PhysicsGravitational Potential Energy and Conservation of Mechanical Energy
Lumi perches at the top of a curved skate ramp, energy meter glowing in hand, watching a rider launch from a standstill and accelerate toward the ground below.
- Calculate gravitational potential energy using PE = mgh for an object at a given height.
- Explain how total mechanical energy remains constant when only gravity acts on an object.
- Predict an object's kinetic energy at a lower height using energy conservation.
- Distinguish conservative forces (like gravity) from nonconservative forces (like friction) using the concept of path-independence.
- Identify how nonconservative forces reduce the mechanical energy available at the end of a path.
Key terms
- Gravitational potential energy
- The energy stored by an object due to its height, PE = mgh relative to a chosen reference level.
- Mechanical energy
- The sum of an object kinetic and potential energy at a given moment.
- Conservative force
- A force such as gravity whose work depends only on start and end positions, not the path taken.
- Path-independence
- The property that the work a conservative force does between two points is the same for every route.
- Nonconservative force
- A force such as friction whose work depends on the path and removes mechanical energy as heat.
Conservation of Mechanical Energy
When gravity is the only force doing work, total mechanical energy E = KE + PE stays constant, so KE_start + PE_start = KE_end + PE_end. As an object descends, gravitational potential energy mgh converts into kinetic energy ½mv², so a loss of PE equals an exactly equal gain in KE. This bookkeeping lets you find an unknown speed or height without analyzing forces or acceleration: simply equate the total energy at two points and solve, which is often far faster than using the kinematic equations.
Conservative Versus Nonconservative Forces
Gravity is a conservative force, meaning the work it does between two heights depends only on the vertical drop, not on whether the path is a straight slope, a curve, or a spiral — this is path-independence, and it is what allows a potential energy to be defined at all. Friction and air resistance are nonconservative: their work depends on the distance traveled and irreversibly converts mechanical energy into thermal energy and sound. On a real ramp these forces drain mechanical energy along the path, so the rider arrives with less kinetic energy than a frictionless calculation predicts.
Worked examples
A 2 kg ball is held at a height of 5 m (g = 9.8 m/s²). Find its gravitational potential energy.
- Use the formula PE = m × g × h.
- Substitute the known values: PE = 2 kg × 9.8 m/s² × 5 m.
- Multiply 2 × 9.8 = 19.6, then 19.6 × 5 = 98.
- The result is in joules.
Answer: 98 J relative to the ground.
On a frictionless ramp a cart starts from rest with 200 J of potential energy. Find its kinetic energy at the bottom (h = 0).
- Apply conservation of mechanical energy: KE_top + PE_top = KE_bottom + PE_bottom.
- At the top KE = 0 and PE = 200 J; at the bottom PE = 0.
- So 0 + 200 = KE_bottom + 0.
- Therefore KE_bottom = 200 J.
Answer: 200 J (all potential energy converts to kinetic).
Activity
Match each ramp position to the correct description of energy at that moment, ordering from greatest potential energy (least kinetic) to least potential energy (greatest kinetic).
Practice
A 3 kg box sits on a shelf 1.5 m high; calculate its gravitational potential energy relative to the floor.
Explain what 'path-independent' means for gravity using the example of two different ramps from the same height.
Common mistakes to avoid
- A real ramp lets a cart reach the same speed as a frictionless one.Friction and air resistance convert mechanical energy to heat and sound, so the real cart arrives with less kinetic energy and lower speed.
- 'Conservative force' means the force saves energy so objects never slow down.Conservative here means path-independent work, not energy saving; it simply lets a potential energy be defined for that force.
Check your understanding
A 2 kg ball is held still at height 5 m (g = 9.8 m/s²). What is its gravitational potential energy relative to the ground?
On a frictionless ramp, a cart starts at rest at the top with 200 J of potential energy. What is its kinetic energy at the bottom where height = 0?
A real skateboarder reaches the bottom of a ramp with less kinetic energy than the potential energy they started with. What best explains the missing mechanical energy?
A box slides down a hill, and we say gravity is a conservative force because its work is 'path-independent.' What does path-independent mean?
Recap
Gravitational potential energy PE = mgh converts to kinetic energy as objects fall, and when only gravity acts, mechanical energy KE + PE is conserved. Gravity is path-independent, while nonconservative forces like friction drain mechanical energy into heat and sound.
Reflect
When have you noticed friction quietly stealing energy from something in motion?