = 120. The total never moves.
Under what condition does an object's mechanical energy stay constant?
The condition is the working part. Energy is never created or destroyed, but friction and air resistance move energy out of the mechanical stores. When they are negligible, nothing leaves, so the total holds still.
A box sliding on carpet fails the condition: friction is large there, so its mechanical energy does not stay constant.
On a frictionless skate ramp, a skater's mechanical energy at the top of a run is 900 J. Air resistance is negligible. State her mechanical energy at the bottom of the run, and the reasoning.
Friction and air resistance are negligible, so the conservation condition is met.
Under that condition, the total mechanical energy of the system stays constant.
Her mechanical energy at the bottom is 900 J, the same total.
At the top of a frictionless slide, a sled holds 30 J of kinetic energy and 60 J of gravitational potential energy. At the bottom its GPE is 0 J. Air resistance is negligible. Enter its kinetic energy at the bottom in J.
Between the top and the bottom of that same run, the skater's GPE falls by 400 J. What happens to her kinetic energy?
The total stays constant, so whatever one store loses, the other store gains.
The gravitational store lost 400 J.
Her kinetic energy rises by exactly 400 J.
The rule is a shortcut: know the total once, and you know it at every point of the motion, with no force analysis along the way.
Boaz says: on a frictionless ramp with negligible air resistance, a sled's kinetic-plus-potential total at the bottom equals its total at the top. Is Boaz right?
Which statement gives the condition for a cart's mechanical energy to stay constant?
A pendulum bob passes its lowest point with 44 J of kinetic energy, 4 J of gravitational potential energy measured from the floor, and negligible air resistance. Enter its GPE, in J, at the moment it hangs momentarily at rest at the top of its swing.
On a frictionless drop with negligible air resistance, a roller coaster car's GPE falls by 500 J. What happens to its kinetic energy over the drop?