Physics Energy

Conservation of Energy — PE + KE = constant

Apply conservation of mechanical energy to free fall, pendulums, roller coasters, and projectile problems. The total mechanical energy E = KE + PE stays constant when only conservative forces act.

E = KE + PE = constant

4 scenarios

Energy bar charts

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Inputs

Scenario

Mass m (kg)

Drop height h (m)

Initial speed v₀ (m/s — usually 0)

String length L (m)

Release angle θ (degrees from vertical)

Initial height h₁ (m)

Final height h₂ (m)

Initial speed v₀ (m/s)

Launch speed v₀ (m/s)

Launch angle α (degrees)

Results

Select a scenario and enter values above.

Energy Bar Chart

Step-by-Step Solution

Conservation of Mechanical Energy

When only conservative forces (gravity, spring) do work, the total mechanical energy E = KE + PE is conserved. Energy transforms between kinetic and potential forms but the total stays constant.

At any two positions: ½mv₁² + mgh₁ = ½mv₂² + mgh₂

This is not valid when friction or other non-conservative forces are present — then energy is lost to heat.

½mv₀² + mgh₀ = ½mv² + mgh = E_total

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